text:
What does a promise of possible funding "based on availability of departmental funding" actually mean?
I'm finishing up my third year of a PhD program this Spring. Until recently, I had assumed that I would have four years of funding as many of the PhD students do. However, after asking the department chair, I was told that "the department resources are stretched (as usual) and we made our recruitment plans based on those cycling off funding, including you. There is always a possibility that our recruitment efforts do not go as planned, but it is unlikely that we will be able to offer a fourth year of funding."
My award letter states that I have three years, with the "possibility of a fourth year based on availability of departmental funding." What does "based on availability of departmental funding" actually mean, legally? Does it mean that the department can continue to recruit new students instead of keeping on current ones?
I'm at a public university. Is there any way to find out whether the departmental funding is actually unavailable? Is it enough to ask HR, or might there be any other resources I should search out?

You were told there is probably no funding. Why does this not answer your question of whether there is funding? When I did my doctorate we all knew you couldn't spend all your funding each year, because you needed to save some for when the funding stopped.

"Is there any way to find out whether the departmental funding is actually unavailable?" As opposed to what? The department is conspiring against you and lying about having enough money?

Why did you assume a 4th year was in the bag when your letter specifically refers to "possibility" of a fourth year? It sounds quite clear actually, I'm not sure why you might think strangers on the internet know better about your department's funding situation than, well, your department.

I don't see why the department wouldn't be able to choose funding new students over funding students with only three years of funding. The award letter only guaranteed you three years of funding; they are not obligated to provide more.

Your institution has definitely met the terms laid out in your award letter, which states that there is "possibility of a fourth year based on availability of departmental funding." This does not mean that you are necessarily guaranteed a fourth year of funding. Even if most students get the fourth year, assuming you will is risky. They promised you three years of funding, and said that they might be able to give you a fourth. They gave you three years of funding, and decided that they can't afford to give you a fourth. As raised by @einpoklum there may or may not be other factors that influence your contract, legally, but any analysis of that would require much more information than what is provided and should be provided by a lawyer, not a random academic on the internet.
Regardless of the precise legality of the decision, I would advise that you spend your time looking into alternative sources of funding rather than try to dispute this decision. Trying to contest will damage your reputation within your institution, make you look foolish (especially if you have a weak case / are perceived by others as having a weak case), and use up precious time you could have spent looking for alternative sources of funding. Speak to your adviser first and foremost, as they have the best understanding of the university and what resources might be available to you (RA or teaching positions, most likely). Your government almost certainty has agencies that award grants that you may be eligible for. There are also non-profits that award academic grants that you may be eligible for, especially if you're an underrepresented minority.

I don't think this answer really sheds light on the matter. It makes an assertion but does not back it up. I think more caution should be taken with this and other answers where there is not legal expertise (at least there appears not to be, correct me if I am wrong). See the answer by einpoklum below.

@ThomasKing What assertion would you like me to lend greater support to?

@StellaBilderman "Your institution has definitely met the obligation laid out in your award letter", you refer to what the letter states but don't lend support to your conclusion.

@ThomasKing I don't understand the complaint. The next two sentences do that. I've also edited my answer to specifically disavow any opinion on the complex legal issues raised by einpoklum

Prior to your edit (and even after your edit) you talk about meeting the obligation. All you do is state what the letter says. At best, you may argue they have met a prima facie obligation, which doesn't help much. Your edit now makes it a bit better.

@ThomasKing I have significantly revised my answer to be clearer and take further into account your and einpoklum's criticisms. Please let me know if you have further criticisms.

Great answer, upvoted. Btw, IANAL but I don’t think the “complex legal issues” are complex at all. OP asked ‘What does “based on availability of departmental funding” mean, legally?’ and you gave the answer any well-educated native English speaker would give. Any legal issues related to other implicit or explicit legal obligations the department may have towards OP are simply beyond the scope of the question, and I don’t see a special need for you to disavow them.

@DanRomik I happen to agree and have said as much in comments, but other disagree and it’s easy enough to write.

What does "based on availability of departmental funding" actually
  mean, legally?

It means if there are funds available, you may have access to them.
You have been told by your department that funding is not available. Why they aren't available isn't particularly relevant.
It's possible you can go digging, but no, it's not enough to "ask HR", as they're unlikely to know the line item budgets of each department. And, to be candid, trying to dig that up to play some sort of legalistic "gotcha!" with your department is likely to do considerable damage to your reputation and standing within the department.

I disagree with this answer. It sounds like funding is available, but the department has decided to spend it on something else (new students) that I would have though has lower priority. I can understand why OP is upset in this situation, even if they don't have legal recourse.

@Thomas I get why they're upset too. But nowhere in the OPs quote is "You're the highest priority for funding". The department spent it according to their priorities. Sadly for the OP, the balance hit 0 before they got to him and funds are no longer available.

No, I definitely would not do a "legalistic 'gotcha!'" but I'm not sure that I don't have funding. As stated, the chair mentioned that there may be funding depending on how many students enter the program in the fall. Even if this matter were not related to me, specifically, I really would like to know what this means legally.

@Parever The department's stance is that you're lower on the priority list than some other students (including potentially new students - this is not uncommon, as they haven't had a chance to get other funding streams and you have as well as those still in their promised 3 years), and low enough that you don't want to bank on it.

@Parever.  There is a chance you will have funding.  You cannot be certain that (a) you have funding for year 4, and you cannot be certain that (b) you don't have funding.  Start seeking sources of funding other than whatever source supplied your first three years.  If I were you I would dedicate at least 15 minutes per day to finding new funding until it's found, without skipping any days.

@LukeGriffiths Never skip Funding Day :)

Is it actually that clear whether it means, if there is funding, you *will* have access to them or if there is funding, you *might* have access to them?

@innisfree  I think the meaning of "based on availability of departmental funding" is entirely subjective.  Whether "funding is available for X" has the same meaning as "whether whoever controls the budget decides to use money for X".  Money used for X is always at the cost of all items other than X.  For example if there is "available" money, and the money is used to buy party favors for the department, then that money is no longer "available".

I am not a lawyer, but a funding possibility of a fourth year based on availability of departmental funding sounds pretty meaningless as a promise. That is, I don't think you have any legal or administrative recourse in your situation.
That said, I completely understand why you are upset. It sounds like you were given the impression that you would probably get a fourth year of funding, based on what happened to other students.
In general, I consider it poor form for a department to fund new students in preference to current students. A good department should put quality (fully-funded PhD students) over quantity (stretching funding to admit more students).
However, it may be the case that they have chosen not to continue your funding because they are not pleased with your academic progress and feel that new students are more promising. If that is the case, then there is little you can do about it. Unfortunately, it happens and my advice to people in such a situation is to find somewhere they are appreciated.
I would suggest that you focus on (i) finishing your thesis as quickly as possible and (ii) finding alternate sources of funding -- teaching, scholarships/fellowships, internships, etc. Alternatively, you could look for options outside academia.
As always, ask your advisor.

My department also had a soft funding promise in a final year and was giving me difficulty about awarding it. You may have luck with my strategy.
Rather than dispute their right to make such a decision, I was able to make a convincing case that the department should prioritize me among the advanced students if funding was available. I explained that although I never brought in a full fellowship, I brought in several partial fellowships and that should make me a strong candidate for an additional year of funding. The rationale was that I had not actually "used" all of the funding in the previous years. My department was also aware of extenuating circumstances that required an "extra" year and so was more likely to acquiesce to my request. It worked.
I would wager that this will be a more fruitful strategy than fighting the department on the wording of the offer letter.
You should, of course, also be talking to your advisor about funding and actively pursuing alternative funding at the same time.

Did you do this before or after you were told that there was insufficient funding? I can see the difference in timeline mattering significantly.

I believe the PhD director made a comment at our annual student forum that funding was not guaranteed and that current students may not get "bonus year" funding that year. Then I went into full alert mode and scheduled a meeting with him.

