ICTP Algebraic Geometry Seminar - Wednesday, 8 March, at 14:00 (Martin Mereb)

[ICTP Math Section]

I C T P  A L G E B R A I C  G E O M E T R Y   S E M I N A R

Wednesday, 8 March, at 14:00

Venue: Leonardo Building - Luigi Stasi Seminar Room



Speaker: Martin Mereb (University of Buenos Aires)

/Please note: the seminar talk will be split in 2 parts/

Part I
Title 1: Character tables, enumerative problems of finite groups and 
polynomial count varieties.

Abstract 1: The study of finite groups often involves examining the 
traces of their irreducible representations, also known as characters. 
In fact, a character table of a group G may be found before the group 
itself is proven to exist. Characters possess many important properties, 
one of which is serving as a basis for functions that are invariant 
under conjugacy classes. In this talk, we will demonstrate how this 
property can be used to derive explicit formulas for counting solutions 
to certain equations within G. Furthermore, time permitting, we will 
explore how these formulas can be applied to compute geometric 
invariants of certain varieties. This talk is particularly relevant to 
students planning to take a course in representation theory.

Part II
Title 2:   Representations of Yokonuma-Hecke algebras and E-polynomials 
of wild Character Varieties

Abstract 2: Counting the number of points on a variety over finite 
fields allows us to deduce its E-polynomial in some cases. One 
application of this approach is in studying Character Varieties, which 
has yielded successful results. Calculating E-polynomials of wild 
character varieties by point-counting methods over finite fields 
involves closed formulas for certain columns of the character table of 
Hecke algebras of finite groups of Lie type studied by Yokonuma. These 
algebras can be studied through deformations of group algebras that 
simplify the computations. This is a work in progress in collaboration 
with Emiliano Liwski.

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela