Spring 2025
The Seminar runs on Tuesdays at STRAND BLDG S4.29. This term, some talks will run from 15:00 to 16:00, and others will be in two parts – an introductory talk from 15:00 to 15:40 and a research talk from 15:45 to 16:30.
29 April, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Alapan Mukhopadhyay (EPFL)
Title: Frobenius and Homological Algebra
Abstract: The Frobenius endomorphism or the p-th power map is crucial in defining singularity classes in characteristic p > 0, especially those appearing in the birational classification of algebraic varieties. On the other hand, the obstruction to smoothness is homological, according to a celebrated theorem of Serre. In this talk, we will show that the Frobenius endomorphism witnesses this homological obstruction to smoothness. This provides an explanation for the effectiveness of Frobenius in detecting singularities, from a homological point of view. The key will be to produce (explicit) generators of the bounded derived category of a variety in characteristic p > 0 from perfect complexes using the Frobenius pushforward functor. Our results recover earlier characterizations of smoothness using Frobenius- such as Kunz’s theorem. Time permitting, we will discuss examples hinting relationship between generators of derived categories and the global geometry of the underlying projective variety. Part of the talk will report a joint work with Matthew Ballard, Patrick Lank, Srikanth Iyengar and Josh Pollitz.
13 May, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Francesca Tripaldi (University of Leeds)
Title: Extracting subcomplexes in the subRiemannian setting
Abstract: On subRiemannian manifolds, the de Rham complex is not the ideal candidate to use to carry out geometric analysis. However, special subcomplexes have successfully been applied in very specific settings, such as Heisenberg groups and the Cartan group. I will give an overview of different techniques used to obtain such subcomplexes, as well as point out their limitations when used on arbitrary Carnot groups, and a possible way to overcome them.
20 May, 15:00-16:00, STRAND BLDG S4.29
Speaker: Shengwen Wang (Queen Mary University London)
Title: Phase transitions with Allen-Cahn mean curvature bounded in Lp.
Abstract: We consider the varifolds associated to a phase transition problem whose first variation of Allen-Cahn energy is Lp integrable with respect to the energy measure. We can see that the Dirichlet and potential part of the energy are almost equidistributed. After passing to the phase field limit, one can obtain an integer rectifiable varifold with bounded Lp mean curvature.
27 May, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Jef Laga (University of Cambridge)
Title: TBA
Abstract: TBA
3 June, 15:00-16:00 STRAND BLDG S4.29
Speaker: Nattalie Tamam (Imperial College London)
Title: TBA
Abstract: TBA
10 June, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Adam Klukowski (University of Oxford)
Title: TBA
Abstract: TBA
17 June, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: TBA
Title: TBA
Abstract: TBA