Thanks for everyone's interest. @dawn this does relate to my situation --  "soft funding promises" made within this department (US), extenuating circumstances, and partial but not full fellowships. Glad you shared.

In the U.S., in mathematics, at an R1, such terminology (though our number-of-years is somewhat different) means that you're really expected to finish in 3, first.
A complication (certainly in the U.S.) is that teaching-assistant hiring/funding decisions for Fall need to be made in January or February before, which is often much in advance of it being clear whether advanced students will finish or not, in that Spring term. Thus, it is presumed that students will finish on time, so that new grad students can be hired as TA's. It's not really about "priorities".
Then, yes, because commitments made to new students are taken seriously, and often recruiting seems to require very specific commitments, financial support of advanced students who've "taken too long" is not at the top of the list for allocations of limited funds.
Yes, I agree that it is probably all too easy to misinterpret the intent of such language, but, in my experience, no one is trying to trick anyone by it. If anything, it's meant to be a warning to "not count on funding in further years".

@Thomas and @Fomite and @StellaBiderman are, with due respect - wrong in my opinion, likely due to lack of legal experience (and lack of union experience).
As any lawyer will tell you, the legally binding obligations of a party to a relationship are not limited by the text of a written document describing that relationship. These may be inferred from the context of the formation of the relations, as well as from custom and from the parties treatment of others. Now, legal systems in different states in the world give different weight to such obligations, in themselves and in context of written documents, but this is a definitely a question to be opined about by someone with relevant legal training.
This does not mean that the university is obligated to continue employing / funding you for the fourth year. It may, and it may not, be thus obligated - or it may be a gray area. Also, I'm not telling you to sue or to threaten to sue, even if you have a legal opinion saying that an obligation does exist. Enforcing legal rights has its own pros and cons (and often takes a lot of time, so @StellaBiderman's practical advice may be quite relevant).
Another point regards the nature of your relationship with the university may have bearing on its obligations. There are ongoing public and legal struggles for the recognition of "funded" PhD candidates as researcher employees of their universities, see:

Why do universities fund Ph.D. students in the sciences?
Education or employment: What is a post-doc? What is a PhD student?

Finally, some universities have Graduate Employee Unions (that's of course related to the previous point). If yours has one, or a nearby university has one, they may be able to act, or already are in the process of acting, to make the period of employment be decided by  clear and fair procedures, and well beforehand, rather than the result of caprice or whim. So - go talk to them.

Are you claiming that there are countries / contexts in which "three years, with possibility of a fourth year based on availability of departmental funding" will be interpreted as "four years of funding"? I think you have an excellent point about consulting the union, and if there is a separate union agreement that says "current student funding will be prioritized over new students" that would be one thing. But barring conjectured other agreements I don't see how the OP could be guaranteed four years of funding.

I also don't feel that hypothesizing alternative agreements in addition to what is presented in the OP falls within the way we are expected to answer questions. There is always going to be the potential for extenuating circumstances. I'm certain that for every  answer on this site I could invalidate existing answers by adding additional context, but I don't think that should mean that every answer should be hedged with as many assumptions as come to mind. We aren't mind readers and can't speak to context except insofar as it is provided by the OP.

I have slightly rephrased my answer to say that they have fulfilled their written obligation to "three maybe four years," rather than claiming that they have fulfilled their legal obligations. I think that that is unambiguously true, and is the thing that the question asks.

@StellaBiderman: No, I'm claiming that in many countries, the courts will not limit themselves to merely reading that sentence, but will consider the customary funding period and other kinds of communications, not necessarily in writing.

@StellaBiderman: Also, following your comment, I've made it clearer I'm not claiming there is a 4-year obligation. Just that it's a complex legal question.

I've substantially edited my answer in view of your and Thomas's criticisms.

"due to lack of legal experience (and lack of union experience)" - Unfounded assumptions are unfounded.

@Fomite: Added "likely".


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Difference between a letter/short article and a full length article?
After 3 weeks from submission, I recieved the below email from the editor in chief of an applied math journal, asking whether I would consider changing my manuscript from full length article to a letter/short article, giving primary reason that the article length is short, so it would suit a short article/letter, and mentioning that the journal publishes short articles of high quality along with full length articles in all regular issues. I was asked to give my decison. I had a look at the letters/short articles of that journal from previous issues and found that they are no different, except in length. So I am not understanding the difference.
I am not able to interpret, whether I have been strongly adviced by editor, and that I better go with it. The editor already had that article with him for 3 weeks, so he might have had a look at it and might be giving strong advice. I also don't fully understand the difference between both modes of publishing.  Do these two have different academic values?
Email:

Dear Mr. XXXX,
I am writing to ask if you would consider to change your submission, XXXX, to a Letter from a Full Length Article. The reason for my request is based on the short length of you manuscript. XXXX Journal publishes short papers of high quality. Please let me know of your decision. The official review process will not proceed until we hear from you. Thank you.
Kind regards,
XXXX
Editor-in-Chief

Does these two have a different academic value?

It could be even a good news but I am from a different field. One in which a short letter is well considered and  more prone to be desk rejected. So in this case you are a step further towards a successful development.   ...But again not sure in maths

In my experience, there is no real difference between "full" articles and "short" articles except for length.
Many journals, especially more recent online-only ones, do not bother with this distinction at all.  An article is simply as short or as long as the article turns out to be. Even with journals that do make the distinction, it often has little impact of the de facto length of the material once supplementary material is included---all that is affected is the fraction of the published "iceberg" that is "above water" in the main text. The peer review process is generally the same, and the perceived value the same, just simply some are shorter than others.
In terms of visibility and citations, short articles are typically just as visible (as you have noticed). I have never seen a citation attempt to distinguish between short and full articles, and most citation formats have no way that one could do so. For those who are affected by publication statistics (e.g., impact factor), that's not affected either: these are calculated by journal, not by article category within a journal.
In short: some things are just shorter than others, and that has little effect on their significance.  The editor thinks your article will work better in "short" than "long" format, so take their offer or risk rejection pointlessly.

Thanks for the answer.Same question I posted as a comment to Allure's answer.

Assuming your mean this: "I wonder why would the editor hold the review process (as he mentions), until he hears my decision?" Your  response does affect how the article will be considered by the reviewers and how it will be revised.  If it's "short", then they'll not be tempted to pick on your for its length.  Complementarily, you won't be able to address revision requests by adding in lots of new material.

But then why doesn't the editor simply say "I think your manuscript can be written shorter and more succinct. Can you do that?"?

From the author's point of view there isn't much difference between short letters and full-length articles, aside from length. Some of the differences not mentioned yet are:

The journal might group its letters together and its full-length articles together. For example its website might have a "letters" section and an "article" section; its print issues might have the letters first then the articles.
Some small administrative changes that you'll never notice unless someone points them out to you, for example the article ID might change. One publisher I worked at had this code where articles with ID 20 are letters, ID 30 are reviews, ID 50 are research articles, etc. If I'm not mistaken this also changes the digits in the DOI.
It's possible the production process is different, with letters being on a fast track since they're shorter and so quicker to process.

These are minor differences though. Since the practical differences are so few I'd just accept the editor-in-chief's suggestion - no reason not to.

Thanks for the answer. I wonder why would the editor hold the review process (as he mentions), until he hears my decision?

@user102868 An obvious reason: he wants to make sure you're happy with it potentially being published as a letter before sending it to his reviewers. If he doesn't seek your consent at this stage, and only tells you what's happened after it's been reviewed, there's a chance you'll say "I don't want that, so I'm withdrawing my paper", and then his reviewers' time will have been wasted. It keeps everyone happy if your consent is sought at each stage. I think it's standard practice.

@user102868 I think Billy is correct. It's also possible the review process is different for letters & articles, e.g. the reviewer instructions are different.

