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What is the process through which a department chooses to invite someone to make a talk at the department?
How is the person selected? How far in advance is the selection process made? When a department makes an offer to have a speaker come, how often is the offer rejected? And what happens if the offer is rejected?

It varies tremendously, based on the type of talk.
To a first approximation, anyone can invite a speaker if they have grant funding to pay for the travel costs (or if there are no costs).  The limiting factor is getting an audience - it's embarrassing for everyone if few people show up - so this typically happens only if it's clear there will be real interest in a talk.
Departments in research universities typically have a number of ongoing seminar series, and often a departmental colloquium as well.  There will be one or more organizers for each of these, who invite speakers and introduce them before the talks.  How the organizers are chosen varies: sometimes they are volunteers, sometimes they are appointed by the chair, and sometimes they got a grant that's paying for everything.  The organizers can then ask whoever they want to speak, although they often solicit suggestions from other department members.
There may also be special distinguished visiting positions or lecture series.  These are quite a bit more prestigious and speaker selections are often made by a special committee.
How far in advance invitations are made can vary: typically many months in advance for a prestigious lecture series, but a seminar invitation may have less advance notice.
As for how often an invitation is turned down, it's rare for someone to express a lack of interest in principle, but it's common for them to be too busy or for it to be impossible to arrange a mutually agreeable date.  I often suggest that someone should come speak sometime in a seminar I organize.  Sometimes they immediately start arranging a date, sometimes they defer it to another time but eventually come, and sometimes it never works out, but even in that case it's never certain it won't happen someday.  If a speaker can't make it, it's no big deal: you just invite someone else.

Sometimes the talk is extremely specialized, in which case a small audience is not an embarrassment.  But I often arrange these as talks for a research group, rather than for a department.

Let me add to @anonymous-mathematician's answer.  If you're interested in having a researcher come speak at your department, the seminar organizers are often open to suggestions, especially if the potential speaker isn't looking for much in the way of travel costs.  Conversely, if you're interested in speaking in a seminar, it can be completely appropriate to invite yourself.  This often works better when you've at least met the organizer of the seminar where you'd like to speak; however, you definitely don't need to know him or her well.  On more than one occasion I invited myself to speak somewhere.  The two or three times I can think of off the top of my head, the organizer was happy to have me.  (I think it helped that I didn't ask for any travel reimbursement.)  And in each case, I enjoyed my trip and I think my audience enjoyed my talk.

At my department, we often have talks by speakers who are already visiting anyway for example to serve on a PhD committee or as part of a collaboration with one of our researchers. This is usually a good opportunity to invite them to speak as they are already here anyway, their travel paid for by the PhD defence or by a research project of someone they are visiting.


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When addressing academic departmental assistants via email, should I use their first name or just Mr./Ms. X?
It seems very common for them to normally prefer being addressed by their first names (since Mr./Ms. seems to be very rarely used in Academia).

My policy : the first time you contact the person, go with Mr. Doe (or Ms. Doe), but sign with your first name. The latter is a signal that you are OK with a "first name email relationship", from this point it will be so most of the time.

To add to this: if they reply with only their first name, you're good on a first-name only basis. If they reply with their full name ("Sincerely, John Doe"), continue to use the Mr. or Mrs formulation.

You should follow the traditions in the region where the recipient is located. For an American or Canadian, I would probably follow @sylvain's advice, as that is the usual standard in the US—formal at first, but becoming less so as time and familiarity grows.
However, here in Germany, I would continue to use the greeting "Dear Mr./Mrs." until such time as I was directly invited to use their first name (this would be the same as the "Sie" to "Du" switch).

In Sweden, and I believe other Scandinavian countries, email communication is very informal, and communication is mostly on a first-name basis, even if you haven't met in person previously. I can call anybody by first name, even the CEO or an esteemed professor, and nobody would frown upon. Even students address (or at least should, nothing makes me feel older than somebody calling me Mr T., or worse, Sir) their tutors by their first name.
I'd almost never use Mr/Mrs in an email when writing in Swedish, but I would do it more often if the recipient is foreigner and is not familiar with the small power distance in Swedish companies and universities. However, I'd usually be more formal when the circumstances require it -- applying for a job/grant, or sending official documents, for example.
Pro tip: -- never, ever call a Professor "Mr. Smith", if you are adressing them by family name. Always use appropriate academic titles, when applicable. I'd spare this for associate professors or below, but some academics in the country where I'm from are pretty prissy about this.
Some academics are prideful, and you need to play to their weakness. Gain favour of such people by addressing them with a higher title than they currently have. A certain (then associate) professor which some would describe as "a cerberus in a skirt" was very friendly to me and helped me with administrative matters on a few occasions since I consistently addressed her as "Prof. S.", especially in front of other people.

I pity the fool who feels older when somebody calls them Mr T :)

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How are the personal assistants for professors usually funded?
As examples, the lab executive assistant at http://www.klab.caltech.edu/people.shtml or the lab administrative assistant over at http://www.gps.caltech.edu/~tapio/people.html#admins

Funding for non-research positions comes from either direct or indirect sources.
Direct sources means writing a proposal that includes funding for personnel such as a lab technician or an administrator for a research center. In this case, the funding is obtained directly through grants.
Most of the time, however, the funding is indirect: the salary is paid by the department, rather than an individual research group. This funding is paid for through the "overhead" charges that are included in research grants. (In some cases, such as public universities in Germany, this funding is also indirect, coming from a grant by the state or federal government given to each professorship.)

I've seen three common ways of funding staff - undoubtedly there are more.

For staff directly related to the running of a research lab, for example senior technicians, lab managers, dedicated programmers for computational research, etc. there may be funding written into the direct salary costs of the research grants their faculty member submits. For example, many of the grants in the field I'm in have direct funding for data managers and the like for the duration of a research grant.
If a faculty member anticipates needing a particular type of help - most often a lab technician or programmer in my experience - they may ask for their salary to be part of the faculty member's startup package for some small number of years before (hopefully) the faculty member can support them through mechanism #1.
Other staff members, such as personal assistants, some research staff etc. are theoretically things that are supposed to be paid for by the rather sizable chunk of a grant budget that goes to indirect costs to the university. Whether or not this occurs in practice is another question all together.

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The archive with all the LaTeX material as a camera ready version
This happened to me for the first time. The organizers of the conference asked everyone to send them the archive with all the LaTeX material as a camera ready version of an accepted paper.
Is this a legitimate request?

It's not at all clear to me what exactly you're asking.  You've submitted a paper for publication and the conference accepted the paper and now they're asking you to submit the paper in LaTeX format.  This is all very standard.  What's your concern here?

@BrianBorchers, yes, exactly, so I will send the LaTeX material.

@BrianBorchers I don't normally publish in CS-style conferences, but I have always thought that "camera-ready" meant "give us the pdf", and Wikipedia confirms. Is it not the case in your field? So I, like OP, find this request unusual.

This means- "we're not going to copy edit your paper, and you must use our standard document class in your paper.  We'll run it through LaTeX and adjust page numbers to fit it into the proceedings volume."

I've notice this becoming increasingly common in CS. It's annoying, but if the conference is well known, it shouldn't be an issue.


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How common is it to write out a script for a talk? What are the benefits?
I have never written a verbatim script for a talk. I have at times written notes or outlines, but I never read from them when presenting (and rarely when  practicing). With enough (weeks) of practice, I can give a pretty good talk. With less practice, I sometimes digress and sometimes omit an important detail. But what I am most interested in is improving my presentation by removing awkward pauses (e.g. while I remember what to say about a slide) and by using appropriate intonation, phrasing, and cadence.
Recently, a friend of mine who is a writing studies doctoral candidate suggested that the first step toward accomplishing these goals is to write out a script for each slide. This is a difficult task, but one that I plan to experiment with. I do not plan to actually read the script during the talk, but to memorize it while practicing.
My questions are:

How common is it to write a script for a talk?
How does having a script help?
How early in the preparation should I have a "final" version?

What field do you work in?  I think this is much more common in humanities and social sciences than in STEM fields.

