Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Mon, 26 Feb 2024
14:15
L4

Hessian geometry of $G_2$-moduli spaces

Thibault Langlais
(Oxford)
Abstract

The moduli space of torsion-free $G_2$-structures on a compact $7$-manifold $M$ is a smooth manifold, locally diffeomorphic to an open subset of $H^3(M)$. It is endowed with a natural metric which arises as the Hessian of a potential, the properties of which are still poorly understood. In this talk, we will review what is known of the geometry of $G_2$-moduli spaces and present new formulae for the fourth derivative of the potential and the curvatures of the associated metric. We explain some interesting consequences for the simplest examples of $G_2$-manifolds, when the universal cover of $M$ is $\mathbb{R}^7$ or $\mathbb{R}^3 \times K3$. If time permits, we also make some comments on the general case.

Mon, 04 Mar 2024
14:15
L4

Significance of rank zero Donaldson-Thomas (DT) invariants in curve counting theories

Sohelya Feyzbakhsh
(Imperial College London)
Abstract
Fix a Calabi-Yau 3-fold X of Picard rank one satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. I will first describe two methods to achieve explicit formulae relating rank zero Donaldson-Thomas (DT) invariants to Pandharipande-Thomas (PT) invariants using wall-crossing with respect to weak Bridgeland stability conditions on X. As applications, I will find sharp Castelnuovo-type bounds for PT invariants and explain how combining these explicit formulas with S-duality in physics enlarges the known table of Gopakumar-Vafa (GV) invariants. The second part is joint work with string theorists Sergei Alexandrov, Albrecht Klemm, Boris Pioline, and Thorsten Schimannek.