Programa de doctorado que propone la actividad

Matemáticas y Estadística

Persona de contacto

Nombre y apellidos: ILYA KAZACHKOV

• Teléfono: 94 601 2652
• Email: ilya.kazachkov@ehu.eus

Breve descripción de la actividad

The course includes 6,5 hours of lectures and 4 hours of problem sessions. The course is given by Francesco Fournier Facio and the problem sessions are led by Elena Bogliolo.

Abstract

Bounded cohomology is a functional-analytic analogue of singular cohomology, with many applications in geometric topology and rigidity theory. Unfortunately, it is very hard to compute, most of all because there is no Mayer-Vietoris sequence. The last few years have seen major advances, with new computations especially in the realm of transformation groups, with applications to characteristic classes of bundles and Milnor-Wood inequalities.

This minicourse will survey the basic theory of bounded cohomology, the foundational results and the main applications, and then focus on these recent advances. The ultimate goal is to sketch the proof of the bounded acyclicity of the group of homeomorphisms of R^n, which uses essentially all tools currently at our disposal to compute bounded cohomology.

Ponentes

Francesco Fournier-Facio obtained his PhD in 2023 at ETH Zürich under Alessandra Iozzi's supervision, and is currently a Herchel Smith Fellow at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, as well as a Henslow Fellow of the Cambridge Philosophical Society.

He works in group theory as it connects to other fields, such as algebraic and geometric topology, operator algebras and dynamics. His PhD thesis was awarded the ETH Medal and the Chorafas Prize, and he was the recipient of a Mary Ellen Rudin Award "for ground-breaking work in bounded cohomology".

Elena Bogliolo is a Ph.D. student in Mathematics at University of Pisa under the supervision of Prof. Marco Moraschini. Her main research interest is bounded cohomology of groups, a variant of group cohomology, introduced by Johnson and Trauber and developed by Gromov. Bounded cohomology is linked to other geometric and algebraic invariants such as simplicial volume and stable commutator length. She has worked on bounded cohomology of (verbal) wreath products and of groups acting on trees with almost prescribed local actions.

Calendario

April 20 (lectures by Francesco Fournier-Facio)

• 9.30 – 10.00 Registration (on Monday)
• 10.00 - 11.15  Course
• 11.15 - 11.45  Coffee break
• 11.45 - 13.00  Course
• 13.00 - 15.00  Lunch
• 15.00 - 17.00 Problem session (led by Elena Bogliolo)

April 21 (lectures by Francesco Fournier-Facio)

• 10.00 - 11.15  Course
• 11.15 - 11.45  Coffee break
• 11.45 - 13.00  Course
• 13.00 - 15.00  Lunch
• 15.00 - 17.00 Problem session (led by Elena Bogliolo)

April 22 (lecture by Francesco Fournier-Facio)

• 10.00 - 11.30  Course

Lugar de impartición

Aula 1.A1, Facultad de Ciencia y Tecnología, Campus de Bizkaia (Leioa)