Two 4-year PhD studentships starting in October 2013 or earlier are available in connection with the ERC grant “Extremal Combinatorics” at the University of Warwick.
What is Extremal Combinatorics?
A typical problem of Extremal Combinatorics is to maximise or minimise a certain parameter given some combinatorial restrictions. The structures that we consider are usually graphs and set systems but they may also be, for example, sets of integers or faces of a polytope. This area experienced a remarkable growth in the last few decades, having a wide range of applications (in number theory, algebra, geometry, logic, information theory, theoretical computer science, etc).
A very recent and actively developing area is graph limits. Roughly, the idea here is to approximate a large graph G by some object W. Now we can deal with W alone (in some sense, we take the “limit” as the number of vertices of G tends to infinity). Remarkably, the set of possible “graph limits” W can be described in many ways: using two-variable measurable functions, random infinite graphs and so-called flag algebras. This gives a general way to apply tools from analysis, ergodic theory and semi-definite programming to finite graphs.
Awards available: 2 awards available
Funding Details:Â Fees and maintenance at the RCUK level
Length of Award: 4 years (PhD)
Eligibility: Due to funding restrictions, available to Home (UK & EU) & Overseas students
Application Details: Apply directly through the PG Admissions system (note reference number)
Further details can be found on the following webpage: http://homepages.warwick.ac.uk/~maskat/studentship.html
Deadline: Â 1st October 2013 (to start in October 2013)Â