@JeffE I am in a STEM field

I think a script is actually more harmful than good. It tends to produce very rigid talks, and it often forces you to concentrate on the script instead of the content and audience. Usually, you know what you are talking about well enough to not need a script, and just pointers. Below are the tricks I use for different kinds of talks.
Research talks
For technical talks on my research or guest lectures on topics I am intimately familiar with (these two have been the overwhelming majority of my talks), I do not make scripts or notes and just concentrate on making good slides. In the process of making slides, I produce an outline which I use to mentally check my timing. The day of the talk, I look through my slides carefully (hunting for typos and other minor mistakes), this reminds me of the exact details I was going to discuss. Since I tend to repeat similar talks, I have become very proficient at estimating my timing.
For some big conferences, I practice talks in my lab before heading to the conference. This greatly improves the talk, especially timing issues and comfort.
I find that this is easy to do because you are usually intimately familiar with your own research and unlikely to forget something. It also allows a relatively fluid and natural talk, and lets you answer questions during the talk without fear of losing your pace.
Usually, I have my final version the day before unless I rehearse in the lab.
Teaching talks
I have done a number of talks as reviews for large bodies of students (50 to 300) to prep them for exams, and smaller groups (20 to 30) during weekly tutorial sections. Here I was talking not about my research, but course material that I had taken years ago. The topics were physics/math and my style was one of interactive problem solving at the board of hand-picked problems that illustrated key concepts. To prepare I had to invest time to carefully come up with good questions and I quickly checked that I could solve the questions as I generated them.
I write down the questions one per page with a few bullet points of the main concept/technique I want to show in the question. However, I do not write down solutions and solve the questions on the spot at the board. This puts a certain amount of stress on me (especially if you are teaching first year engineers) but I find it produces much better pacing for the students (since I naturally slow down a little at the harder parts) and actually solving the questions as you present them instead of copying a solution from your notes to the board keeps you in the zone and actually reduces errors. Not having notes in your hand (except to write down the problem statement) also lets you worry about just two things: the board and the students.
The caveat is that you have to very comfortable with the material (but why are you teaching it if you are not?!) and you need to have the confidence to laugh at yourself and recover from occasional mistakes.
Usually, I have the final questions and plan a few days ahead of time. However, there is no 'final version' of the actual talk, since it depends completely on the audience.
Popular talks
My only opportunity to give a popular talk was at TEDx McGill 2009. This was incredibly different from other talks I am used to. Thankfully, all of the speakers were coached by the organizing committee ahead of time (including a full dry run through). The key message was to treat this not as a presentation, but as a performance. I did not prepare a script (and were were advised against preparing one), but I did make notes on cue-cards that I held during the performance. Except for the very beginning (where I was unusually nervous) I never looked at the cue cards, and mostly held them for comfort.
I had my final version about a week before the talk and my ready-for-dry-run version about two weeks before.

I think the most important factor to keep in mind is the personal comfort level of the speaker with respect to giving presentations. For some people—particularly people working in a non-native language—having a prepared script allows them to relax sufficiently and be able to get through the talk. For other people, having a prepared script acts more as an encumbrance than an aide. I've seen people rehearse talks to the point of practically being memorized—and then get completely flustered when they accidentally skip past a slide or are faced with a small technical glitch in the presentation itself.
So, I would disagree with Charles and Artem and say that you should find whichever method is most effective for you. Personally, I am not able to rehearse talks beyond going over what are the key points I want to address on a slide. If I go through a talk like that more than twice or thrice, I start getting "locked" into certain words and phrases, and then I start falling into the problems that the other posters mentioned regarding the pitfalls of a memorized talk. You may find a memorized speech is the most helpful possibility; if that's the case, then our opinions of what is the "best" approach don't really apply.

+1. The answer to this question is really simply "try a few methods, see what works for you, and practice that method a lot".

Script only the introduction
I can only echo what Artem said about the disadvantages of a script.
That said, I often advise to write out the introduction of the talk beforehand in full detail. This way, you have a backup. So far, I have never ended up using the prepared introduction, I’ve always had at least slight variations. But if – for whatever reason – you get stuck, you can recourse to the prepared script. If nothing else, this is extremely comforting and reduces anxiety.
A talk should not feel like a performance
Of the talks that I’ve heard (instead of given), those that were obviously based on a script were among the worst. They were bad performances rather than good talks. A talk (in general) isn’t meant to be a performance – it’s meant to convey information; like you would do in a discussion with friends:
The “chat with friends” should be archetype after which to model a talk, not the “theatre performance”.1
Use cue cards

I sometimes digress and sometimes omit an important detail.

This can be helped by notes (cue cards). But you have to train yourself to look at these from time to time (I can never remember doing this). I usually end up plastering my slides with huge sticky notes that only show up on the presenter’s display (supported at least by Keynote). Not elegant but effective.
A word on slides
You said that you want to remove awkward pauses “… while [you] remember what to say about a slide …”.
This may be an indication that your talk needs revising for two reasons:

If you cannot remember a detail, is it really important?
You should have nothing to say “about a slide”. Slides are there to visually support your talk, not the other way round. If you don’t remember what to say about a slide, cut the slide. This sounds like a harsh judgement but it will improve the talk.

1 Except when it isn’t, of course. TED talks were mentioned. But even here, all the best talks feel like a friendly chat rather than a performance, even if they are in reality a well-rehearsed performance.

Your conflating reading verbatim from a script with a "performance". I agree with everything else you say though (just semantic difference on what a performance is, +1).

@Andy Well, we agree that a talk is in a way always a performance. But for me at least, theatre performance implies acting out a script, and many people treat a talk (wrongfully) as such.

I agree with Andy: Every talk is a performance, but just as you suggest, a good performance doesn't look like a performance.  Also, +1 for brutally cutting slides.  Slides support the story, not the other way around.

Scripting is great. Do it. Write out every single word. And then redraft and edit it, just as you would if it were a journal article ...  except, remember that the audience is completely different. So redraft and edit it, with the real audience in mind. You are scripting a performance; so redraft and edit it as a script for a performance.
Then rehearse it. Over and over. Until you know about 70%+ off by heart (i.e. word-for-word); and you've got a really strong opening and really strong close, each of which you know 100% off by heart. With each run-through, you'll find yourself doing a bit more editing, re-ordering words, shuffling sentences.
Now put your script away, and do a couple of dress-rehearsal run-throughs without the script at all, so that your performance is close-ish to the script, but by now, it's getting a bit looser, more natural. So you can concentrate on timing, breathing, pitch variations, body language, and saving some resources for picking up continuous feedback from your audience.
And now you're ready to go!
YMMV. It works sometimes for me.
Try it out, at least once, and see if it works for you.

I really dislike memorising anything word for word as most of that effort will only be useful only for a single occasion. That said - I have to admit that sometimes a talk is important enough to be worth that effort - especially if the talk is one the you will be giving on many occasions.
However, the disadvantage of memorising a talk is that it is hard to sound natural. It's difficult, but not impossible. Actors demonstrate this. Generally it is much better to just us a script as a guide. Practise individual chunks from memory a number of times and play around with the various ways of wording it. Instead of having to remember the exact words, you now only have to remember one out of a number of options. You will become much better at discussing the topic and your ability to improvise will improve.

I also tend to write out notes, but at an early part of the preparation, I tend to write out something very much like a script. I use this to make sure I'm covering what needs covering, and cut down where I tend to ramble on. This also helps me determine if I'm going to fit inside the time budget, and if not, what to cut down on. A couple practice runs with the polished script and then I reduce it to a single page of notes.
One of my most memorable professors appeared much smarter because she eliminated all those "err" and "umm" from her speech. Instead of an "umm", she'd be silent. I'm not successful in replicating this as most of my coworkers take that pause to be a sign that I am done speaking, so they can now start their turn speaking.


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What are the key features of a short (15 min) conference presentation?
I am preparing to give a conference presentation from scratch.
What is an effective ratio of introduction / methods / results / conclusion slides?
How can I balance the details of research without loosing the audience on key points?
In my experience, 90% of conference talks are dull and there may be one or two at any given conference that are really inspiring. What makes a "great" talk?

The LaTeX Beamer User's Guide contains useful hints on short conference presentations. Those are applicable even if you use another tool to actually prepare the presentation. See http://www.tex.ac.uk/tex-archive/macros/latex/contrib/beamer/doc/beameruserguide.pdf

Don't have too many slides. It's my pet hate when speakers have 50 slides for a 15 minute talk.

(edited to extract the key points from the main reference)
Ian Parberry's guidelines were always essential for me. Firstly I will give a personal replies to your answers and subsequently I will extract the main points of the Ian's guidelines which are the basis for my answer.
Personal perspective

What is an effective ratio of introduction / methods / results / conclusion slides?

My own rule of thumb is to allocate 2-3 minutes per slide, which gives max. 6-8 slides including the envelope (the "title" and the "end+questions?" ones). That is, we have about 5 real content slides of which for introduction I allocate 1 for motivation&context, and 1 to problem definition.
The body gets whatever it needs, but shouldn't exceed 4 slides, with at least a single one dedicated to a sketch of a worked example. The audience doesn't need to know how exactly I am doing the magic, I must however make them trust me and see what I am doing as plausible.
The summary/conclusion/future work gets 1 slide.

How can I balance the details of research without loosing the audience on key points?

Stress the motivation, the relevance of the problem and only sketch your solution so that an example which you provide will be plausible enough.
Your talk is an advertisement for your paper. You are doing your best to assure that people learn something and you imprint some key points in their heads (the problem description and a sketch of the main idea solving it). You don't need to explain the details, just sketch the main principles. You want to compel the audience to either read your paper that day in the evening and base their own work on it (hence citations!), or ensure that sometime in the future when they will face a problem, they'll remember that there was this guy speaking about something along the same lines, so let's check it (hence possible citations!).

What makes a "great" talk?

For me, it's grounding in reality. Show me what impact your stuff has on me. Speak about an application I might care for, even if it will be only a hypothetical one. If the result cannot be framed as a machine, or software, such as a lot of (non-computational) game-theory, then speak about implications to the society. Strike whatever chord, which makes your results tangible. It all boils down to answering a single question for every single person in the audience: Why should I care?!
But even if you do the all the positive advice right, there's a more important point, namely what you shouldn't do. For example I tend to speak a lot (see my posts at this site :-) ). My main drill during preparation of a talk is to throw away everything non-essential. Moreover, I am often writing down notes about what not to say. Many otherwise great talks are ruined by the presenter *speaking too much and showing off. I don't want to be impressed by your smartness, or charisma per se, I want you to simply educate me!

