Noncommutative deformations of curves

Speaker: Michael Wemyss, University of Edinburgh

Title: Noncommutative deformations of curves

Abstract: In three dimensional algebraic geometry, certain surgeries called flips and flops naturally arise.  Roughly speaking, these cut out rational curves from the ambient variety and glue others in their place.  I will explain what these are, give some common examples, then explain how to attach new invariants to each such surgery.  The new  
invariants will be constructed using noncommutative deformation theory, and so I will explain what this is, and why studying noncommutative deformations is actually necessary.  In the setting of 3-fold flops, I will briefly give some applications to both derived autoequivalences in algebraic geometry, and finite dimensional algebras.  This is based on joint work with Will Donovan.