Time: 16:15-17:45

Location: Mondi 2

Speaker 1: Anna Sisak (Hausel group)
Title: Fourier transforms in geometry

Abstract: Inspired by the classical Fourier transform acting on functions, Mukai, in 1981, introduced a functor which roughly maps coherent sheaves on an abelian variety to those on the dual abelian variety. In my talk, I will show through examples how the Fourier-Mukai transform acts on simple coherent sheaves and explain how this can lead us to an extension of Mukai's theory to real tori.

Speaker 2: Gianluca Tasinato (Wagner group)
Title: Hidden topology in promise graph colourings

Abstract: It is well-known that finding a 3-colouring of a given graph that is promised to be 3-colourable is NP-complete. One might be interested in a relaxed version of this problem, e.g., finding a colouring of a 3-colourable graph that uses $k$ colours for a fixed $k > 3$. Under which conditions on $k$ does this problem become tractable? While this question has been around since the 70's, and many people agree on what the answer should be, there is surprisingly little known to this day.

This question falls into the more general class of promise graph colouring problems and in my talk, I will outline how and why (equivariant) topology can be a powerful tool to study them.