Workshops on Algebraic Geometry and Representation Theory; Fall, 2015, 2016, and 2017; Chapel Hill, NC

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

This award supports participation in workshops on algebraic geometry and representation theory to be held in Fall 2015, 2016, and 2017 at the University of North Carolina, Chapel Hill. These mathematical topics are subjects of intense current work and much recent research progress. The first workshop, "New Developments in Moduli and Geometric Invariant Theory," will be held November 20-22, 2015. The workshop website is http://www.unc.edu/~sawon/UNCworkshop15.html. The goals of the workshops are to support younger researchers, by providing them with opportunities to disseminate their latest research results and interact with senior researchers, and to strengthen ties between mathematics departments in the Southeast. Each workshop will consist of ten talks spread over three days, allowing plenty of time for additional discussions. Participation of graduate students and postdocs will be encouraged. At least thirty graduate students are expected to attend each workshop, where they will learn about the latest progress in the field. Spaces that parameterize geometric objects and/or solutions to algebraic equations are known as moduli spaces, and are central to the study of algebraic geometry and representation theory. Typically they are constructed as quotient spaces using geometric invariant theory. The structure of these moduli spaces, and how they depend on the quotient construction, is an important area of investigation that has recently seen the influx of transformative new ideas: The theory of Bridgeland stability conditions and stable complexes has advanced to the point where it is now finding applications in the theory of moduli spaces of sheaves; the birational geometry of moduli spaces can now be studied using variation of stability conditions; and the effect of a wall-crossing on the derived category of a moduli space can be measured, just as the effect of more general birational modifications on Gromov-Witten and Donaldson-Thomas invariants can be determined in many cases. The first workshop will bring together experts in these areas, with an emphasis on the work of younger mathematicians. The second and third workshops will cover other topics in algebraic geometry and representation theory, and will focus on the most significant current developments.