@user102868 it also may be that there are specific criteria for a "Letter" (such as page length) that your paper currently does not meet - for example, it might be one page too long to fit the letter requirements. Agreeing to publish it as a letter implies agreeing to restructure the paper to fit in these constraints, and that would need to be done before the review process.

I speculate that the editor wants to accept, but only as a letter/short article, rather than a full length article. I consider declining the editor's offer as a path to rejection. But, I might be wrong...

You could try to solicit more information, e.g., rather than responding, you could give the editor a call, which might result in them providing more details that will help you make a decision.

You could propose a counter-offer, e.g., suggest extending the article, since "[the editor's] request is based on the short length of you manuscript" (that might be  calling the editor's bluff), which might also result in more information to make a decision.

I answered the question before it was edited (by a third party) to ask something different.

If you don't have to do any extra work, I would say fine, call it whatever you want.  (It's not like your CV or h-index or Google Scholar will have a purple brand on the letter articles.)  If it requires extra work (like further cutting, reformatting, etc., I would tell the editor to pack sand...and be prepared to go elsewhere if he insists.)

A letter is to a particular party/individual/group if you will.
A short article could be a continuation of a news report/release/update.
A long article would be a presentation, body, and closing from beginning to end.

Your answer seems to stem from common definition of those words in regular media or common language. Most of what you write is wrong for academic publications.

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Applying Late to Mathematics Graduate School
I have posted a similar question to this previously, but would like to reword it and re-ask it.
I just recently completed my undergraduate studies with a degree in mathematics from a relatively well-known US university. During my time as an undergrad I took many advanced (first and second year graduate courses) as well as one-one reading courses with professors on topics in Probability and mathematical analysis (topics like stochastic differential equations, large deviations theory, linear/nonlinear PDE at the level of Caffarelli and Cabre, as well as topics in Calderon-Zygmund and Littlewood-Paley theory).
Due to my indecisiveness and the insistence of my family for me to find "gainful employment", I chose to not apply to graduate school, and instead work full-time in private-industry (quantitative-finance). The work is challenging and sufficiently interesting, and of course pays well, but I still feel that I would be remiss if I did not purse a PhD in mathematics (or related fields). My main issue (in my mind) is letters of recommendation. While I am confident that the professors I have worked with would be willing to recommend me, I am in some sense taking a non-traditional route by delaying my application (for example after one year of working). In turn, I am afraid that the more time I take for asking a recommendation, the less-likely it is that my professors will remember me and be able to write a strong letter for me.
Does anyone have recommendations as to a best course of action here? I am wondering whether I need to bite the bullet and apply to programs this year, and hope they offer deferrals (for say, one year of time) although I'm not sure how the current situation (with covid etc.) could impact this. If anyone here is on mathematics graduate decision boards (or any graduate decision boards for that matter), I would appreciate your input. I am also wary as to the perception of "non-traditional" applicants as my self and how they might be perceived by admissions committees, although it is too late to modify that status.

I doubt working for a year between undergrad and PhD would be considered "non-traditional". I think around half the PhD students in my department did something between undergrad and PhD. One even had a 20 year career in another field before switching to physics. I don't think you'll be at a disadvantage.

Futhermore, what is motivating you to get a PhD? "Feeling remiss" is not going to cut it on a personal statement, and lukewarm motivation will hinder your application just as much as a weak reference.

So just to be clear on the timeline, your plan is to start a PhD program in Fall 2022, so that you'd be applying in the winter of 2021-22?

@NateEldredge Yes - that would be my ideal timeline.

There's an easy way out of this dilemma: talk to your professors now, tell them that you intend to apply to graduate programs in another year, and that you hope they will be willing to write recommendations.  The professors can then draft a letter right away, or at least notes for a letter, while their memories of you are still fresh.  When the time comes for you to apply, they can update their draft to discuss any additional accomplishments you have achieved in the intervening year, and send it in.
I don't think that a two-year gap between undergrad and grad school is likely to make a big difference in admissions, especially if you describe it as your plan all along.  You just want to avoid giving the impression of "I went to go work in industry but immediately discovered I hated it / got fired / etc, so now I'm applying to grad school because I can't think of anything else to do with my life". If it were five or ten years, there might be some impact, but that's not the case here.

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What are the signs that it is time to switch from thesis to capstone track?
The Master's program (Software Engineering) I'm enrolled in offers both a thesis track and capstone track. Currently I'm enrolled in the thesis track and I've completed all of the required coursework for the thesis track, but I've been stuck in the thesis proposal process for over a year now1 and I'd like to just graduate and be done. I suspect that I'm being "encouraged" to switch over to the capstone track without the Research Advisor outright saying it. What should I take as the signs that it's time to make the switch?

By stuck I don't mean that I don't have a proposal, I mean that I've been submitting revisions about once a month for the past year with conflicting feedback being received and no real progress towards having a Thesis Director.

Isn't trying for a whole year enough of a sign to switch? What is holding you back?

@T.F. Well, normally I would agree with that assessment; however, the average time from "concept to acceptance" is around nine months so the extra three months might not be that long. Plus, most of the feedback on the concept and proposed solution has been positive.

Please clarify the difference between the "thesis" and "capstone" tracks—are you saying it's the difference between being admitted to PhD candidacy versus a terminal master's program?

@aeismail I'm not sure how to clarify those terms as their meaning seems to be fairly standardized across academia in the United States. Depending on the school you apply to after the Masters, it could be the difference between being admitted to a Ph.D. program... or not. My understanding is that strength of the school I'm attending likely be more relevant than if I did a thesis or a capstone project.

Ask point-blank. Stop letting your advisor be "nice".

@JeffE - LOL, I have! My exact words were along the lines of, "Point blank, do you think this proposal can be turned into a viable thesis or am I better off switching to the capstone track?"

Yikes.  That suggests that your advisor doesn't know or doesn't care.  A month between revisions is too long.  Switch to weekly revisions, or more often if possible.  Give your advisor (and yourself) a deadline for a definitive answer. Consider finding another advisor.

@JeffE Well, I'm still at the proposal stage (with a 54 page thesis proposal :/) so there is only one option for an advisor and I bumped up the number of revisions before in the past. However I was getting really good feedback during a proposal workshop followed a couple weeks later by one-on-one session during which the proposal was effectively eviscerated and I've had to start writing a new approach to the same problem from scratch.

I can understand it would take a year for PhD thesis proposal. For master thesis, no way !

This answer might not be applicable to everyone; however, today I met with the Associate Director of Professional Programs at [tier-one university]. I was informed that barring extenuating circumstances, if a student doesn't have an accepted proposal and a Thesis Director assigned after a year then they should switch over to the capstone track to ensure they are able to successfully finish their degree.

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text:
Can leaked nude pictures damage one's academic career?
I have an ex who has posted nude photos of me online in the past, linked to my online social media, and posted my full name and where I live. I am concerned he may do so again once he finds out I'm now in a PhD program (he's very jealous of any success I have), and may link to my school bio page, or worse.
Revenge porn is illegal in my state, and the case against him is currently pending. I have also gotten the photos taken down with a DMCA letter (I hold the copyright over the photos in question). At this point, I am concerned with how a future attempt could affect my career.  I can handle the embarrassment now that I've been through it once, so if that's the biggest concern, I can deal. I just don't want to lose a career over it, given how small academia really is and how a reputation might follow one around.
My question is, if I don't change my name (I've considered this, assuming I can keep him from finding out) and my photos are circulated and discovered by faculty or students, how likely am I to be thrown out of my PhD program or later lose a job as an untenured prof? Is a name change worth it?
(If it makes any difference, they are essentially just topless portraits; I'm not engaged in any sexual activity or anything weird, and were taken 10 years ago when I was very young and foolish.)

Comments are not for extended discussion; this conversation has been moved to chat.

