# Applications of noncommutative deformations

## TL;DR

This paper explores noncommutative deformations in algebraic geometry, focusing on contractions of varieties and their applications to derived symmetries, providing new insights into the structure of these geometric transformations.

## Contribution

It introduces a noncommutative enhancement of the contraction locus in algebraic varieties, advancing understanding of their derived symmetries and geometric properties.

## Key findings

- Defined a noncommutative enhancement of the contraction locus
- Connected noncommutative deformations to derived symmetries
- Provided applications to the structure of contractions in algebraic geometry

## Abstract

For a general class of contractions of a variety X to a base Y, I discuss recent joint work with M. Wemyss defining a noncommutative enhancement of the locus in Y over which the contraction is not an isomorphism, along with applications to the derived symmetries of X. This note is based on a talk given at the Kinosaki Symposium in 2016.