Programa de doctorado que propone la actividad

• Matemáticas y Estadística

Persona de contacto

Nombre y apellidos: Montserrat Casals Ruiz

• Teléfono: 94 601 5296
• Email: montserrat.casals@ehu.eus

Breve descripción de la actividad

Advanced course on Representations of group algebras into division rings andapplications.

The course includes 21,5 hours of lectures and 7,5 hours of problem sessions. The course is given by Andrei Jaikin Zapirain and Sam Hughes and the problem sessions are led by Pablo Sánchez Peralta.

See the website: https://sites.google.com/site/gtabilbao/conferences-workshops/representations-of-group-algebras-into-division-rings-and-applications?authuser=0

Abstract:

We describe the theory of representations of the group algebra KG over a field K into division rings, as developed by Cohn and Malcomson. We show how this theory relates to ordinary and mod-p L2-Betti numbers when G is torsion-free, and we discuss several recent applications.

Further, we will survey the theory of l^2-homology. More specifically, we will look at some of the formulations of the homology groups (via l^2-chains, via von Neumann algebras, and in a more restricted setting via skew fields).  We will highlight some recent applications of the homology groups and we will demonstrate a number of methods for computing them.

Ponentes (incluir breve curriculum de las/los ponentes)

Andrei Jaikin

Is a full professor in the Department of Mathematics at the Autonomous University of Madrid and a member of the Institute of Mathematics.

He completed his undergraduate studies in 1995 at the Faculty of Mechanics and Mathematics at Moscow State University and earned his Ph.D. in 2001 at the University of the Basque Country.

Andrei Jaikin's mathematical interests have evolved from studying group-theoretical problems concerning finite and profinite groups to exploring the interactions between group theory and other areas of mathematics, such as topology and number theory. His work is characterized by the significant use of ring-theoretical methods.

He has more than50 research articles and preprints, some of them published in the most prestigious journals such as Annals of Mathematics. From 2010 to 2016, Jaikin served as an editor for the Journal of Group Theory and is currently an editor for RevistaMatemáticaIberoamericana and the Journal of Algebra.

He has led seven national research grants as Principal Investigator and supervised four Ph.D. students, with two more currently under his guidance. Additionally, he has mentored numerous Master's and undergraduate theses.

Sam Hughes

Is a young mathematician whose interests span group theory, algebraic and geometric topology, and more recently complex algebraic geometry. Despite being at an early stage of his career Hughes is a recognised leader in his area.

He obtained an EPSRC funded PhD from the University of Southampton (UK) in 2021. For his thesis, he received special mention for the Reinhold Baer 2022 prize. He worked at the University of Oxford from 2021 to 2024as a postdoctoral research associate. Since October 2024, he is a Humboldt fellow at Universität Bonn.

He has 15 papers published in indexed journals (14 of which are first quartile mathematical journals according to SciMago) and has also written one published survey and a further 12 preprints.

In 2024 he supervised the masters theses of 3 MMath students, 1 OMMS MSc student(who wonthe project prize), and 1 MFoCS MSc student. Four of the five students achieveda top gradeof 1st class (above 70) and three of them scored marks above 85 (an exceptional mark). He has alsosupervised four undergraduate summer projects.

Calendario

March 24 -28 (lectures by Andrei Jaikin)

March 31 - April 2 (lectures by Sam Hughes)

Lugar de impartición

Facultad de Ciencia y Tecnología, Campus de Bizkaia (Leioa)