Unfortunately, the right to be forgotten has not been applied in the US yet. (Possibly stupid) suggestion: contact Google to ask them apply this rule to you, since they already have the algorithm to handle it.

@qsp Once you properly take it out of the passive voice, it sounds a lot less unfortunate that the Right To Force Others To Forget You hasn't found greater traction worldwide!

"how likely am I to be thrown out of my PhD program or later lose a job as an untenured prof?" - extremely unlikely - people with far more controversial pasts are not ejected from academia.

Please note that DMCA takedown requests are meant for copyright violations, which only applies here if you were also the one making said pictures. While it is definitely one of the most effective tools, if someone else (e.g. your ex) made the pictures, you have no legal basis for using it.

Yes, the pictures were taken by me and I hold the rights to them.

@qsp yet? What makes you think it will ever happen? "Right to be forgotten" is an utterly silly concept that makes no sense in practice. Its implementation is a mess in Europe. I don't see the US adopting it any time soon ... or ever.

@Jasper the photographer do not automatically get rights.  The photographed subject usually has first rights, and that needs to be signed off.  (A well known one would be the embrassed frat boys in Borat.)  The OP most likely did not sign any legal documents, the courts will side with her on a DCMA takedown.

@Nelson This may of course differ from one country to another, but in general, I believe the copyright lies with the one making the picture. A quick search on Google gives many sources supporting that this is the case in the U.S. while I know that this is the case in my place of residence (NL). The Borat case you talk about was about a lot of things (fraud, misrepresentation of a contract, etc) but not about copyright. That also goes to show that there's a lot more involved than just copyright when it comes to photos. However, DMCA only governs copyright...

INAL, but this screams at me libel. If he really is jealous of your success, and is taking these actions in order to "take you down", it's possible a libel suit regarding possession and distribution of these could be an option.

@Nelson In the US the photographer owns the copyright to pictures that they take, not the subjects. The subjects may have a right to privacy that could be used to prevent the distribution of the photo, but they don't own the copyright. A subject may also have personality rights (right of publicity) that could allow them to control the distribution of a photograph or dictate licensing terms, but again this is not copyright.

Ownership of the copyright is the US is affected by employment situation. A photographer working for herself own the copyright by default (but can sell it to the subject); if the photographer is doing "work for hire" than her employer owns the copyright (and if the subject is the employer ...). I can go down to the photography studios at a couple of department store in town today and get my family photographed and come out either with or without the copyright depending on who I see and how much I care to pay—one place gives me all the original files.

If you are fired or not hired due to nude photos, that could be grounds for wrongful dismissal or a discrimination suit. Obviously, a suit like that would likely damage your career even more than the photos though.

I think you can generally trust faculty to be adults when it comes to graduate admissions and a tenure track job.
The biggest problem I would see is when you teach (future undergraduate) students. I'm not sure how you would want to deal with them.
I would say that university administrators tend to be adversity shy and could be a problem.
I would instead look to see if a lawyer might help you DMCA the sites hosting the images as well as file either a legal complaint or restraining order against you ex.  This latter bit is best asked on Law Stack Exchange.
University registrars and faculty are used to students having to change their name due to a variety of circumstances. You should be able to get new transcripts and letters issued under your new name without issue. But the abuser can also link images to your new name unless you can prevent him or he loses interest; so a name change is not a foolproof solution.

Many of the students will have similar photos in existence from their younger, more foolish days.

I wouldn't worry about the students, unless you plan to become a very unpopular professor. One or two idiots might find it funny to show around any pictures, but i'm sure their fellow students will deal with them quite efficiently.

When you say the biggest problem would be students, do you mean the OP's peer PhD students, or the undergrads that the OP may eventually teach as a TA or professor? (I assume the latter, but it would be good to clarify.)

OP says they "can handle the embarrassment". I don't think students can pose other threats more significant than embarrassment.

@FedericoPoloni The OP shall be ready for "but you're the funny girl with small tits" comments when the teacher needs some authority. This is not just about public embarrassment, this is more about conflict handling. IMHO it is slightly different, but I agree that from the post, the OP seems ready for that this could happen.

@yo' I have honestly never understood the authority issue in the context of teaching, in Academia. There's no authority needed for any purpose: students may choose whether to attend or not, whether to be polite or not, whether to like you or not, whether to hand in the homeworks or not. The purpose of the teacher is by no means to discipline the students.

@GennaroTedesco While I agree on the fact that the students may choose whatever they wish, you are a teacher (like it or not) and you shall build authority if you want to lead a successful course. It's not like you're responsible for the students, but you're at least responsible for that the "good" students get what they eager for; for that you need authority (of all the hard-working, mediocre and poor/uninterested students).

@yo' I don't see how leading a successful course needs authority: on the other hand, I would say, if you do then you're most likely doing it wrong.

Without authority, you'd have students chatting, which disturbs other students. You need some authority to handle this. It could be simple "stop chatting or leave", but even for saying that you need some authority. Maybe we have a different idea of what this word means? I take it's very general meaning...

@yo' in a college setting it usually boils down to "you're an adult, and you know better". Plus, when it's really loud or disruptive I've seen fellow students tell someone "Shut up already would you two? You're disrupting the class.".

@FedericoPoloni Perhaps, though students could go home and tell their parents or others things like "my professor is a porn star" and they could complain/petition to people in administrative/regent positions to have her removed. While such attempts would hopefully not be successful, it could still cause quite a bit of headache that OP should ensure they are prepared for.

@TylerH - yes, that is what I meant about students being the problem and administrators being adversity/publicity shy.

http://www.askamanager.org/2012/11/when-your-online-reputation-takes-a-hit.html Some of this advice might also help you. I'm so sorry!

My question is, if I don't change my name (I've considered this,
  assuming I can keep him from finding out) and my photos are circulated
  and discovered by faculty or students, how likely am I to be thrown
  out of my PhD program or later lose a job as an untenured prof? Is a
  name change worth it?

On the main question, consider the answers and comments on your question as a sample of academic reaction to your situation. I see lots of sympathy, support, and attempts to think of ideas to help you. That is what I would expect from your department if your ex were to try anything while you are a PhD student or professor.
I don't think a name change would be effective in your situation. To continue your academic career you need to maintain some contact with your old life to get letters of recommendation, degree transcripts etc.
However, if you are going to do a name change it would be best done before you start writing papers. Even if you are willing to abandon all connections to your early papers, you will still be publicly part of a network of collaborators, and your ex might be able to guess your new name from co-authorship.
Your ex wants you to curl up and hide. Every day you spend living your own life, ignoring him, and succeeding at what you want to do is a victory for you and for everyone who thinks revenge porn is a contemptible betrayal of trust.

"On the main question, consider the answers and comments on your question as a sample of academic reaction to your situation. I see lots of sympathy, support, and attempts to think of ideas to help you."
This has made me feel a lot better. I certainly hope it is not an issue in the future, but it helps to know that as long as I can hold my head high (and hopefully be a good, respected professor, so that students don't make a big deal of it), I should be fine.

@P.Lombert Honestly, if someone gets creepish about it as a fellow coworker tell them it is unacceptable and deplorable behavior and if they continue to treat you in that manner that you will report them to human resources. There's a difference between people knowing about it and people harassing you about it, and the latter definitely shouldn't be allowed at your institution (I'd hope).

How likely am I to be thrown out of my PhD program?

Zero likelihood. You will not be thrown out.
You would not be violating any rules or regulations; and while a few people might - unjustly - form a poor opinion of your character, well, lots of academics form poor opinions on the character of lots of PhD candidates - usually for more valid reasons. Others have elaborated on this point more, I'd say it's pretty obvious.

How likely am I to ... later lose a job as an untenured prof?

