**Speaker: **Antonio Díaz (Universidad de Málaga)**Title:** Fusion systems for profinite groups**Place:** Room Seminar C3b**Date:** Friday March 29, 10h-11h

**Abstract:** For both finite groups and compact Lie groups, there exist algebraic structures that encode their fusion patterns as well as their classifying spaces at a given prime. In this talk, I will introduce similar ideas for profinite groups and, in particular, for compact p-adic analytic groups. In particular, we will study classifying spaces and stable elements theorem for continuous cohomology. We will provide some concrete continuous cohomology computations. This is an ongoing joint work with O. Garaialde, N. Mazza and S. Park.

**Speaker: **Jesper Moller (University of Copenhagen)**Title:** Counting p-singular elements in finite groups of Lie type**Place:** Room Seminar C3b**Date:** Friday January 25, 12h-13h

**Abstract**: Let $G$ be a finite group and $p$ a prime number. We say that an element of $G$ is $p$-singular of its order is a power of $p$. Let $G_p$ be the {\em set\/} of $p$-singular elements in $G$, i.e. the union of the Sylow $p$-subgroups of $G$. In 1907, or even earlier, Frobenius proved that $|G|_p \mid |G_p|$: The number of $p$-singular elements in $G$ is divisible by the $p$-part of the order of $G$. The number of $p$-singular elements in a symmetric group is known. In this talk we discuss the number of $p$-singular elements in a finite (untwisted) group of Lie type in characteristic $p$.

The situation in the cross-characteristic case will maybe also be considered.

**Speaker:**Letterio Gatto (Politecnico di Torino)

**Title:**Hasse-Schmidt Derivations on Exterior Algebras and how to use them

**Place:**Room Seminar C3b

**Date:**Friday January 18, 12h-13h

Abstract: In the year 1937, Hasse & Schmidt introduced the so-called higher derivations in Commutative Algebra, to generalize the notion of Taylor polynomial to positive characteristic. Exactly the same definition can be phrased in the context of exterior algebras, by replacing the ordinary associative commutative multiplication by the wedge product. Hasse-Schmidt derivations on exterior algebras embody a surprisingly rich theory that candidates itself to propose a unified framework for a number of theories otherwise considered distincts, such as, e.g., (quantum, equivariant) Schubert Calculus for complex Grassmannians. In the talk we shall focus on one of the simplest but most powerful tools of the theory, the integration by parts formula. It will enable us to guess the shape of the vertex operators arising in the representation theory of certain infinite dimensional Lie algebras. In spite of the fancy vocabulary used in the abstract, the talk shall be entirely self-contained and no special prerequisite, but elementary multi-linear algebra, will be required.