And finally the key points from the Ian Parberry's guidelines for giving a good talk, emphasis mine.
General advice

Communicate the Key Ideas: select 1-2 main high-level ideas and present them in a crisp and crystal clear way.
Don’t get Bogged Down in Details: do not even attempt to discuss the details, unless you you have brisk answers to possible questions you open that way.
Structure Your Talk & Use a Top-down Approach: go the least-surprise path, i.e, the audience needs a story a wants to be able to follow it. The structure should stay crisp: 1) solid motivation/intro, 2) main points/body, 3) technicalities, if really necessary, 4) conclusion.
Know Your Audience: allows you to skip some common-knowledge in the audience, as well as select what is important to them and what do they care for.

Structure of the talk
I added the emphasis to the points which I consider crucial.
The Introduction

Define the Problem
Motivate the Audience
Introduce Terminology
Discuss Earlier Work
Emphasize the Contributions of your Paper
Provide a Road-map

The Body

Abstract the Major Results
Explain the Significance of the Results
Sketch a Proof of the Crucial Results

Technicalities

Present a Key Lemma
Present it Carefully

The Conclusion

Hindsight is Clearer than Foresight
Give Open Problems
Indicate that your Talk is Over

+1 for introducing a good reference.

How can I balance the details of research without losing the audience on key points?

From my perspective, the key to giving a 15 minute talk is to omit all of the details.  Many audience members don't care, the few who do can read your paper, and in any case it's impossible to convey any serious details clearly and correctly in such a short time.  If you try, then much of the audience will stop paying attention; you'll end up wasting their time and missing a great opportunity to present your work.  Instead, your goal should be to ensure that everyone leaves with some understanding of what you've done, and that some of them are inspired to learn more.
This means you should focus on the big picture.  What did you do, how and why did you do it, and what have we learned from it?  In mathematics, I'd focus on context, motivation, definitions, theorem statements, examples, and intuition.  It's OK to give a brief proof outline or sketch, but nothing detailed or complicated.  If you can't summarize it in a few sentences, it's too complicated.
There are various ways short talks can go wrong.  For example, some of them try to compress 30 minutes of content into 15 minutes by talking fast and barely explaining anything, while others simply omit the background and context needed to understand the presentation.  However, there's a common difficulty behind many bad talks: they focus on the speaker's desires and goals rather than the audience's.  Ultimately, you need to design your presentation to fit the background and interests of the audience and the time available, rather than what you wish you could tell them.

Great advice on focusing on the big picture. For such short talks, especially on conferences, I'd focus more on the results than the methods. It's a great opportunity also to practice your elevator presentation -- describing shortly what you are working on to (almost) complete neophytes on a social gathering without being boring.

On omitting detail: The point of a short research talk is to convince the audience to read your paper, not to make reading your paper unnecessary.

+1 @JeffE . A 15 min. presentation is a kind of advertisement for your publication.

While 15 minutes is on the longer side for what I'm about to suggest, I think it's still useful.
In a 15 minute presentation you don't have time to think of things to say on the fly. It's important that you have a story nailed down fairly tight. While you don't need a full script for what you're going to say, you should have a fairly detailed plan of what you're going to say (even upto key sentences and transitions).
As others have pointed out, you'll have to eliminate most details. THIS IS OK ! The audience will only (at best) get a high level idea of what your work is about and only the briefest glimmer of a technique or tool. So in order to decide what to say, you should ask yourself the following:

Why should I (the listener) care about your work ?

Answering this question will help you decide what to keep and what to throw.
As for your last question, a great talk is a strange mix of details, high level concepts, and inspiration. If it were easy to describe it, all talks would be great :). But if you shoot for a talk that people will remember, that is both more attainable, and easier to construct.

Consider the point of the talk; you want to convey to the audience what it is you did and what your results were. Similar to a paper, you'll want just enough background to bring those who aren't familiar with your subfield up to speed, and barely any conclusions as the audience will draw their own conclusions.
With that in mind, you'll want something similar to the following:

1-2 min — background
5-6 min — methods
3-4 min — results
1 min — conclusions, thanks, etc

Note that you'll probably want to leave some time for questions, so you should err on the side of shorter rather than longer.
From my experiences, you will want to really prepare for this. As discussed in more detail in this answer, this is really the main forum for you to sell your work. You'll want to make sure you put forward your best possible face. All the usual points related to public speaking apply here as well: talk slower (yes, slower... slower than that, even), be concise, be clear, make good use of slides, etc.

Note the usual disclaimer that this may vary from field to field.

I think in any conference presentation (whether it is 10 minutes or 60 minutes), there are only two parts that are absolutely necessary:

What is the problem that you studied. Explain it as carefully as possible, in the simplest possible form; make it as easy to understand as possible. Do not assume that some parts of the setting are obvious to the audience; make everything explicit.
What is the new result that you obtained. Again, explain it as carefully as possible, in the simplest possible form. Proceed slowly; even if you could state the result in 5 seconds, spend much more time on it. Make sure the audience has enough time to digest what was your new main contribution.

If these parts necessarily take 15 minutes, it is OK. I do not think anything else is absolutely necessary.
Of course there are lots of things that would be nice to have, time permitting: background, motivation, related work, a very rough overview of some methods that you used to obtain the results, conclusions, etc. But none of these parts are as important as explaining what was the research question and what was the new result.

By the way, if it appears that this approach results in a boring talk, most likely your own idea of what is your research question is wrong. Think big, go one level up.
Example: You have studied thingy X (something technical and complicated) and your work shows that X has property Y (something easy to understand), and this is cool, as it is the first example of a thingy with property Y.
Bad:

Problem: We study the properties of thingy X. (But explaining X takes forever. It is complicated, technical and boring. And why would you want to study it anyway.)
Result: We show X has property Y. (But now you would still have to explain what is Y. You are already running out of time, and you have already lost your audience.)
You feel like you would have wanted to talk about motivation, related work, and methods, but you are already overtime, and nobody is following anymore.

Good:

Problem: Is there a thingy with property Y? (Now this was much easier to explain. You have got plenty of time to also mention that this is a famous open question posed by Professor Bigname in 1950s.)
Result: Yes, we give the first example of such a thingy! (That was easy. And now to make sure that everyone gets the big news, you can spends some time explaining that in prior work others have come close, but nobody has been quite there.)
And now you still have lots of time left, so you can tell something about the particular thingy X that you put together. All of this is extra. You can be sketchy, just give some highlights of the main ideas. Everyone in the audience already knows where you are aiming at and what is the big picture; they can fill in the details or look it up in your paper if it matters.

Some things to think about (from the point of view of a mathematician, but I hope some of this might be relevant in other fields too): Does your main result have a special case or two that would be easier for your audience to understand than the general result (without being trivial)? If so, you might just present that (or those) special case(s), and add at the end one sentence to the effect that your full result is more general.
Does your result require terminology that people might not know? If so, does it really require that terminology, or could you perhaps get by without it? If you really need the terminology, budget enough time to explain it and, if possible, relate it to something your audience already knows.
The background information (previous results, open questions) that motivate your work is likely to be too much to present in full in the limited time available.  Select just enough of that information to be understandable and to provide some (not necessarily all) motivation for your work. Having presented some motivation, you can add one sentence saying that there is additional motivation, which you don't have time to explain in the talk.
In two places, I've suggested adding a single sentence saying "there's more"; you should indicate your willingness (or even eagerness) to discuss the "more" later with anyone who is interested.

A nice discussion on this can be found here: http://presentations.catalysis.nl/presentations/presentation.php.
If your talk is in mathematics, you might also want to look at https://mathoverflow.net/questions/29866/presenting-a-paper-dos-and-donts.
Some other tips I've heard:

Use one slide per minute.  For a 15-minute talk, use only 15 slides.
The first part of your talk should be understandable by any adult (if your target audience consists of adults).  The next part should be understandable by your peers (same field as yours, e.g., mathematics, but not necessarily the same subfield, e.g., number theory).  The next part should be understandable by your peers working in the same subfield.  The last part should be understandable by you. (Although some believe this last part is too much).

My goal when giving a talk is to convey information in a way none have presented or expressed before. The constraints being:

easy to understand for complete novices
interesting for experts

My mindset is also to aim for 10-12 minutes when allocated 15 minutes. It is always better to finish early than it is to go over your time. It ALWAYS leaves a bad taste in my mouth when a speaker exceeds their allotted time. It's disrespectful and inconsiderate of other people's time.
I also subscribe to the 1 slide per 1 minute MAX philosophy. In terms of time per section (borrowing from @eykanal's reply), but whichever section has your contribution then the time spent there should be doubled (e.g., I assume in the Methods section):

2 min Background
4 min Methods
2 min Evaluation
2 min Results
2 min Conclusions
1 min Future Work

There are many good answers. I especially like the second half of the answer from @walkmanyi, especially as concerns the structure of a short talk. I disagree with most the time amounts given. I have found great success with:

7 minutes of background
5 minutes combined methods, results, conclusions
3 minutes of questions

If a separate time is given to questions, then 9 to 6 in favor of background.