Extremely unlikely.
You can't be fired for this reason, as, again, you've not done anything that merits being fired. As an untenured member of faculty your employment does, however, often depend on good relations with administration or senior faculty, and that in turn - with very low probability, mind you may be impacted by your nude photos incident, if people start gossiping about it.
Unless your job is at a super-religious super-conservative school, I really don't see it happening, and even at such a school its likely the effect would be not to want to give you tenure / promote you / socialize with you - at the worst.

Is a name change worth it?

No, it won't help and it may have a negative effect.
First, it's pretty easy for him to find you out - since he knows what you're doing in life, academically and until this time, geographically. It will probably not even be much of an effort (unless you avoid all social networks, all publicly-visible jobs including teaching, and so on).
Second, if anything, changing your name signals you believe you have done something wrong, something you're ashamed of. And you have not done any such thing! The only wrong was for him to publish the photos, not for any of you to take them.

they ... were taken 10 years ago when I was very young and foolish.

You were certainly not foolish for taking them. It's extremely common, especially these days. I would venture to make a two-bit psychological assertion and say that you should not conflate being ashamed of being seen topless by strangers with shame for having been the victim of your boyfriend's revenge. I would say the first kind of shame is wholly unnecessary - but that's a question of personal morals; what's definitely true is that the person who needs to be ashamed for the photos having been published is just your a*****e boyfriend, not you!

First, I'm sorry this happened and that you've had to learn to "get over the embarrassment", which you never should have had to do.
Second, I think you should consider just letting this go.  You said the photos are already down, so I assume they aren't the top search that comes up when you google your name?  And even if they are, that will fade over time.
The reality is that as long as they're "hidden" from casual searching, you've covered the vast majority of concerns.  If someone is really going to dig into your past, the sort of digging that might turn up old deleted photos, they might just as well turn up your name change too.  Especially since I imagine you'll need to link back to your old name for transcripts, if nothing else.
To address one comment I saw, I would absolutely not tell your department.  This was a crime against you, and isn't anyone's business.  If they find out about it on their own, I expect they'll treat it thusly.  It shouldn't be an unpleasant surprise to them, because this isn't about you.  The only ones who should be unpleasantly surprised to find this are your ex's future employers.
You can't control what others might do, but recognize that if they respond negatively to this sort of thing that it's an indictment against them, not you.

I would be extremely surprised if any faculty or faculty member would look down on you for this, possibly unless their religion is involved, although for some topless portraits, I still think it would be unlikely. Even if some old fuddy-duddy did secretly harbour a negative view of it, they would not want to openly dwell on it. Revenge porn scandals are well known to all, and are disgusting to all, certainly of professional age, but the disgust is at the poster, not the victim.
I really think if you have legal proceedings, you say photos are down, it is best to try to leave it alone, it is hard to see any other action not making it more likely that photos will be more of an embarassment for you.
One suggestion if the ex was to do it again, and you feel he will continue, which is definitely wholly dependant on many factors that only you might be able to gauge, is, as silly as it sounds - tell his mum ( or family, whatever). legal proceedings are hard with stuff like this, but in a lot of family dynamics, family disapproval can be extremely powerful, especially around such a horrible crime. Dangerous game though, obviously.
Really though, nobody is going to be against you on this, the media is full of this stuff constantly, some topless pics are very tame compared (I'm really not trying to play down your embarrassment, it is a very horrible thing). And academia, more than some fields, is not where you generally find the type that might mock you for it, maybe in wolf of wallstreet type environments.

Funny enough, he was living with his parents when this happened. The state police went to his parents house when everyone was home and took the family computer to run the scans. His mother is a very conservative, religious woman. I can only imagine when she said/did to him.

Well, that sounds great. This kind of act is the sort of thing that will hang over his head for the rest of his life, his family will never look at him in the same way, irrelevant of whether a conviction can ever be achieved. It's not the same as other wrong-doings like stealing etc, it is a real show of being a nasty person. And almost certainly, as it's known about, he wouldn't dare do it again, it would just be crazy.

Get on with your PhD, it's hard enough concentrating anyway. As everyone on here will know, it is really hard not to be distracted by stuff, especially this. Don't let him win, it's over. (I hope that's not patronising)

For your PhD program, the university rules should be pretty clear about what is serious enough to be chucked out.  Normally that needs something like a criminal conviction.  So it seems unlikely that you'd have problems there.
Similarly as a professor/lecturer, you'd be an employee.  At that point your employment contract will be relevant, and again you would need to be guilty of gross misconduct to be fired.  It could be an issue if the pics surface during the hiring process though, because it's very hard to prove why you haven't been asked back for a second interview.  Of course "at-will" employment is an issue, but most places would rather hold onto good people than train up someone unknown.
Thing is though, it's not like you're the first person this has happened to.  There's a laundry list of Hollywood A-listers who've had naked pics of themselves broadcast without their permission, never mind all the regular Joes and Janes who've been double-crossed by their exes.  And more intriguingly, the wife of the President-Elect of the USA once posed for a lesbian photoshoot for a well-known porn magazine, with pictures publicly available and not able to be taken down.
I've had a similar problem with my ex.  In her case, she posted stuff to my company's Facebook page.  My boss has enough class that his question was not "what are you up to?" but "please can you stop her doing this again?", because clearly it wasn't done with my consent!  Luckily I didn't have to get the cops involved.  And TBH, if the people you're working with are likely to be unprofessional about this, you really don't want to be working there anyway.

I must confess that I thought of Melania Trump when reading the question as well.  Two comments: (i) the OP didn't choose to have her photos shared, so in my view her actions are not just not "serious enough to be chucked" out -- rather she has done nothing wrong.  (ii) You characterize Trump as posing for "a lesbian photoshoot for a well-known porn magazine."  That seems a bit much.

(ii) You characterize Trump as posing for "a lesbian photoshoot for a well-known porn magazine."  That's simple fact.  That's what the photoshoot was, and it was a soft-porn magazine.  Exactly who touched what where, we'll never know, but that's what the photoshoot was purporting to show.

This is not very relevant to the site or the question, but the magazine in question would, when translated into American periodicals, lie somewhere between Maxim and Playboy.  The phrase "porn magazine" seems to connote magazines which primarily specialize in nudity and/or sexual content, so seems to give the wrong idea.  "Exactly who touched what where, we'll never know, but that's what the photoshoot was purporting to show." Again I think you're stretching to make this sound more extreme than it actually is, but since I for one don't care "who touched what where," I'll let it drop.

Frankly, we live in a time where no "misdeed" ever can be assumed to stay hidden forever; you can assume that there is simply a photograph of anything you do in your life; you can assume that anyone will be able to plant cameras or take drone photographs at any location and time, at a level that was previously only accessible to top specialists of the secret arts.
As therefore unsavoury exposures become increasingly more common, my estimate is that minor slips will therefore, in future, be of diminishing importance and offer less potential of threat.
My experience is that with the more boldness, chutzpah and/or indifference you would treat any confrontation of that kind, it sends a message that you are not influenced by that and that it's not an effective way for anyone to exert power over you. This is not a guarantee that it won't have an effect on a hiring committee, but, frankly, a hiring committee that is more worried about youthful misdeeds (if these should indeed be considered misdeeds) rather than the professional quality of a candidate is not worth its salt - and, as for students, you can remind them that you were one of them, once, too.

If this happened with one of my graduate students, I wouldn't care about the photos. I would care that someone with a personal grudge was harassing my research assistant, and I'd consider what might be done to see that the harassment stops. I think this view is shared by quite a few people in academia. We are concerned with the your contributions to research and teaching, and your personal life isn't our business for the most part.
However, indiscretions as minor as those you describe can and have damaged people's careers. So I think it is prudent to take reasonable steps to limit how these photos are connected with you. I would tread carefully with regard to acknowledging them at all, unless you know beyond any doubt that they are genuine unaltered photos and you are compelled to address them.
How you approach the issue has a lot of influence on how others will handle it. If you can manage to take it in stride and not let it affect your activities at the university, that will probably be noted and appreciated.
I think this is much less of an issue in a graduate program and in college teaching situations where we are all, ostensibly, adults. Unfortunately, all it takes is an administrator or person in a position of sufficient authority with the wrong attitude to make this difficult for you.

