Abstract: A point process on $\mathbb{R}^d$ is a random discrete (hence countable) subset. The most well-known example of a point process is the Poisson process which is characterized by complete independence of what happens in disjoint regions of the space. A determinantal point process is different, in that there is inbuilt repulsion between points. Surprisingly many naturally occurring point processes turn out to be determinantal. Examples are eigenvalues of various models of random matrices, uniform spanning trees of a graph, zeros of certain random analytic functions, non-interesecting random walks, etc. This talk will give a brief introduction to determinantal processes.
Pre-requisites: Knowledge of Poisson process will be helpful but not necessary. The talk will be aimed at the level of B.Stat 2nd or 3rd year.
Abstract: Impartial games are where two players alternate moves, and the same set of moves is available to both the players. Typically the player able to move last wins. These are useful things to know when you sit in the back row during a boring lecture. We shall learn about such games (and the some of the math underlying it) by actually playing the games. You’ll get to know about exciting games that you have not possibly heard about before!