An interesting comment about presentations can be found here. The author is professor of Computer Science, thus some things may not apply in all cases. Moreover, I think that the advice is very extreme, which actually makes it interesting.
In the case of the area of management, this resource may be helpful.
These notes were the result of a session at one of the Academy of Management meetings.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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How can I apply to be an adjunct faculty?
I am currently a staff researcher at a public research university in the US. While a tenure-track position may be in my future, I would like some of the opportunities and responsibilities now.  In particular, I want to be able to write grants as a PI and advise students and postdocs. I believe that I can do this as an adjunct faculty, but I have a few questions about where to start:

What are common steps required to become an adjunct faculty?
Where can I find additional information (e.g. would a university-wide policy be given at the university website?)
Assuming I speak with the department chair, what should I say? Are my justifications sufficient.
How could I sell my case, other than my (demonstrated) ability to obtain funding and (undemonstrated) ability to be an advisor?

related but distinct: What are the roles and responsibilities of an adjunct faculty?

This isn't really an answer to your question as written, but a first thing to consider is who (if anyone) currently has a position of the sort you'd like in your department.  If someone else does, then that sets a precedent you can look into.  If nobody does, then that's more complicated.  It could be that nobody else wants this, or that the department cannot or will not do it.

Be aware, too, that the administrative and departmental conceptions of both the privileges and responsibilities of adjuncts vary hugely from place to place. In many places, adjunct faculty do not serve on any committees, and it would be nearly universal that, in particular, they'd not be on the hiring and tenure committees, and not vote on hiring and tenure.
The question of being "allowed" to be an official advisor (as opposed to the obvious possibilities of informal mentoring) also surely has different answers different places. In some institutions, it is quite anomalous for "non-tenure-track/tenured faculty"  to be allowed to "advise". You'd need to ask.
At worst, adjunct faculty are marginalized in terms of job security, voice in departmental matters, and are given the least desirable teaching responsibilities, etc. Hopefully this is not the situation at your institution, but, for example, a move from "research associate" to "adjunct faculty" might be, and might be perceived as, a step down, with unanticipated negative consequences for you. Hard to know without "being on the ground" there in your particular situation.
Also, beware that various administrative "official" statements on such things do not match practice, so unofficial, off-the-record information may be essential.

I wasn't looking for any move to a different position - just an unpaid title with privileges.

Formally, a "title with privileges" is a new position, paid or not.

@JeffE, my point was that the potential for it to be perceived as a "step down" shouldn't be as great if I retain my primary full time position and gain a title - (although admittedly I can't speak for the entire population of people perceiving my status).

You really really really need to talk to your department chair.  Even having the title of "adjunct professor" on your CV may rob you of status.  At my own university, for example, "adjunct professor" almost always means either "underpaid teaching slave" or "someone who's left but retains a courtesy title so their grad students don't have to jump extra hurdles to finish their degrees".  For us, the job you're describing is called "research faculty".

I'd strongly concur with @JeffE's appraisal of how such a position would look on your CV, now that I think about it. "Adjunct", in sciences, is far, far more often a stigmatizing status than an improvement.

@jeffe and Paul - I am glad I did ask; however I have to balance that stigma against the cost - specifically listing two big awards on my  CV under funding as "co-author" and "lead author" rather than "co-PI". It is very frustrating. And lacking co-PI is proving to have meaningful consequences beyond how the grants appear on my CV; it also makes it easier to be dismissed - even subconsciously - by actual PI's. [emoticon with single tear of self pity here].

I was thinking 'and as a bonus i could be a professor without having the pressure of tenure - or the arbitrary process of finding a new workplace - As a workaround, Would it be unethical to omit the adjunct prof on my cv?

What are common steps required to become an adjunct faculty?

Ask your department chair.

Where can I find additional information (e.g. would a university-wide policy be given at the university website?)

Ask your department chair.

Assuming I speak with the department chair, what should I say?

"I'm interested in becoming adjunct faculty.  What's the hiring process?  Why yes, I do happen to have my CV with me."

How could I sell my case, other than my (demonstrated) ability to obtain funding and (undemonstrated) ability to be an advisor?

Ask your department chair.

Yeah, this varies tremendously between schools.  For one thing, it depends on whether they view it as an easily granted formality ("Sure, we think you'd be a fine advisor, and if you bring in any grants we'd love to take the overhead") or as nearly equivalent to a tenure-track hire in difficulty.

It can vary between departments in the same school even (at least at mine). Also, the status may bring a name on a web page, or an actual office (overhead can vary).

-1 your answer is accurate, but not particularly informative.

@Abe The point that JeffE and Anonymous Mathematician are making is that "some guy on the internet" can't give you advice that will be accurate for your situation, because situations vary dramatically from department to department.  You need to ask someone from your school (and preferably, your department) to know how they view adjunct faculty status.  And there's no one better to ask than your chair.

@DanC I understand this point, but then, wouldn't it be logical to vote to "close as not a real question" (if real == answerable)?

@Abe I think "Ask your chair" is a great answer.  It used to be that knowing the answer was a really important skill.  In the information age, it's often more valuable to know where to find the answer.

@DanC Okay, now I see your point and have +1'd


text:
Is it a good idea to contact professors before applying to grad schools?
I've seen some universities encouraging students to contact with the faculty before making applications. For example,  this one. On the other hand I've heard some people saying that they are waste of times because professors receive several such e-mails every year and they don't even have time to look at them.
So, is it good idea to make contanct professors before making the application? Can it increase my chances of acceptance? Can it ever backfire me?

It'd be helpful to give your field and country.  The answer to this question is very different for different fields and different countries.

@NoahSnyder The link is to a CSE department in the US, I think that makes it pretty clear, although it probably should be in the main text.

Related: Details an applicant should include/exclude in an introductory letter to a prospective grad school adviser?

This really only works as a strategy if you have something truly meaningful to say. If you have to force yourself to do it and struggle to come up with something to say in your email, you're not helping yourself. Faculty get tons of email all the time and every year - as you say - get emails from prospective students, many of whom will not be admitted and in whom they invest no effort. So, if you genuinely think you're a good fit for a program/lab and have solid questions in mind to ask the faculty/PI of that lab that will communicate your quality and fit, this may be viable. But, I would definitely not recommend it as a general strategy.

By put some effort into it, this usually means that you have at a minimum read their website and in most cases have read one of their more recent papers and thought about 'why' you find the work interesting and how it relates to your interests and/or what you have done in the past. Your first email should be short (1-2 paragraphs max ... if a conversation ensues great ... but a professor is more likely to read a shorter email ... "think more; write less" is my motto).

From the link you provided,

To increase your chances of admission to our program, you are strongly encouraged to discuss your research interests with one or more faculty from our department prior to your application.

It sounds an invitation for you to contact the faculty members. In cases like this, I would recommend you to contact them. Find the faculty memebers whose research interests are close to yours and write e-mails to tell them that you are interested in what they are doing. I believe those e-mails won't hurt your chance to get admitted because they ask you to do so in the first place. How much it will help you remains to be seen. As the web page says, it increases your chances of admission.
However, if you do not see such invitation on their web pages then I agree with Thomas that don't contact them unless you do have truly meaningful things to say.

I would add regarding "interest in what they are doing" that an applicant makes sure it's actually what the faculty member is doing now as opposed to what you may have seen/read from them, which might not be their current interests/work.

@Thomas I agree. Actually, this would be a good reason to write to them to confirm their current interest/work.

Australian context: If by graduate school, you are referring to doing a PhD, then in Australia the standard first step is to find an academic willing to supervise you. The university will typically have additional requirements, such as regarding grades and prior academic experience. In particular, if you want a scholarship for your PhD, grades will be very important. Even if your grades a little lower, there is sometimes the option to commence  a masters by research and convert to a PhD thesis at a later stage. Furthermore, if an academic is keen to supervise your project, then they are likely to do what they can to facilitate your application. So in summary, contacting academics to enquire about PhD supervision is essential.

Yes, it is a good idea.  And, yes, it can backfire.  I regularly receive inquiries from individuals interested in "joining my lab," laying fairly bold claims to be moved by my research.  They can be both annoying and humorous because I am very active in research but my area of study does not have any type of "lab model."  In most cases, these types of inquiries are generic messages that are essentially copied to a very large number of professors, with hopes of getting a reply.  It is very easy to see through this snowball approach, and the outcome is invariably a deleted message.  The most qualified individuals do their homework and tailor the messages to demonstrate knowledge and genuine interest in the topic area.

If there is a particular professor in mind, it may be a good idea to contact him.  After I retired, I received a few such inquiries, and wrote back telling them I was retired an no longer taking students.  This is another reason (different from "improve your chances").

Canadian context: I applied for four Master degrees in three different universities (Concordia, UdeM, UQAM) in Montreal.
I've contacted beforehand teachers or head of departments. I was welcomed by everybody I talked to.
Three out of four applications were succesful. I even found two people offering to be my thesis co-director months before the start of the first term. In this latter case I met three different professors before my official application was processed. The head of department encouraged me to do so.
The only university I did not contact beforehand –I was an undergraduate at this one– refused my application. (I did not bother talking about my application, because the people processing it knew me already, apparently they felt neglected that I did not try to suck up to them during the last term.)
So, from my experience I would advise to do so, but, and it's a big big but, I had very good reasons to contact them. I had a three page proposal for the subject of an eventual thesis.
I was asking them for advice, I wanted to know if my proposal was something I could do at their university or not. I wasn't wasting their time or trying to look good, I was talking only about what we could do together,about their expertise, asking to use their brain for something they were familiar with. Basically, asking to do the job they are paid for.
On the other hand, I advised my wife to do the same two year ago, when she wasn't sure of her academic orientation. She did it with 3 different programs at two universities, contacting professors or department officials.
She was constantly brushed off or refered back to their website.
They felt she was wasting their time, because she had only hard "technical"  questions (fees, hours, amenities, agenda...)that could be answered perusing through documentation or questions so "soft" (what's the atmosphere like" "I wonder if that program is for me") that they could not be answered.