Most likely it will never come up in the first place, unless the ex re-posts them somehow.  I wouldn't mention them unless someone raises the issue first.

Good for you for defending yourself and being in a PhD program. I wish you great success.
I agree with the other posters that topless photos are unlikely to hurt your career, although I would add that you may have problems if you're at a religious institution. For example, topless photos could get you expelled from Liberty University, a Christian college run by Jerry Falwell's son. A professor was fired from Wheaton College after wearing a hijab in solidarity with Muslims, although the school claims it was for her views on Islam. According to this article, professors at religious colleges "have been fired or forced to resign for coming out as transgender, for getting pregnant outside marriage, or for getting divorced".
On the positive side, there might be sympathy for you as the victim of a crime from some religious colleges. Brigham Young University recently announced an amnesty policy for sexually assaulted students, who "will no longer face the possibility of punishment for honor code violations, such as drinking or extramarital sex."
To summarize, if you're at a secular university, you should be okay. (I assume you would have said so if you were at a religious university; correct me if I'm wrong.) You should think twice before becoming a faculty member at a university with religious requirements, although these vastly vary by denomination and geography.

Apparently, you were good on these photos. So, in private talks, do whatever you wish, but in PhD matters, it's none of their business. Nobody will ever dare say a word if you do proper research. If asked, you can be witty or not, depending on your skills ("Ha-ha, you were not that good 10 years ago!"), but do change the topic immediately ("Could we speak about the zeta-function?").
Other than that, try to pay as little attention as possible to these matters; they will only take your time and make you procrastinate.

If you were to go and work in a situation where security is concerned, this may effect your suitability for the position. This is not about the fact that you let the photos be taken or the content of the photos, it is about the fact the photos exist and that you wish to keep them private.
There is some risk that someone may pursued you to do things against the interest of security in exchange for them doing/not doing something with the photos. Depending on how high the security is for the position you wish to hold if this will effect you. In terms of academia, this will most likely effect what projects you can work on e.g. you will be unlikely able to get national security clearance so any law enforcement projects would be unlikely for you to work on.
ps although this is like @DVK's answer the reason behind the answer is different.

I downvoted this answer because I do not believe that anyone would be denied a security clearance because nude photos of them exist.

please look at https://news.clearancejobs.com/2010/02/16/sexual-behavior-and-security-clearances/ both "sexual behavior that causes an individual to be vulnerable to coercion, exploitation, or duress;" and
"sexual behavior of a public nature and/or that which reflects lack of discretion or judgment." would be classed here and these are both "Conditions that could raise a security concern and may be disqualifying"

From your link: "Of approx 1160 cases ... in 2009 only 36 cited “Sexual Behavior” as a security/suitability issue. Almost all of these 36 cases involved criminal conduct, and about half involved criminal convictions for sexual offenses. Involvement with prostitutes was cited in 4 cases, 5 cases cited possession of child pornography, and 15 cases cited sexual acts with children. The remaining cases involved voyeurism, exhibitionism, and compulsive, self-destructive viewing of pornography."

and "Most sexual misconduct is either not a potentially disqualifying condition for a security clearance or can be fully mitigated by “passage of time without recurrence” and the absence of any susceptibility to blackmail or coercion."

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Should a TA point out a professor's mistake while attending their lecture?
I faced the following situation a few days back. I am doing my teaching assistance work under a professor.
I attended one of his classes as a TA during which he was teaching some technically wrong stuff, which he assumed as true. Since most of the class were students of the course, they do not know which statements are correct and hence are not in position to rectify the professor's mistakes.
There are more than five other TAs but no one pointed out the problem. I don't know whether the TAs know what is correct.
I stayed silent and observed whether anyone would point out the mistake but the class ended without anyone realizing the professor's mistake. The reason for my silence is this question.
Is it offensive to the professor to point out such mistakes? My question boils down to: Is it proper etiquette to point out mistakes that a professor makes during their lecture?

Unfortunately, every answer here can be right and every answer here can be wrong. It depends entirely on the personality of the professor and your relationship. I urge caution in your position.

I dont understand this question. Are you afraid of some snappy retort, in case you are actually wrong, or do you think the prof will remember your name and give you a bad mark when you turn up for an oral exam in his office next year?

It might be helpful to elaborate on the nature of the mistake.  There is a huge range of things that a 'mistake' might be and how you react is highly dependent on the specifics. For example,  'technically wrong' (or not completely 100% accurate) statements can be essential in many intro classes because getting bogged down in the minute details can be harmful for the overall understanding of the topic for the average student in the class.  You don't want to be teaching intro calc and bring up a point that is only pertinent to people taking grad level analysis courses.

Are you absolutely, 100% positive, no questions asked, sure you are right and what the professor is teaching is incorrect? I ask this because what you are suggesting is that from among the set of (professor, 5+ TA's and class(es) of students) no one but you has caught the mistake. Are you sure?

Possibly relevant question over at [matheducators.se].

It depends on the type of mistake. All mistakes must get fixed to make sure the students don't learn anything wrong. However, how to best fix the mistake depends on the situation.
If it is a small mistake that can be fixed easily (e.g. a missing minus sign) I would recommend bringing it up on the spot. The 'cost' to the teacher and impact on the lecture is minimal but the benefit is potentially significant.
For more serious problems in a derivation/ argument like the one you described I think the cost benefit analysis often comes down in favor of waiting until the end of the lecture and informing the professor then. Then the professor can prepar a correction lecture explaining clearly what the mistake was and what the fix is. Trying to fix a mistake like the one you described on the fly can easily end up in a very chaotic lecture in which nothing is clear anymore and the students get very confused.
In general, don't worry too much about politeness and etiquette but more about what's best for the students. Your job is to be the best teacher!

I like this answer and upvoted, but I think "inform the professor" could be phrased better.  There's certainly a non-trivial chance here that OP was the one in the wrong, not the professor.

@NoahSnyder what is a trivial chance? Did you mean non-zero?

I was about to write something similar. Correcting an error in a sign is usually welcome as it is a mistake. Telling that the whole concept they are explaining is wrong requires caution: meet with him in private and ask this to be explained to you, this opens a good opportunity for discussion.

@KamiKaze: Sorry, “non-trivial” is mathematician-speak.  It means “moderately difficult” (in sentences like “that exercise is non-trivial”) or “moderately large” (in sentences like “there’s a non-trivial number of people who believe in ghosts”).  In the latter setting it’s suggesting a larger number than “non-zero” would.

@NoahSnyder This is the first time that I heard it is used for "moderatly large". I still don't really get it, because 0 would be the only trivial chance. Trivial in the sense of negligible. But still thank you for the explanation.

Since you're talking about the cost/benefit of waiting to bring a larger mistake to attention after class, I'd point out that the primary function of a course is the instruction of students. If the students learn something incorrectly, they will then begin studying it incorrectly. There could be a period of several days between the instruction and any possible 'correction lecture' during which the damage could be magnified.

There's "dangers" at both ends of the spectrum, one is you are wrong not the professor, and the other is that you look the fool for making a big deal out of something already obvious to everyone, perhaps even which was pointed out already when you weren't paying attention.

I  had a situation once in an English lesson where a teacher was trying to teach a concept of word derivation, but the word she used as an example did not exist and was an exception to the rule she applied. Because she did not notice the mistake and confidently continued explaining the concept using this word as an example, I felt the need to interrupt her by telling her that I believe it to be an exception. She assured me that it existed, so I asked her to check another source if I am wrong. She googled it on the projector, leading to many students disrespecting her. What did I do wrong?

