Counting coloured 3d partitions using Jacobi algebrasOberseminar Darstellungstheorie

by Ben Davison (University of Edinburgh)

Friday May 16, 2025, 3:30 PM → 4:30 PM Europe/Berlin

Endenicher Allee 60/room 1.008 (Mathezentrum)

A partition of a positive integer n can be visualised as a Young diagram: a configuration of n 2d boxes lying in the corner of the page.  The count of partitions of natural numbers are encoded in Euler's partition function; this is the formal power series in t, having as its t^n coefficient the number of partitions of n.  As well as having an elegant infinite product presentation, this partition function is related to the cohomology of Hilb_n(C^2).  This is the space of colength n ideals in the polynomial algebra in two generators, which is an important module in geometric representation theory.