If you'd only go to a given school if you get into the lab of a very short list of profs, you might contact them, explaining your situation, to see if they'll be accepting students.  One can certainly argue about whether this is a good approach, but if that's really the situation, it's a big time and money saver.
Now, aside from the above, can this improve your chances?  If the admissions committee is trying to align recruiting with the needs of faculty, I think "mabye" (at least for a fairly typical student recruitment in the US)


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Where and how to search for research problems?
Where and how can an independent researcher search for research problems in a paticular field, assuming that a person doesn't have direct contacts with anyone knowleageable about that field?
And once you get a research problem , how can you get an idea about the approximate time that will be required to solve that problem? My area of interest is mathematics.

@CharlesMorisset: Bad suggestion.  Most mathematicians should consciously avoid those problems, except perhaps as long-term inspiration, at least until after tenure.

Reading recent papers is a good way to come up with ideas for things to work on.  For example, the last section of a paper often lists open problems and possible topics for future research, and they may also be scattered throughout the paper.  Of course the author or other readers may be working on them, but that difficulty is unavoidable for any problem that isn't communicated privately to you.  Some of the advantages of this approach are:

You have some evidence that the answer isn't already known.  Of course maybe the author just didn't know it, but at least you are getting an expert opinion (which is particularly helpful if you aren't an expert yourself).
Your work may be of interest to other readers of this paper.  This avoids the difficulty of making up a topic and then discovering that you are unable to interest anyone in it.
The published papers on the topic let you calibrate your level of knowledge.  If you can read them, then you probably know enough to work on extensions.  If you can't, then you need to learn more.
There's some reason to think progress may be possible.

By contrast, I would absolutely avoid working on famous problems.  They satisfy 1 to 3 nicely, but the "famous" requirement specifically filters out any reasonable likelihood of a full solution, and progress towards a solution may be very difficult.  Unless you are extraordinarily talented or lucky, choosing problems because of their fame is a big step in the direction of becoming a failure as a researcher or even a crackpot.  Even if you are extraordinarily talented, there's no harm in starting with a warm-up goal, and this avoids the difficulty that many people have trouble estimating their own abilities.
As for how long it will take to solve a research problem, this is unanswerable.  If you are really lucky, you might make important progress within a few weeks.  If you get stuck in a rut or are missing some background, you might work fruitlessly for years on a problem that's not actually all that difficult.  And of course problems vary enormously in their difficulty.  With enough experience, you might be able to estimate how difficult or time-consuming certain problems might be, so you could guess what might make an appropriate Ph.D. thesis problem, for example.  However, even experts are sometimes wrong, and developing this sort of feeling takes substantial research experience.  When you are starting out, I don't think there's any reliable way to guess these sorts of things.  This is one reason why Ph.D. advisors are important: they can offer feedback and advice based on intuitions the student is still developing.
If you are working on research without experience or expert guidance, you could use the following guidelines.  Don't give up too quickly: anything worth publishing is worth spending weeks beating your head against with no apparent progress.  (Of course I don't mean staring at a blank piece of paper, but trying ideas and discovering they don't work, looking at special cases and examples, studying background that may be relevant, etc.)  Once you have a solid background in the relevant mathematics, which could take a long time depending on the field, you should probably be getting somewhere over a period of months.  By "somewhere", I don't necessarily mean clear progress towards a solution, but you should be able to articulate an understanding of the problem you didn't have when you started, you should be coming up with tangential or spin-off ideas that may not solve the problem but could be interesting in their own right, etc.  The ultimate test of successful research isn't whether you accomplish your original goals, but rather whether you find something interesting along the way.  On the other hand, if months go by and you don't seem to be coming up with any interesting ideas or understanding, then this is probably not a fruitful research topic with your current level of background and experience.
Of course you shouldn't take any advice like the last paragraph too seriously.  Research is a highly personal topic, and many people have different research styles.  However, it may give you an idea of one reasonable approach.

Suppose a problem is open for some  four five years and not much progress has been made on that problem.Is it safe for a masters or a phd student to try out such problems or should they be avoided as they can be considered "hard"?

It really depends on the circumstances.  If the problem has attracted a lot of attention and famous people have tried hard to solve it, then it's risky.  (It's still worth thinking about, as a learning experience and just in case you have a great idea, but you shouldn't bet your career on solving it, so it's wise to work on other things too.)  On the other hand, there are more interesting things to do in mathematics than there are mathematicians, and plenty of approachable problems go unsolved for years because everyone is busy with other things.


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What percentage of phds in math actually get a tenure track academic job?
I'm interested in knowing what percentage of math phds actually succeed in landing a tenure track academic job?
Also, does a phd from AMS Group 1 guarantees you an academic job in top universities? If not what other factors come in to role to play?

This is not a particularly useful exercise. The success rate of the population will tell you little about YOUR chances of success. You are better off focusing on ways to improve YOUR chances.

Yes, that's why I asked the second question.

What percentage of PhDs want a tenure track job bad enough?

As a crude approximation if overall staffing numbers remain stable a professor only needs to create a single replacement over the course of his career, which works out as one out of the average number of successful phds students per professor.

In Physics it's 2.7% according to Physics Today (quoting the number out of the top of my head, I can double-check tomorrow), and less than 1% become full professor.

Also, keep in mind that the very first selection of who gets an academic job is who wants an academic job.

I think in math, many people want academic jobs.

NOTHING absolutely guarantees you an academic job in a top university.  Not a PhD from Harvard, not a solo paper in the Annals (or Science or Nature or ...), not a Fields Medal.  Nothing.

I can't help but notice that the answer to the first question here should be a number, but the answers given are narrative. It seems it was not off-base to assume things about the asker's motivation, but the question is also interesting from a statistical point of view, which has not been addressed.

No. No one single factor guarantees you an academic job in a top university.  Whether or not you land such a job is a combination of many things.  These include,

talent
hard work
motivation
quality of research
quality of teaching
ability to network and get along with people
ability to communicate (both orally and in writing)
success in securing external funding
luck.

If you want such a job, here's what I recommend.  Choose an area that you're passionate about, go to the best school (most challenging and "highest rated") that you can get into, and work with an adviser with a strong publication record.  At each step along the way, surround yourself with (and learn as much as you can from) the most successful people possible.
You can find a partial answer to your question about percentage by reading the annual Survey of the Mathematical Sciences (by the American Math Society):
http://www.ams.org/profession/data/annual-survey/annual-survey

What exacty do you mean by talent,hard work and motivation? How can a employer measure these qualities? Is it by just looking at your quality of reasearch?

By talent, I mean natural ability.  By motivation, I mean desire to do whatever is necessary.  And possibly the most important of all is hard work.  Employers may not be able to measure these qualities directly, but they can measure the results of these qualities.  For instance, if you work insanely hard, you're more likely to polish the writing in your papers, which will make them likely to get into better journals, etc.

motivation also wouldn't necessarily be evaluated or seen by an individual employer, but if you are more motivated, you put more effort into the job search, you apply to more schools, thus improving your chances of finding a position.

I understood in the Netherlands somewhere around 5% ends up in a research position. This also includes people who after their PhD leave academia, so the percentage for those willing to continue is a bit higher. Ofcourse, as others already said, these general statistics do not say what your chances are, but it does illustrate that it is hard to find a position. In the Netherlands, it is important to get, apart from a good publication record, into a prestigious grants system (Venice, Vidi, Vici system). The first step is essentially a prestigious postdocs, the second leads to assistant professorship (fixed position), and the final one to full professorship. Getting into such a winning streak is important, successful projects make it easier to get new ones, I.e. the successful become more successful.

An additional parameter to consider is fashion: some research fields are deemed sexy and some aren't (and that assessment changes with time unpredictably!), and your chances of finding a position depend on the current perception of your field by the senior faculty.

As I said in the comments: The success rate of the population will tell you little about YOUR chances of success. You are better off focusing on ways to improve YOUR chances.
To answer the second part of the question, most hiring committees at top universities for tenure track jobs primarily considered your publication record, your ability to secure funding, and your fit to the department. The fit to the department is tricky. It generally includes either research area or ability to teach a class, but may also include departmental politics. Sometimes an applicant can be such a poor communicator (often discovered during the interview) or be a known pain in the ass that this can influence the decision, but generally the decision is based on publications, money and fit. I would venture to say that more often than not the rankings do not chance based on the interviews/campus visits.


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How does your area of research affect your chances of getting job in academia?
I've heard that the trendiness of your area of work is one of the important factor that has am impact your chances of getting job in academia. How far is this true?
Also, how do I decide what areas are trendy and what areas are not in the field I'm interested that is mathematics?