@KamiKaze Non-trivial when used for chance would to me as a mathematician mean 40-80% depending on context. In this particular case I would read it as an intentional euphemism for more likely than not.When used about how hard something is it varies, but when said to a student it usually means "if you spend a month working on it there's a chance you will figure it out".

All mistakes must get fixed to make sure the students don't learn anything wrong. - Couldn't agree more. That's a moral and ethical obligation with very deep implications in fields such as health sciences and many others.

@TemporaryName: It's hard to say. It seems crazy to me that a single mistake led to "many students disrespecting her"; did the students not realize that everyone makes mistakes? (And for that matter, languages are not as hard-and-fast as we sometimes pretend. You haven't given details, but it wouldn't surprise me one bit if her example actually does exist in some dialects, and/or in older forms of the language, but isn't common enough in standard present-day English to appear in the source she checked. Perhaps she'd encountered the word in Shakespeare?)

@Kami Kaze: This is the first time that I heard it is used for "moderatly large --- I've sometimes seen this usage, but I think both in math and elsewhere the most common meaning is "not trivial", where "trivial" means small enough that it can usually be ignored or it isn't worth worrying about. So rather than "moderately large", nontrivial more likely means being large enough that it probably shouldn't be ignored. That said, I think the stronger notion of being moderately large is much more common in math than elsewhere.

@ruakh Admittedly, it must have been due to a series of mistakes that were pointed out (or at least noticed) by several students over a period of time. I still think that my initial remark sparked this trend and feel bad for it. The word she used IIRC was "thankness". I initially told her that she left out the "-ful" and when she began explaining to me that it is not needed because of the aforementioned rule, I told her that I do not believe "thankness" to be a word and she could check immediately or after class whether my assumption was wrong. Could be Shakespeare, you're right.

I spotted an error with a professor's example and, having checked and confirmed my work over the weekend. I went to his office the next week with the example and showed him. He was happy with the correct example.
My surprise was that he presented the corrected example clearly stating I had sorted it to the whole class - nearly fell off my chair!
So, go for it and be polite. Any good professor will be pleased.

You know your professor better than we do, but I have only experienced professors who were thankful when their mistakes were pointed out (also by TAs).
It's not bad etiquette:

it helps everyone involved to learn something new.
you point out the mistake in a friendly and factual manner, so they can save their face.

Everyone makes mistakes and can err, even a professor. It's not embarrassing, but a wrong reaction might be. But my respect for someone being glad about their mistakes being corrected always just grew. This especially shows that they care about teaching their students.

I asked in general because I can be a ta for a professor with whom I'm not familiar...

I like this, but it is a best-case scenario.  Unfortunately, not all instrucors feel this way.

I'd say it depends on both the lecturer and the mistake. In some circumstances it could possibly come off as the TA trying to look smarter than the lecturer, which would not be advisable. Telling the lecturer afterwards generally will have the effect of giving the lecturer a chance to rectify his mistake the next lecture without losing face. But, as I said, it depends on circumstances. A relaxed,  senior lecturer may welcome the mistake being pointed out in lecture, but they will probably say as much if told about it after the lecture (or they may say: thanks for not saying anything till now!)

Check with the professor outside of class time; find out what their preferences are. They may want all corrections publicly and immediately, or all corrections privately and later, or they may ask you to make a judgement call as in @user2705196's answer ("how important is this correction? can it easily be fixed on the fly?"). Make sure to be diplomatic, qualifying your comments by saying that you might be mistaken (even if you're pretty sure you're right).

you might actually be mistaken (consider double-checking your concerns with some of the other TAs before going to the instructor)
this might be a low-level course where the instructor has decided to sacrifice some technical correctness for the sake of clarity
maybe the instructor would rather not interrupt the flow of class/would rather correct mistakes later or in a different venue (e.g. posting corrections on the class web site); this presents obvious problems with students spending more time being confused, or absorbing incorrect material before seeing the corrections, but it's the instructor's decision about how to run the class.
maybe the instructor is an insecure jerk and doesn't want to be corrected at all, unlike many of the site members who have commented or answered here saying they'd always want to be corrected. In that case you should do whatever you can to fix the problems in a separate channel (e.g. in lab or tutorial sections); you can even (quietly!) organize your fellow TAs so that you're all presenting the corrections (as in @mkennedy's answer). You should still be diplomatic (and make sure that you don't mess the students up, e.g. make sure that they know what the "correct" answers will be for testing purposes)

Yes, it’s usually good to point it out, but be polite and careful about how you do so.
Some good ways to point something out:

“Should that f(x) in the last equation be f(y)?”
“For the third step, should we be assuming that the marginal cost is positive?” [when your suspected mistake is a missing assumption]
“I’m confused; you said that ZFC is a complete theory, but I thought that because of Gödel’s incompleteness theorem we believe it’s not complete.  Am I misunderstanding something?”

Some important general principles to bear in mind:

Make sure you don’t embarrass the lecturer.  So, phrase it as to suggest the mistake was more like a typo or oversight, or your own possible misunderstanding, not their stupidity or ignorance.
Make sure you don’t embarrass yourself, if it turns out you’re wrong. So always phrase it with some uncertainty/questioning, never as a bald un-hedged statement.
If the lecturer doesn’t agree about the mistake, leave further discussion until after the class.  Arguing it out in class will embarrass at least one of you, and waste everyone’s time.
Minimise the disruption to the lecture.  Try to phrase it clearly and concisely, and give it at a good moment — soon enough that it’s still fresh in everyone’s mind, but wait a little for a “paragraph break” if necessary rather than interrupting the flow.
If you’ve previously corrected mistakes and the lecturer accepted them but seemed annoyed, check with them before doing so further.  They may feel that e.g. you’re nitpicking unnecessarily about unimportant details, in a way that’s not worth the time or disruption.  Whether they’re right or wrong, that’s a pedagogical judgement call that you should probably respect.
In the end, remember that the buck stops with the lecturer, not with you.  A good lecturer should gracefully and gratefully accept useful corrections.  If they don’t, and mistakes recur, then you won’t be able to single-handedly rescue their lecture course, and trying will probably make things more confusing for students, not better.  So accept that you can’t fix this course, file it away as a useful lesson for your own future teaching, and (if the mistakes are really serious) discuss it with some other experienced faculty member(s) to see if it’s possibly worth reporting.

This so depends on the personality of the professor and is not really about etiquette but rather about personal relations.
At one postgraduate pure mathematics class I attended in Cambridge, the lecturer wrote down a theorem and one of the students immediately said out loud 'that theorem cannot be true: consider the counter-example of...'. To most of us, it seemed he had a good point.
That lecturer, a Fellow of the Royal Society, and noted for self-possession, was able to explain kindly why the supposed counter-example was not relevant — something that was far from obvious. But I can readily imagine that a less self-confident professor, not good at thinking on their feet, would have been thrown by such an intervention. Not all professors have complete mastery of the subjects that they are teaching.

I think it is generally more allowable for students than TAs, though it depends on whether the class was set up as a lecture or a seminar.

The fact that the lecturer took it in stride does not mean the remark was not rude.  However, as someone who's attended a lot of math classes, I would more likely put my money on Asperger's than rudeness on the part of the student.

@MatthewLeingang Were you there? You must have been! That is precisely the correct diagnosis. Nevertheless, I know some lecturers who could not have coped with such an intervention.

@JeremyC Like I said, I've been in the research math world a long time and have witnessed a lot of students such as you describe.

Ask a non-assertive question rather than pointing out errors
I agree with user2705196's answer, but will refine it a bit:
When relevant Instead of saying something like

Professor, I think you were wrong to state that X, it's actually Y because Z.

try:

Professor, can you elaborate a bit on how X agrees with Z?

this way - if you got it wrong, they'll explain it (and it would still help other students, who might have the same misconception as you); and if you got it right, there's a good chance the response would be "Oh, Z? It should be Y, sorry" - and then the Professor has corrected his/herself.

My practice was to always point out a mistake (politely) and I prefer my TA or students to call me out. I am only human.
However, I know some faculty could take that the wrong way. If you are working with a professor who you think might not react well to being called out in front of the class, then try pointing out an error or outdated information after class (in private).

Good point. For any professors out there, I recommend mentioning to the TAs something to the effect of "If I make a mistake, go ahead and bring it up right then" if you'd like that to occur; if not, say you've got a system you prefer, obviously don't do that, but my point is that communication is key for this kind of thing, and you want your subordinates to know exactly how to handle such a discrepancy, rather than, say, post a thread about you on Academia.SE :)

I recommend not pointing out the error during class time.  I would follow up with the professor in the privacy of their office.  No one wants to look stupid but everyone makes mistakes.  I would have all of your supporting evidence in hand and then ask about it in a private situation. If the instructor was indeed mistaken this will allow them to offer a retraction and correction in the next class period.

I would +1 you if you dropped the last sentence. I mean, you would gain the Professor's favor, but that's not the appropriate motivation IMO.

Step 1: Do not assume that you are correct. Approach the situation with humility, not assertiveness.

First, review the lecture and notes and try your hardest to figure out why the professor presented what they did. Ask other TAs to better explain the misunderstood portion. Do not claim that the professor said something wrong but rather present your confusion.
IF you cannot justify the professor's explanation then approach the professor and ask them to lead you through the explanation according to your notes. The hope is that they see their mistake and will say "Are you sure I said that during lecture?" to which you can reply "Yes, I am certain but I did not want to detract from the lesson at hand."

I've had both. In one case I proposed a 3rd option that was within the rules he put forth and it worked, and in one case I approached after the class and discussed my confusion/questions.
In the former even though I had proof of something (I'd worked it out because, you know, thinking outside of the box) I was unable to get him to acknowledge it. It was unfortunate, because mine was creative AND 'cheaper' to implement.
In the latter, the professor listened, stared at the drawing, laughed, and said "In the 15 years I've been teaching this class, no one has pointed that out. You're right- it's wrong".
So...
I would never consider pointing out something in class as there may have been liberties taken with the example/material to make it simpler to present. An after class discussion is most useful. And showing that you have strong interest in the topic for further diving, assuming said Prof is devotee of the material, will lessen any negative impacts of 'nit-picking'.
However you may still have a Prof that is a complete and utter .... pr*ck. It happens. In that case, just let it go. And you may have to determine what you want to do on an examination where the correct answer is what you know and the correct answer is what he knows... and they don't agree. .... but you didn't ask that ;P

Indeed an embarrassing situation and public rectification must be avoided, at least in environments where discussion is not a part of the game. This is my experience.
Talk to the teacher and s/he will fix that.

As a student, when I believe the professor has made a mistake (big or small) I always frame it as a question. Like if I see the professor accidentally left out a minus sign, I will just politely ask why the minus sign went away from that term.
Often times the professor did make a mistake, but often times they didn't as well and I accidentally missed a step that they did. This saves the potential embarrassment of trying to correct the professor and being wrong, as well as being a learning opportunity if I missed something.
Keep in mind the possibility that the professor was not wrong and that you missed something.
I imagine you could do the same as a TA. Since it's after the fact now, I would ask during office hours.

I was a TA for class being given by a respected visiting professor. I attended the lectures because it was my first time being a TA for this class and I'd only gotten a B when I'd taken it the previous year!
He made mistakes, generally a few each lecture. Sometimes I would ask a question about it and he would fix it. Sometimes I would get a friend of mine to ask. I kept very complete notes and would hand out errata/corrections in lab every week.

The TA shouldn't correct the instructor during the lecture. It undermines the instructor's authority and distracts the students.
Write down the mistakes and let the instructor know afterwards. The instructor can then choose to remedy this by sending an email to the class, correcting himself in the next lecture, etc. He will also have the option of asking you to correct him during the lecture next time, if he is fine with that. On the other hand, from his tone you may discover that he is uninterested in the corrections to begin with - a discovery better made in private than in front of a class.

"Undermining authority" is a poor argument for being silent about mistakes.

@einpoklum I think more careful reading of my answer will reveal that I do not advocate being silent about mistakes, but rather taking care in when and how the mistakes are discussed.

Ok. Well, "undermining authority" is a poor argument also for being temporarily silent about mistakes.

In my classes, there was a culture of "don't cause the professors embarrassment". The best way to avoid this was to, after class or in an e-mail, ask the professor:
"Hey, so the you were talking about x being y way, but I read somewhere else that x was z-way. Could you please clarify this with me?"
Since you're a TA, that should mean that you have ample time, even face-to-face, to talk to your professor about that.
Asking in the middle of class interrupts the flow of the class, however asking the professor separately, then them correcting it at the beginning of their next class allows them to let it flow a little bit better.

Tell him after class.  There will be some profs that don't care but others who would be annoyed with an in class interjection.  This is a simple safe default.
And it's not just about putting the prof on the spot but that lecture is a sort of participatory conversation between the students and lecturing prof.  You are interjecting yourself into that dynamic.  Again, some won't care...but a few would prefer that students either rise to correct (or not).  In addition, in the case that you're mistaken, it will definitely be derailing for the class in a way that a mistaken correction by a student (the real participant/recipient of the lecture) would not.


text:
Applying for PHD programs in FLORIDA. I have a question about legal questions?
On an application form for PhD programs in Florida, they ask:

"Have you recieved disciplinary action?"
"Have you ever been arrested for, been convicted of, or entered a plea of "guilty" or "nolo contendre" (No contest) to a crime (excluding traffic offenses not involving death or serious bodily injury), or been adjudicated or required to register as a sex offender?

My friend that is asking was arrested for DUI (driving under the influence) with serious body injury. She is not sure if that is a Traffic Offense or a Criminal Offense.
Has anyone else experienced, or have good information pertaining to this question?

A traffic offense would typically be something that resulted in a ticket (e.g. speeding) that you pay or, perhaps, go to traffic court. A DUI is decidedly a criminal offense that you can be prosecuted for in real (non-traffic) court.

Thats what where were thinking aswell. Thank you for the valuable comment.

The exclusion is strictly limited to offenses not involving death or serious bodily injury... Clearly your friend cannot use the exclusion, and therefore must report that arrest on the application.

@JonCuster Can you please turn this comment into an answer?

The answer to the question depends upon the specific state/jurisdiction  where your friend was arrested.

A traffic offense would typically be something that resulted in a ticket (e.g. speeding) that you pay or, perhaps, go to traffic court. A DUI is decidedly a criminal offense that you can be prosecuted for in real (non-traffic) court.
As an aside, when you have a security clearance you absolutely must report arrests, but usually they will also explicitly mention a dollar value for traffic tickets, above which you must also report.
Good luck to your friend. They will need to be able to clearly explain the situation and the resolution.

Believe it or not in Florida a DUI is a traffic offense. A very serious one that can carry jail time but still a traffic offense but your friend has the bodily injury component that will change facts as it clearly states bodily injury. Report.

While I can understand at some level that a DUI is a traffic offense (its driving after all), I strongly suspect that that is not the intent of the question, though - the arrest for DUI (with bodily injury) is rather different from getting a ticket for 5 over in a 30 zone...

As another counter example to "DUI is decidedly a criminal offense" is Wisconsin. The first OWI is (sadly) not a criminal offense. It's only a civil traffic violation.

I'd check whether it was even legal to require this information (maybe it is, I don't know US law); in many states in the world it is illegal to require this information from people in a government-regulated organization except when strictly necessary.
If you can't get around it, tell your friend she can say "no". At worst she can claim to have made an honest mistake and you could take responsibility for having given her incorrect advice (to get her off the hook at her school).