Valentina Grazian, University of Padova
Exotic fusion systems
Abstract: Fusion systems
made their first appearance in a 2006 paper by Puig and have since
then been investigated by many researchers around the world. A
fusion system is a structure that encodes the properties of
conjugation between p-subgroups of a group, for p any prime
number. Given a finite group G, it is always possible to define
the saturated fusion system realized by G on one of its Sylow
p-subgroups S: this is the category where the objects are the
subgroups of S and the morphisms are the restrictions of
conjugation maps induced by the elements of G. However, not all
saturated fusion systems can be realized in this way: when this is
the case, we say that the fusion system is exotic. An important
research direction involves the study of the behavior of exotic
fusion systems (in particular at odd primes).
In this talk we will present an overview of recent results
concerning the classification of saturated fusion systems on
certain families of finite p-groups, highlighting the developments
on the understanding of exotic fusion systems at odd primes.
Jerzy Weyman - Jagiellonian University
ADE
correspondence for finite free resolutions.
Abstract: I will discuss
recent results joint with Lorenzo Guerrieri and Xianglong Ni on
finite free resolutions over local rings. The main result is the
classification of perfect ideals of codimension 3 in the linkage
class of a complete intersection (licci ideals).
The proofs are based on a connection of the problem to root
systems of type T_{p,q,r}.
In particular one proves that if T_{p,q,r} is a graph of type ADE
then every perfect ideal with the resolution of corresponding
format is licci.