# The boson-fermion correspondence on (asymmetric) ice

**Date**: Monday 9 December 2019, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Integrable Systems, Algebra, Geometry, Seminars, Applied Mathematics, Seminars, Pure Mathematics, Colloquium, Algebra, Geometry and Integrable Systems**Cost**: Free

#### Dr Christian Korff, University of Glasgow. Part of the Algebra, Geometry and Integrable Systems Colloquium.

The boson-fermion correspondence is an important map which plays a key role in representation theory (for example finite dimn’l modules of the symmetric group) and classical integrable systems (the KP hierarchy). In my talk I will show that its extension to the Hecke algebra connects it also to the asymmetric six-vertex model in statistical mechanics which describes ice and other ferroelectrics. Time permitting we will discuss the boson-fermion correspondence also for the cylinder and show that this leads to the definition of an infinite-dimensional coalgebra in the Grothendieck ring of the Hecke algebra whose structure constants are the Gromov-Witten invariants of Grassmannians.