Hi, I’m Liam, one of the lecturers here at the University of South Wales. I studied my undergraduate degree here from 2008 to 2011 (back when we were called Glamorgan University). Having greatly enjoyed my undergraduate experience, I stayed on to do a PhD in Combinatorics and I have been a part-time lecturer here since 2014.
My research is in the area of enumerative Combinatorics, mostly elementary work involving position chess problems. When most people hear the phrase chess problem the first thing that comes to mind are the checkmate in X moves problems and other similar problems to do with actual game states of chess. Positional chess problems are a little more abstract than that, they do not even have to be proposed for the standard 8 by 8 chessboard!
Let me give you an example. First, you need to know that two chess pieces are considered independent if neither piece can move to each other's position in a single move. This leads to the independence problem that asks, for a certain chess piece on a given board, what is the maximum number of copies of the piece that can be placed on the board such that all pieces are independent of one another (an independent placement). This maximum value is known as the independence number and is the solution to the independence problem. If we generalise the 8 by 8 chessboard to an m by n chessboard then the solution to the independence problem, for a give chess piece, is a function of m and n. Finding that function and proving the result always gives the solution (so in this case the maximum value) is the essence of solving a positional chess problem.