Schedule for 2024-2025
November 27th, 2024
Speaker: Alessio Di Prisa (Scuola Normale Superiore di Pisa)
Title: Equivariant algebraic concordance of strongly invertible knots
Abstract: In 1969 Levine defined a surjective homomorphism from the knot concordance group to the so called algebraic concordance group, which is a Witt group of Seifert forms.
Studying symmetric knots and in particular strongly invertible knots, a natural question is whether it is possible to define an appropriate equivariant version of algebraic concordance.
In this talk we briefly recall Levine's construction and we highlight some of the difficulties occuring when trying to define its equivariant analogous.
Finally, we define a notion of equivariant algebraic concordance for strongly invertible knots, we show some of the differences with the classical case and (time permitting) we will give an application of this theory to the study of equivariant slice genus.
November 22nd, 2024
Speaker: Lorenzo Cortelli (SISSA)
Title: Regular foliations on compact complex surfaces
Abstract: Arising naturally from a various mathematical problems, foliations are versatile objects, relevant to geometry and mathematical physics alike. Submersions, actions on manifolds and differential equations are just a few of the possible ways to define a foliation.
In this talk we'll focus on holomorphic foliations, introducing the most commonly used tools of complex foliation theory and ultimately giving a classification of all regular foliations on compact complex surfaces. Residue-like index formulae and Kodaira's work on complex surfaces will play a fundamental role.
November 15th, 2024
Speaker: Alaa Boukholkhal (ENS Lyon)
Title: Isometric Immersions: A historical overview
Abstract: The problem of isometric embeddings is fundamental in differential geometry. In the 1950s, John Nash provided a complete solution to this problem, marking a significant turning point in the field. In this talk, we delve into the historical context of this problem, highlighting the distinction between the C^1 case and the smooth case. We then detail Nash's revolutionary results, providing insight into their impact and significance in the field. Finally, if time permits, we will explore the h-principle and other flexibility results.