Webinars

The VBAC is launching a series of Webinars due to the pandemic situation, which take place every 2 months. The first VBAC webinar was A tribute to C. S. Seshadri organised in September 2020.

We invite researchers, and in particular young and female researchers, to apply to give a talk in our webinar series by following this link. We welcome proposals on any topic related to VBAC, in a broad sense.

Upcoming VBAC Webinars

All times are in UTC (GMT). Advanced registration is required; follow this link to register.

Cohomology of Higgs moduli spaces and the P = W conjecture, 18 January 2021

15:00 - 15:45   Junliang Shen (MIT): Cohomology of the moduli of Higgs bundles

Abstract: The moduli space of Higgs bundles and Hitchin's integrable system lie at the crossroads of mathematics physics, representation theory, and geometry. In this talk, we focus on cohomological structures of these moduli spaces from the aspects of non-abelian Hodge theory, hyper-kaehler geometry, and mirror symmetry. We will discuss recent progress on the P=W conjecture as well as connections to some other open conjectures concerning Higgs moduli spaces. Based on joint work with Mark de Cataldo and Davesh Maulik.

15:45 - 16:00 Questions and break

16:00 - 16:45  Camilla Felisetti (Trento): P=W conjectures for character varieties with a symplectic resolution

Abstract: Character varieties parametrise representations of the fundamental group of a curve. In general these moduli spaces are singular, therefore it is customary to slightly change the moduli problem and consider smooth analogues, called twisted character varieties. In this setting, the P=W conjecture by de Cataldo, Hausel, and Migliorini suggests a surprising connection between the topology of Hitchin systems and Hodge theory of character varieties. In joint work with M. Mauri we establish (and in some cases formulate) analogous P=W phenomena in the singular case . In particular we show that the P=W conjecture holds for character varieties which admit a symplectic resolution, namely in genus 1 and arbitrary rank and in genus 2 and rank 2.

16:45 - 17:00 Questions and further discussion

Non-reductive geometric invariant theory, March 2021

15:00 - 15:45 Eloise Hamilton (IMJ-PRG)
15:45 - 16:00 Questions and break
16:00 - 16:45 Frances Kirwan (Oxford)
16:45 - 17:00 Questions and further discussion

Previous VBAC Webinars

K-stability, 23 November 2020

(Click on the title of the talks for slides and video.)

15:00 - 15:45  Simon Donaldson (SCGP/Imperial): K-stability and scalar curvature

Abstract: This will be an overview talk about existence results in complex differential geometry connected to the notion of K-stability. We will explain the analogies with the corresponding results, going back to Narasimhan and Seshadri, for holomorphic vector bundles and outline some strategies of proofs that have been employed. We will illustrate the general with a discussion of the case of toric manifolds.

Talk Slides: Donaldson

16:00 - 16:45  Chenyang Xu (Princeton): An algebraic construction of K-moduli space

Abstract: K-stability of Fano varieties has become a fast developed topic in algebraic geometry. One major output is the construction of moduli spaces of K-(semi,poly)-stable Fano varieties, which resolves a number of pathological issue for families of general Fano varieties. The purely algebraic construction is built on a systematical study of K-stability using higher dimensional geometry, including a more comprehensive understanding of the notion of K-stability (for Fano varieties).

Talk Slides: Chenyang

Talk Video:

A tribute to C. S. Seshadri, 9 September 2020

13:00-13:40 M. S. Narasimhan: Reminiscences of my association and work with Seshadri
13:50-14:30 T. Gómez: Parabolic Bundles
14:40-15:20 V. Balaji: C. S. Seshadri, my mentor, a mathematician and a remarkable person
15:30-16:00 Time for those who want to share their reminiscences and appreciation of Seshadri.
For further information, including videos and slides, see: A tribute to C. S. Seshadri