COW/EmSG/GLEN Joint Summer School

7 - 11 September 2020

The COW (Cambridge-Oxford-Warwick), EmSG (East Midlands Seminar in Geometry), and GLEN (Glasgow-Liverpool-Edinburgh-Newcastle) algebraic geometry networks are joining forces to present an online summer school in algebraic geometry in September 2020.

The summer school will feature three series of talks, each containing five lectures. Talk series will be delivered by postdocs affiliated with one of the three networks and will be targeted towards a graduate student audience.

Sessions will be hosted by ICMS and delivered online using Zoom. Zoom access information will be distributed to registered participants in advance of the event; a link to the registration form may be found below.

LMS logo

This event is kindly funded by the London Mathematical Society.

Speakers

Talk series will be delivered by the following speakers; titles and abstracts may be found below.

Mini-Presentations

In place of a poster session, we are hoping to feature a number of "mini-presentations" by current PhD students and/or postdocs. The format will be very short (5-10 minute) slide presentations on some aspect of your research. If you would be interested in giving such a mini-presentation, please indicate this on the registration form. For planning purposes, we ask that anyone hoping to give such a presentation registers their interest in doing so by Friday 14th August.

Registration

We ask that all attendees register by completing the form linked below. Zoom access information will be distributed to registered attendees in advance of the event.

Registration form

Titles and Abstracts

Francesca Carocci - The geometry of moduli spaces of stable maps to projective space and modular desingularisation via log blowups

Moduli spaces of stable maps have been of central interest in algebraic geometry for the last 30 years. In spite of that, the geometry of these spaces in genus bigger than zero is poorly understood, as the Kontsevich compactifications include many components of different dimensions meeting each other in complicated ways, and the closure of the smooth locus is difficult to describe.

In recent years a new perspective on the problem of finding better behaved compactifications, ideally smooth ones, has come from log geometry. This approach has proved successful in a series of examples and log geometry is now becoming a natural setting to study modular resolutions of moduli spaces.

The aim of this series of talks will be to see how log geometry techniques apply to give modular smooth compactifications of moduli spaces of stable maps to projective spaces in genus one and two; we will also explain why the latter are interesting from an enumerative point of view.

In more detail: we begin by studying the deformation theory and the global geometry of moduli spaces of genus one and two stable maps; we then give a brief introduction to log schemes, line bundles on log schemes and log blowups and conclude by exhibiting the log modification resolving the moduli spaces of maps in genus one and two and explaining their modular meaning.

Soheyla Feyzbakhsh - Bridgeland stability conditions and geometric applications
I will first describe the notion of Bridgeland stability conditions on triangulated categories. Then I will focus on stability conditions on the bounded derived category of coherent sheaves on curves, surfaces and threefolds. In the end, some recent applications of Bridgeland stability conditions in classical algebraic geometry and Donaldson-Thomas Theory will be explained.
Liana Heuberger - Constructing Fano varieties via mirror symmetry

Mirror symmetry conjecturally associates to a Fano orbifold a (very special type of) Laurent polynomial. Laurent inversion is a method for reversing this process, obtaining a Fano variety from a candidate Laurent polynomial. We apply this to construct new Fano 3-folds with terminal Gorenstein quotient singularities.

In this series of talks, I will go through some of the basics of toric geometry to showcase how one can use combinatorial data to systematically build geometric objects. We will restrict our attention to the well-studied Fano case, for which there is concrete evidence that the mirror theorem holds in many cases.

Organisers

This event is being organised by the organisers of COW, EmSG, and GLEN. Contact details may be found by clicking on the names below.

This page is maintained by Alan Thompson and was last updated on 08/07/20. Please email comments and corrections to A.M.Thompson (at) lboro.ac.uk.