Understanding the Notion of K-stability using 3-folds

Understanding the Notion of K-stability using 3-folds

The main objects of study in Algebraic geometry are ‘varieties’, which are basically the geometric counterpart of solutions to polynomial equations. One of the most interesting questions to ask about a variety, is to determine whether it is ‘K-stable’. A conjecture by Yau-Tian-Donaldson gives an algebro-geometric way of looking at the notion of K-stability and many recent developments give very explicit ways of determining this property.

In this talk, my goal would be to give you a rough idea of why this is very interesting to study, by looking at an explicit example of a Fano 3-fold. We will first look at the basic concepts that would be required to do this, using some simple examples and then take you through an example of a 3-fold slowly. We will look at how best to describe the 3-fold using notions that are familiar to us and then describe how one would determine the K-stability of the same.

This is joint work with Jesus Martinez Garcia, Ivan Cheltsov, Costya Shramov, Kento Fujita, Carolina Araujo, Ana-Maria Castravet, Anne-Sophie Kaloghiros and Hendrick Suess.

Speaker

Nivedita Viswanathan, University of Edinburgh

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)