ULB-USC minicourse on non-negative curvature and biquotients
Brussels - Santiago de Compostela - 2-10 April 2025
Guest lecturer
Jason DeVito, Department of Mathematics and Statistics, The University of Tennessee at Martin.
Abstract
Biquotients are natural generalizations of Riemannian homogeneous spaces, and are of paramount importance in the study of closed Riemannian manifolds with non-negative or positive sectional curvature. This minicourse will cover the main metric constructions used with biquotients as well as methods for determining their cohomology rings and characteristic classes. The focus will be on concrete examples.
Outline
Day 1: A brief survey of Riemannian manifolds of non-negative or positive sectional curvature with an emphasis on compact Lie groups and homogeneous spaces.
Day 2: Biquotients and Cheeger deformations.
Day 3: Biquotients - Wilking's doubling trick.
Day 4: A crash course in spectral sequences.
Day 5: The cohomology ring of homogeneous spaces and biquotients.
Day 6: The characteristic classes of homogeneous spaces and biquotients.
Venue and schedule
This is a 9-hour minicourse that will be divided in 6 sessions, the first three of them at ULB and the last three sessions at USC, according to the following schedule. Participants will receive a link to connect via MS Teams to attend the lectures not taking place in their university.
First week: Départment de Mathématique, Bâtiment NO, NO7.109, Campus de la Plaine, Université Libre de Bruxelles (ULB).
Wednesday 2, Thursday 3, Friday 4: 16.00-17.30
Second week: Facultade de Matemáticas, Aulas 9-10, Universidade de Santiago de Compostela (USC).
Tuesday 8 (16.00-17.30, Aula 10), Wednesday 9 (15.00-16.30, Aula 9), Thursday 10 (16.00-17.30, Aula 10)