One problem with being trendy is that what is trendy now is not the same thing as what will be trendy in the future. At the start of your PhD you might be 10+ years away from "getting a job"

Trendiness can be factor, but a much more important factor is what needs the hiring department has. If they're chock full of topologists, it doesn't matter how "trendy" your work in topology is: there's a good chance they might be looking to expand in other areas.
OTOH, if they're looking in your area, then being at the cutting edge can't hurt. The danger of course is timing: trends rise and fall quickly, and what might be trendy right now might not be so in a year or two (maybe in mathematics, trends move more slowly).
So I'd argue that trendiness, while one potential factor, is not a universal key factor at all. Every department has their own needs.
As regards your second question, usual measures of "trendiness" include the relative frequency of publication in that subarea. In CS, it's relatively easy to determine this via conference acceptances, but in math I'm not sure how you'd go about measuring this frequency. It also helps to attend big meetings and listen to where the buzz is. An advisor can also be helpful in this regard (especially if they're pre-tenure and need to keep track of trends themselves :))

To piggy back a bit off of this, if you actually follow job listings that might be a good way to identify trendy fields, at least in terms of areas of expertise depts. want to hire! Also I would note there are some schools in the social sciences that specialize in particular areas, and so even if they are chock full of people in that area already they are frequently open to more (tends to be good schools, but not the top schools in my field, so their "hook" is some specific area of expertise).

Regarding the third point of Anonymous's suggestion, here's an article Topical Bias in Generalist Mathematics Journals by Joseph F. Grcar in the december 2010 issue of the Notices of the American Mathematical Society.
In many branches of mathematics, the so-called "generalist" journals are perceived more prestigious and publish many of the best results. Typically they claim that they publish papers of the highest quality in all branches of mathematics. However, they don't necessarily accept papers from each field equally likely. In fact, as the linked article's figures clearly suggest, there are clear biases for/against certain branches if you count the papers of a certain topic published in generalist journals and compare the number with the total number of papers of the same kind.
Since good generalist journals are among the most prestigious publication venues in many branches of mathematics, by looking at statistics like this, you may be able to detect prejudices about branches among mathematicians, which is mentioned in the linked article. So, if your definition of "trendy" is highly correlated with this type of prejudice (which I think it is because, all else being equal, the number of publications in prestigious journals in your CV increases your chance of getting a job in academia), it can be a fairly reliable measure of trendiness.
The Annals of Mathematics Anonymous mentioned is definitely among the very top generalist journals. So checking the latest issues may tell you something about what's hot in mathematics now.
The big caveat, however, is that it only publishes 50 or so articles in each year. So, if you only look up in recent issues, your statistics can't be extremely reliable. Using a record of several years defies the purpose of knowing what's trendy right now, so you're in a bit of a conundrum. Making things more complicated, each generalist journal has their own bias as well; different journals tend to publish papers of different topics more frequently.
So, it might be better to take samples from multiple generalist journals which are considered among the top journals by many. Those journals typically publish an extremely small number of papers though. For example, the Journal of the American Mathematical Society published only 32 papers in 2011 (and 35 in 2010) according to ISI Web of Knowledge. Some prestigious generalist journals publish even fewer papers. (I'm not going to talk about which journals you should use for this purpose because it's inevitably controversial and subjective.)
In any case, if you want to check what kind of topic is discussed in a given journal, you can do that quite easily by MathSciNet. The American Mathematical Society classified branches of mathematics and gave a code number to each branch. And they've been keeping track of publications in mathematics. Just search for the MSC code of your field with a specific journal in MathSciNet and see how many hits it returns. This way, you can see how trendy your field is as well as which prestigious generalist journal likes your kind of mathematics more.
This method doesn't always work equally well though, e.g., if you're interested in applied mathematics or mathematical sides of computer science, what the Annals of Mathematics loves nowadays may not be the most reliable measure that reflects what's trendy right now. Another example is when your field became fashionable relatively recently so there isn't a good catch-all MSC code yet. For instance, arithmetic combinatorics has seen a miraculous revival in recent years in mathematics. Ann. of Math. and other prestigious journals are publishing papers in this field, but there isn't a good MSC code to capture this.

I would recommend that you work in an area of mathematics where big theorems are currently being proven. That usually means that lots of moderate theorems are also being proven.
Some ways to see what these areas are:

Go to national conferences; for example attend the (US) Joint Math Meetings and go to the hour-long invited talks.
Go to your department colloquium every week, if you have one.
Browse through the tables of contents for recent issues of the Annals of Mathematics, and see what areas are getting lots of papers published. (This is a sign not only that these areas are "trendy", but also that they're seeing significant ongoing progress.)
Look at colloquium schedules for top-10 institutions, and/or institutions similar to where you hope to get hired. See what kinds of topics the speakers are lecturing about, i.e., what kinds of topics the professors there want to learn about.
Browse the Math Jobs Wiki, click through to the web pages of successful job candidates, and skim their papers.
(The most important) If you are in grad school, and have not yet chosen an advisor, find out whose students have gotten jobs similar to what you hope to get, and/or are doing interesting work now.


text:
Switching from one area of graduate study to another?
Is it possible to switch from one area of graduate study to another in US universities? For example, suppose someone has enrolled in a computer science phd program. Can he switch over to math(or physics) phd program in the same school later?(or say from applied mathematics to pure mathematics?)
What are the steps for doing for doing that?

In general, transferring to a different department requires a fresh application. While many departments will be sympathetic to applications from students alresdy at the university, they will still require all the formalities associated with a new admission.
However, the procedures vary wildly from place to place, and you must check with your local institution (if you have one already).
Other factors that can mitigate or complicate this process: if there's a standard procedure for doing this, if the two departments historically are comfortable with movement back and forth, if the departments are in the same college/school within the university, and so on.

In most cases you have to apply for admission to the new program, as most American universities admit by department or college for graduate studies.
It is much more difficult to switch from one PhD program to another, as you not only have to apply again and be admitted by the department offering the degree, but you must take the PhD qualifying exam in your new program. Also, depending on how closely aligned the fields are, coursework taken in your original program may or may not be applicable to your new program. It is generally easier to switch Master's programs but still will normally require a new application.
Many departments or colleges limit the number of courses you can apply to a graduate degree taken in another program. In the Master's program I teach in, it is three, and they must be courses that would have reasonable application to our degree. We routinely accept students changing programs, unless their academic performance was sub-par in their previous program, i.e. any Cs, even if their GPA is satisfactory, and/or any course failures.


text:
Does doing a postdoc mean a commitment to an academic career?
I have heard that it would be a bad idea to take up a post-doctoral position, if your ultimate goal is to work in industry. The basis of this maybe that it is harder to be hired for an opening at a company, maybe because you would seem unsure of your direction, or would be over qualified for a junior role.
If there are no ideal jobs available at present, should I take up a post-doctoral position as a safe option, or easy way out, in the meantime?

When I was a young undergraduate, the word of wisdom is that of economics: the more time you spend in academia, the later you enter the industry's pay scale. So compared to other individuals with the same number of years of experience total, you'd be paid less. (It was used to illustrate the Dean's point that you shouldn't go into a PHD program for the money: a BSE with four years experience often ends up better paid then a freshly minted PhD.) I don't know how much of that is still true now.

@WillieWong: now if I could only get to find a job outside academia, I would really love to follow your advice, but apparently with my skills it's rather hard, and I am constantly forced back in.

No. There are many reasons you may want to do a postdoc; gain experience in a particular subfield, get to know the research of a particular advisor, work with a particular research group or department, or even to work with a industry group, in the case of industry-sponsored postdocs. You may be asked why you chose to go the postdoc route when you are eventually interviewing for industry positions, but it is by no means a declaration that you are going "academia-only". Note that this is particularly true during recession periods; it's much easier to get a postdoc than a "real job".

In what field is it easy to get a postdoc?

@Anonymous - In almost all academic disciplines that I'm aware of it's obtain a postdoc position than a professorship position.

I'm writing in from the biotech industry. I hold an MSc, but obviously I work with a lot of PhDs and have observed many PhD hires. Most PhD level industry positions REQUIRE time spend at a post-doc position. This would be either in academia or industry, but academic post-docs are infinitely more common. If you are being hired at a company straight out of a PhD program, that position will (9 times out of 10) be a temporary post-doc position itself.
Be aware that there have not been nearly enough PhD positions in industry to go around for the last 5 years at least. And many companies have strict policies against hiring PhDs for non-scientist positions. I've seen many times a research associate (BS/MS) position post, and we receive up to 100 applications from PhDs that go straight to the trash.
My recommendation for a transition into industry would be:
Do your PhD and post-doc research in the most prestigious labs possible and publish in the most prestigious journals possible. This is because other PhDs will hire you and be impressed by your boss' name and publication record - so it's the same idea that holds if you were to stay in academia.
Skill set is important, but in most cases is not what gets you hired. It is assumed that you can be trained to use any protocols or equipment in house.
Maintain contacts with everyone you know who is or moves into industry, including people at the BS/MS level. Referrals are extremely important and sometimes the only way to get in. Seek out projects that are collaborations with industry labs and go to every industry-sponsored event on your campus. Ask the professors in your department if any graduates or former post-docs moved into industry and try to get in contact with them.
And bottom line: no hiring manager will blink if they see a post-doc on your resume, as long as it lasted less than 5 years and you have results to show from it. And in many cases, managers expect or require some type of post-doc experience for a career position.

