Abstract:
In this two part seminar, I will give a short introduction to Berezin calculus. In brief, Berezin calculus (otherwise known as superanalysis or Grassmann analysis), is an extension of ordinary calculus to functions of anti-commuting variables. The utility of Berezin calculus is that it allows us to rigorously define spaces which behave like manifolds, but in some sense have "negative dimension". Although this appears to be a rather odd idea (pun intended), a deeper inspection will reveal that several strange coincidences in ordinary mathematics actually originate from this supermathematical world. As an application, we will discuss spin systems with target spaces given by supermanifolds, and explain how we can use these to study ordinary problems in combinatorics and probability.
Biography:
Andrew is currently a Faculty Fellow of Mathematics at NYU Shanghai, having joined the department in 2020. Prior to this, he completed his PhD at the University of Cambridge, and his MSc at the University of Sydney.
His research lies at the boundary between probability theory and mathematical physics, and explores how tools from one field can be used to solve problems arising in the other. His recent work is centred around a research programme that aims to understand how and why non-Markovian random walks are connected to classical lattice spin systems, particularly those with supersymmetry. Outside of this, he has interests in random matrix theory, statistical mechanics, and supermathematics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai