# The Sheffield Geometry and Physics Seminar

The Sheffield Geometry and Physics Seminar (SGaPS) runs two-talks seminars on a fortnightly basis, starting in October.

## Time and venue

The seminar will take place Mondays in Room J-11, Hicks Building, with two talks back-to-back at 13:30-14:30 and 14:45-15:45.

It is organised by Andrea Brini, Luca Giovenzana and Ivan Tulli.

## Speakers & dates

### 19 February 2024

Andrew Neitzke (Yale): Abelianization of Virasoro conformal blocks

Given a Riemann surface C and a central charge c, one can define the notion of "Virasoro block" on C, introduced in the context of conformal field theory. The space of Virasoro blocks carries various interesting algebraic and geometric structures. I will recall this story and then describe a new scheme for constructing Virasoro blocks at central charge c=1, by relating them to simpler "abelianized" blocks on a branched double cover of C. This is joint work in progress with Qianyu Hao, inspired by work of Coman-Longhi-Pomoni-Teschner, Iwaki, Marino, Bridgeland and others.

Hannah Dell (Edinburgh): Stability conditions on free quotients

Bridgeland stability conditions have been constructed on curves, surfaces, and in some higher dimensional examples. In several cases, there are only so-called “geometric” stability conditions which are constructed using slope stability for sheaves, whereas in other cases there are more (e.g. coming from an equivalence with representations of a quiver). Lie Fu -- Chunyi Li -- Xiaolei Zhao were the first to provide a general result explaining this phenomena. In particular, they showed that if a variety has a finite map to an abelian variety, then all stability conditions are geometric. In this talk, we test the converse on surfaces that arise as free quotients by finite groups. To do this, we will develop a method to study stability conditions on any triangulated category with a group action. This is joint work with Edmund Heng and Tony Licata.

### 04 March 2024

Franco Rota (Glasgow)

Title: Non-degeneracy invariants of Enriques surfaces.

Abstract: Every Enriques surface Y has an elliptic pencil, and every elliptic pencil on Y has two multiple fibers, whose reduced support is called a half-fiber. The non-degeneracy invariant of an Enriques surface is defined to be the maximum number of half-fibers meeting each other at exactly one point.

This invariants influences the projective geometry of Y, as well as the structure of its derived category. In collaboration with R. Moschetti and L. Schaffler, we study techniques to compute non-degeneracy. These mix computer algebra and classical geometric methods. I'll illustrate our results in a few examples and I'll outline future directions.

Lea Bottini (Oxford)

### 18 March 2024

TBA

### 22 April 2024

TBA

### 29 April 2024

TBA

### 20 May 2024

TBA

### 03 June 2024

TBA