DIAMANT
Day 2 (Wednesday 23 April) @ 13:30–15:00
Pieter Belmans (Utrecht University)
Algorithms for quivers and quiver moduli
The word quiver is nothing but a shorthand for a directed multigraph. In representation theory we study all the different ways of assigning vector spaces to the vertices and linear maps to the edges, and call them representations. This allows us to encode many interesting problems in linear algebra, and obtain great results in noncommutative algebra. Usually the classification of these different assignments involves continuous parameters, which an algebraic geometer organizes into moduli spaces, called quiver moduli. Their geometry reflects properties of the classification of representations.
Many questions about the representation theory of quivers and the algebraic geometry of quiver moduli can be reduced to explicit problems involving bilinear forms. I will give a gentle introduction to quiver representations, and discuss some of these algorithmic approaches to a priori hard questions, illustrating them using software.
Matthew Kwan (IST Austria)
Exponentially many graphs are determined by their spectrum
As a discrete analogue of Kac’s celebrated question on “hearing the shape of a drum”, and towards a practical graph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by their spectrum (of their adjacency matrix). In this talk I’ll introduce the topic and briefly discuss some joint work with Ilya Koval.