I am currently involved in a Marie Curie financed Academia-Industry collaboration. I am doing one year in industry (hired as a software developer) then two years in academia (hired as a postdoc) then one final year back in industry (again hired as a software developer). I have no interest in an academic career path for a plethora of reasons that I won't delve in.
The point is that academia has no alternative contractual access for project-oriented hiring (I call them "disposable scientists") hence the "postdoc" is basically a catch-all contract type to get someone to work on an academic project within academia. It can be intended as a professional step to establish yourself on an academic career path, but by no means it must be intended only as such.

Does doing a postdoc mean a commitment to an academic career?

No. However, if your goal is to work in industry, that is where you should be looking for work. A post-doc would be better than a stretch of unemployment. This is because many companies treat recruiting like dating in high school: you are desirable if you already have a date/job and you have cooties (or something else is wrong with you) if you are single/unemployed.


text:
arXiv preprint and final paper differing by sections and appendices
Because of the style of a journal, and the space limit, I was asked to remove a section and all appendices.
While I have no problem with that, I want to preserve it in the arXiv preprint.
So:

Is it OK to have different final papers and its arXiv version? (perhaps with the comment, e.g. "Sec 3.4. and Appendices A and B only in the arXiv version")
Is it OK to cite in a paper its own arXiv version? (e.g. derivation of (15) is in [5]?)

One problem that can come from situations like this is ambiguity when people reference specific locations in your paper: if I cite “Migdal 2012, §3.2” does §3.2 mean the same thing in the arXiv version as in the journal version?  To some extent this can be avoided by careful arrangement of the material — e.g. if a section is omitted from the middle, that’ll change the numbering of later sections, but if what’s omitted is the second half of a section, that won’t affect anything else.


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Preprint services other than arXiv (for other fields)
While arXiv is great, it covers only topics in physics, mathematics and computer science.
Are there any good preprint storage places for other scientific disciplines?

arXiv certainly does not only cover topics in physics, mathematics and computer science. Just on the front page you also find finance, biology, statistics and nonlinear sciences represented as major categories.

@WillieWong I am aware of it, I just I didn't go into details. However, the other fields you mentioned are of applied mathematics (or cs).

everything is applied mathematics if you dig far enough :-). Quantitative biology (stuff like genomics and protein folding) is really quite specialised and outside what one would usually consider mathematics or computer science.

@WillieWong bonus points for "everything is applied mathematics" :)

@WillieWong The problem is there are only a few disciplines within a larger set like "Biology" that could recognize arXiv, and even less that consider it valuable or something that won't mess with your prospects for publication.

@EpiGrad: but in the cases where the rules about prior publication applies, wouldn't that kill pretty much all pre-print services?

@WillieWong True. It was just an objection to the occasional tendency of arXiv users to overestimate the use of arXiv because some biology pre-prints appear.

@epigrad: looks like you and I are being nitpicky about different extremes! :-) (I perfectly agree with your last comment, by the way.)

This question would use an accepted community-wiki answer summarizing all the given answers with a 2-liner description of each system.

The state of preprint services has changed since this question was asked in 2012. I think that the answer that I provide below about the OSF is close to the correct answer in 2017.

The OSF provides a general open preprint infrastructure that is connected to a range of preprint services. Importantly, it is not owned by a commercial publisher.  It supports a number of discipline-specific preprint services many of which use the ArXiv name under licence.
The list of preprint services is growing over time.
For further information go to: https://osf.io/preprints
In general, no matter what the discipline you can post to:

OSF preprints https://osf.io/preprints/

However, the OSF supports the following discipline-specific preprint services. Presumably, if your preprint aligns with any of these disciplines, then you would be better off posting to them.

Psychological Sciences.  PsyArXiv https://osf.io/preprints/psyarxiv/
Social Sciences. SocARXIV https://osf.io/preprints/socarxiv
Engineering. engrXiV https://osf.io/preprints/engrxiv
Agriculture and Allied Sciences. AgriXiv https://osf.io/preprints/agrixiv

More discipline-specific preprint services using the OSF framework are being added on a regular basis: https://cos.io/blog/public-goods-infrastructure-preprints-and-innovation-scholarly-communication/
Useful features of OSF-based preprint services

Strategy for long term archiving
Integration with Google Scholar
Integration with OSF projects which allows you to link other materials such as data, code, and materials
OSF is a not for profit entity run by academic researchers (contrast this with SSRN, Figshare, ResearchGate; i.e., no ads and goals aligned with academic community)
The functionality of OSF preprints is improving on a regular basis. See features road map
You can choose a licence
You can link to the doi of the subsequently published manuscript.

This should be the answer.

@JB Agreed. I guess its tricky when the answer changes over time. This preprint service emerged only after the question was asked, but it should prove to be the logical home for papers that don't align with the ArXiV.

true enough. Incidentally, even arXiv is searchable via https://osf.io/preprints/ now!

The Center of Open Science (head of OSF) is partly sponsored by the US Defense Advanced Research Projects Agency (DARPA), involved in developing new military technologies. Not my cup of tea.

Ones more aimed at social sciences (that I am aware of) are;

Social Science Research Network (SSRN)
The National Bureau of Economic Research (NBER)
The recently-founded SocArXiv (link to search and upload preprints)

SSRN is dominated by economic and legal research (and NBER is obviously focused on economics).
Another I recently became aware of is Academia.edu, although this appears to me more like a personal website that has the option to upload working papers than an organized repository like SSRN or arXiv (here is an example profile page on Academia.edu).

In Germany, there are also the Social Science Open Access Repository (SSOAR) and EconStor.

One should be aware of Academia.edu's crazy Terms of Service. It is in conflict with the copyright policies of many publishers, even some OA ones.

Note that concerns have been raised about SSRN since Elsevier purchased it

Thank you Jeromy - IMO the complaints about SSRN to date have been overblown - but I agree one should now be aware they are owned by Elsevier. Probably we should also mention just posting papers on your own website - google scholar will still pick them up eventually.

It seems that neither option presented below are taking new submissions. I keep the answer here for historical interest.
One option is:

Philica which occupies a bit of a strange place. It is a free, open-access journal that publishes immediately and in any discipline. The website comes with a non-traditional review system. It is in between what one may call a pre-print server and what one would call an electronic open access journal.

Nature Precedings used to take submissions, but no longer does:

Nature Precedings: a pre-print repository run by Nature Publishing Group that focuses on chemistry, biological sciences, and earth sciences. Edit: As bobthejoe noted below in the comments, Nature Precedings is no longer taking new submissions; though it will for the foreseeable future remain a repository for the pre-prints already submitted.

Unfortunately, we will now have to say RIP to Nature Precedings.

Philica has been downed too?

@Ooker: Google has a cached copy of Philica from February 25 of this year. From the look of it, the list of "Most recent articles" appears to be mostly nonsense and Spam, with titles like "Tips On Hiring Dulles Airport Shuttle" or "Basics Of Selling Your Family Business ". That may explain why the website's account now appears to be "suspended".

in that case, I guess a downvote for not being useful is appropriated? :)

Better yet, vote this answer up since I think it is currently the best option of everything presented so far. Mine only has more votes by virtue of being older.

Figshare is a rather new service (compared to ArXiv) that is just starting to gain momentum. I haven't used it personally, but they have partnered up with some other Open Access players, most notably and recently with PLoS (Figshare will host supplemental data for all PLoS journals). As far as I know, there is no restriction regarding the fields the submissions must be in.
It is a repository, the service is free (unlimited public posts, 1GB private posts). No review or moderation; the submissions will be posted immediately under CC-BY. Each submission is given a DOI. I cannot find info about how many submissions they have received and posted.
NOTE: Just checked with Figshare through twitter, and after one year they have 200,000 files shared by users (could be papers, figures, charts, data, etc)
Edit: just realized I should also mention the following:
PeerJ was just launched very recently (like in the last month or two I think). It's a journal but has its own pre-print system. You can submit unlimited number of public pre-prints in their preprint server PeerJ Preprints, which has its own ISSN number. You will be able to submit your pre-prints subsequently to their peer-reviewed journal. The journal is gold OA and charges what I believe is a one-time membership fee. The journal has limited scope (does not publish in the Physical Sciences, the Mathematical Sciences, the Social Sciences, or the Humanities ), not sure what the pre-print service will look like yet and it is worth checking out later on.

Figshare looks interesting, but I think it would have some limitations as a preprint server.  One is the mandatory CC BY licensing (which is incompatible with many journals), and the other is that I don't think there's a culture of scanning through Figshare announcements for the latest papers.  If you post a mathematics paper on the arXiv, many of the leading experts will notice it the next day.  Currently, Figshare seems to fulfill the hosting aspect of being a preprint server but not the publicity or dissemination aspect.

I agree that it will still need some time to grow to have the structure that ArXiv has currently. With more OA players on board and community input, hopefully that will happen soon. I wasn't aware of the CC-BY licensing issue with journals though - am now curious. Do you have examples of journals with which the CC-BY licensing could create an issue for submission?

Probably you could get away with it by simply not telling the journal what you did, but it strongly conflicts with the publishing agreements of most non-OA journals.  For example, if you don't choose a gold OA option, Springer insists on a transfer of exclusive rights, which is impossible if you have already released the paper under a CC-BY license.  (There are exceptions for some things like the arXiv, but I'd be very surprised if they allowed a CC-BY license, since letting people do that for free would undermine their gold OA options.)

