The usefulness of algebraic structures

Title

The usefulness of algebraic structures

Speaker

Prof. Maria Julia Redondo (GTIIT, Universidad Nacional del Sur and CONICET)

Time and Location

Jun. 12, 2023, Monday, 19:00-20:00, E509 (Education Building, 5th floor)

Pizza will be provided after the seminar

Abstract

In this talk I will consider several examples that can be easily solved if the sets considered are endowed with an appropriate algebraic structure. For instance, we will find a closed form formula for the sequence of numbers in a Fibonacci sequence.

Given an equivalence relation on A, we know that, under some conditions, the quotient set inherits the algebraic structure from A. I will introduce the notion of higher structures that will allow us to lift structures from the quotient set onto A.

Biography

María Julia Redondo is a Professor at Departamento de Matemática, Universidad Nacional del Sur (Bahía Blanca, Argentina) and a Researcher at CONICET. She received her Ph.D. in Mathematics from Universidad de Buenos Aires in 1991 for her work in cyclic homology of hypersurfaces under the supervision of Dr. Orlando Villamayor, and her main contributions in this area were done during her participation in the BACH group (Buenos Aires Cyclic Homology). She has supervised two Ph.D. thesis and is currently supervising other two graduate students. Her research project focuses on the representation theory of finite dimensional algebras. She has been using topological and homological methods, mainly Hochschild cohomology, in order to study finite dimensional algebras and their module category. The aim is to find invariants to classify algebras taking into account certain properties. In order to get better insights into the many difficult open questions on these invariants, there is a constant need for actual computations. Although usually very difficult, several calculations have successfully been carried out by Redondo for many algebras given by quivers and relations. Besides obtaining new explicit results, she has been using different approaches. This explicit computations allow her to describe, in some particular cases, the algebra structure of the Hochschild cohomology.