Does mathematical model for conccurent computations exist? Turing machines can represent any computation. Can they also represent concurrent computations? Eg. multiple computations that can happen at the same time?

If yes, how are the concurrent computations represented and is it possible to convert them into turing machine?

And do they mathematically describe things like race condition and deadlocks?
As already suggested above, process algebra or process calculus is the place to start. Quoting freely from the respective Wikipedia page,


  History
  
  In the first half of the 20th century, various formalisms were
  proposed to capture the informal concept of a computable function,
  with μ-recursive functions, Turing Machines and the lambda calculus
  possibly being the best-known examples today. The surprising fact that
  they are essentially equivalent, in the sense that they are all
  encodable into each other, supports the Church-Turing thesis. Another
  shared feature is more rarely commented on: they all are most readily
  understood as models of sequential computation. The subsequent
  consolidation of computer science required a more subtle formulation
  of the notion of computation, in particular explicit representations
  of concurrency and communication. Models of concurrency such as the
  process calculi, Petri nets in 1962, and the Actor model in 1973
  emerged from this line of enquiry.
  
  Research on process calculi began in earnest with Robin Milner's
  seminal work on the Calculus of Communicating Systems (CCS) during the
  period from 1973 to 1980. C.A.R. Hoare's Communicating Sequential
  Processes (CSP) first appeared in 1978, and was subsequently developed
  into a full-fledged process calculus during the early 1980s. There was
  much cross-fertilization of ideas between CCS and CSP as they
  developed. In 1982 Jan Bergstra and Jan Willem Klop began work on what
  came to be known as the Algebra of Communicating Processes (ACP), and
  introduced the term process algebra to describe their work.1 CCS,
  CSP, and ACP constitute the three major branches of the process
  calculi family: the majority of the other process calculi can trace
  their roots to one of these three calculi.