I don't think there's anything special about Springer here (I just mention them since I was looking at http://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683101-0).  Some non-OA publishers, particularly non-profit ones, may be fine with a CC-BY paper, but I think most would not.  In any case, if anyone is considering doing this, I would urge them to check out their favorite journals and make sure they would be OK with it.

Thanks for pointing this out. Just found another post in stack exchange regarding this: What are risks or disadvantages in uploading to figshare or related services?. I personally like OA & CC-BY but also recognize the reality of the situation, so yes it is better to check first.

I always thought of FigShare as more of a data repository than a preprint server, and a brief look (at least in the CS discipline) shows mostly datasets, not so much the papers themselves. Then again, CS often publishes in ArXiv, so who knows what other disciplines use FigShare for.

To complement the other answers,
in mathematical physics there is mp-arc in addition to arXiv,
and in biology one has biorXiv which is apparently modelled after arXiv.

Next to bioRxiv, there's also medRxiv.

HaL ("hyper archive en ligne") is a French open archive repository that covers all fields. As far as I know it is open for submission beyond people working in French departments. It can automatically deposit on arXiv for papers whose topic is covered.

I'm not sure why this hasn't come up on this thread yet:

PubMed Central is the main open-access repository in the biomedical and life sciences. It has its own added metadata, and it is the mandatory recipient of all research funded by the National Institutes of Health and a number of other funding bodies. There are also specific versions for Canada and Europe.

There are some more specialized ones for math:
Linear Algebraic Groups and Related Structures
Cryptography

For the geosciences and earth sciences (climatology, meteorology, geomorphology, oceanography, etc.) the American Geophysical Union (AGU) now allows and encourages pre-prints to Earth and Space Science Open Archive (ESSOAR) for AGU journals. They also host PDF's of posters from meetings including the annual meeting.
Most of the papers coming out from coworkers in AGU journals are hitting ESSOAR.
https://www.essoar.org/

F1000Posters (http://f1000.com/posters) is an open access repository that hosts posters and oral presentation slides in biology and medicine, and can also be considered a pre-print server.
It allows researchers to extend the visibility of their work outside of the conference hall, maximising the return on the time, effort and money invested in creating each presentation. Many of the posters are submitted with their subsequent research article added to them when it is eventually published. It also completely free to submit.

For linguistics, there's LingBuzz.

Optimization Online is a preprint site for papers in optimization: http://www.optimization-online.org/

If your purpose is only to have an openly available version of your paper that you can link to (and that people can find using Google Scholar), you can also upload it to your institutional or personal website. At least in CS, this is allowed by pretty much all major publishers I am aware of (and more frequently allowed than ArXiv). Google Scholar will pick up your paper eventually.
Additionally, some universities host their own ePrint servers for their own students and faculty. Again, this is not really a place to find new interesting research, but a great way to get your paper hosted and indexed by Google Scholar et al., and is also commonly allowed by publishers.
As a bonus, both of these options do not require you to register any new accounts or upload your paper to some (potentially commercial) third party service, which may be a plus, depending on your personal stance on these matters.
If your purpose is to also "get the word out" about your paper, one of the other mentioned repositories is obviously the better way.

I think academia.edu and authorea are also possible answers to OP's question

In economics, there is also MPRA.
EDIT: https://mpra.ub.uni-muenchen.de/
MPRA is a repository run by the Munich University Library and has a description here. https://blog.repec.org/2009/08/27/mpra-the-munich-personal-repec-archive/

Welcome to academia.se! Could you please add a link for our benefit, expand the abbreviation, and maybe quickly describe this e-print server?

Also please disclose your affiliation with this site (which seems to exist).


text:
What's the timezone for anywhere on inhabited Earth?
I read in this call for papers for some symposium:

Paper Submission: Saturday, 2nd June 2012 anywhere on inhabited Earth (disregarding Baker and Howland Islands)

What's the timezone for anywhere on inhabited Earth? UTC-11:00 all year long?

Great.  Now someone is going to travel to Baker Island with a laptop and satellite internet link, submit a manuscript at 23:01 local time, and raise a stink when it's rejected :)

Please avoid posting answers (particularly wrong answers) in comments. This is a good example of a question where short answers are perfectly acceptable.

UTC-11:00 is indeed the most natural interpretation. Anywhere on Earth normally means UTC-12:00, but since that time zone is entirely uninhabited it leaves UTC-11:00 as the last inhabited timezone.
There may be technical reasons for conference management software to use UTC-11 as the cutoff instead of UTC-12, see e.g. here.

Interestingly, this convention has its own Wikipedia page. It states:

Anywhere on Earth (AoE) is a calendar designation that indicates that a period expires when the date passes everywhere on Earth. It is a practice to help specify easy to understand deadlines...without requiring timezone calculations.... For any given date, the latest place on Earth where it would be valid, is on Howland and Baker Islands, in the IDLW time zone (the Western Hemisphere side of the International Date Line). Therefore, the day ends AoE when it ends on Howland Island.

Curiously, your instructions state to disregard Baker and Howland Islands, so your deadline is technically an hour before Anywhere-on-Earth time. Still, the intention is clear: "by the end of the day on 2 June 2012, for any reasonable definition of 2 June 2012."

Ah, just noticed Anyon already found this wikipedia page. Alas.

The point is just that wherever you are in the world, if you do it by Saturday 2nd June 2012, it will be OK.

Thanks,  I prefer clear cutoffs.

Unless you are on Baker or Howland Islands, that is :)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Why do many PhD application sites for US universities prevent recommenders from updating recommendation letters, even before the application deadline?
I've noticed that many PhD application sites for US universities prevent recommenders from updating the recommendation letters, even before the application deadline. Why?
Example:

Hmmm. Sick of dealing with too many bad documents and the necessary communication that it requires? Guessing. Are you sure it is "many"?

@Buffy >50% in the 20 univs I've done this year (CS departments). Updating a PDF on a site requires no communication, and if sick of dealing with too many bad documents then better allow updating them to fix mistakes.

Surely because they don't want to have to check for updates every day? Be able to make decisions based on a stable situation? It's not like they don't tell you that when you "commit", you can't change it... they do.

@paulgarrett but why prevent even before the application deadline? Don't they decide after the application deadline?

A good point, but, still, some people try to "get a jump on things" before the deadline, to spread the work out over a longer time... as opposed to having to figure things out in a huge rush over the winter holidays, etc. Simplicity?

One should not assume that these systems are administered by people who care about graduate admissions.

Is it possible that a number of R1 universities have agreed to unify their procedures as they have generally done with deadlines?

Consider that it's the other way around. The minimum effort functionality is a system that allows a single submission. Allowing updates is more complex, so unless someone specifically asks and pays for it, the ability to update isn't going to be added.

@user1937198 I think that's exactly it. Probably it didn't even start with this alert, because the people creating the application software never even considered someone would want to update, they're just making a form that accepts a PDF. Then some rare person complained that they wanted to update, and their fix to the software was to add a notice that you can't do that.

Now you have me wondering why that would even be necessary. Just about every recommendation letter I wrote or got was about a long timeline and many interactions, adding another semester wouldn’t have significantly changed things. Are you wondering this just because of the notice (which would underline this isn’t necessary) or would you actually and often have use for updates?

@MisterMiyagi for example if one has forgotten about an important point

This is most likely a technical limitation rather than a policy decision.  I doubt that most admissions committees care one way or another whether recommenders can update their letters through the admission portal, and so many admission portal systems simply don't bother to include an update feature.  The "you may not edit" message is simply to advise you of this, to encourage you to double check your letter before uploading it.
On a practical level, if as a recommender you have an important reason to update your letter (e.g. you uploaded the wrong document, or your letter contains major errors, or something important happened with the student after your letter was submitted), you should contact the admission committee directly, e.g. by emailing the graduate chair or department chair.  You can generally find their email addresses on the department's web page.  However, since this will require some manual intervention on their part, you shouldn't do it just to make minor corrections (e.g. spelling) that don't significantly change your overall recommendation.


text:
How can I list all papers citing a given paper and hosted on a given website?
I tried Google Scholar but it seems unable to list all papers citing a given paper and hosted on a given website (e.g., https://aclanthology.org/ or https://arxiv.com). Did I misuse Google Scholar and if not, which search engine can list all papers citing a given paper and hosted on a given website?

In Google Scholar, I tried the "search within citing articles" option:

But it doesn't seem to work with search search operator:

Google Scholar does not index papers by websites. So, no there is no way to do strictly what you are asking. However, Google Scholar indexes articles by publication source (journal, conference, working paper repository, etc.). So, you would need to reframe your search accordingly.
In fact, the two websites you listed are very different. As far as I can tell, ACL Anthology is effectively a scholarly database (equivalent to JSTOR, EBSCO, or Google Scholar itself) that aggregates articles from many different sources. I don't think Google Scholar would ever duplicate what ACL Anthology is doing or even try to record or make available that an article is available on ACL Anthology and EBSCO and Scopus, etc. That doesn't make much sense to me.
However, arXiv is indeed a publication source in its own right: it is a preprint archive. Google Scholar certainly records this information. You just have to filter your searches by arXiv:

Go to Google Scholar.
Click on the three bars for options.
Choose Advanced search".
In the field "Return articles published in", enter "arXiv".
Enter your other search options accordingly.