## Wall-crossing in Mathematics and Physics

### May 24-28, 2010

Department of Mathematics

University of Illinois at Urbana-Champaign

There has been considerable recent activity on wall-crossing phenomena related to Donaldson-Thomas invariants on Calabi-Yau 3-folds. The aim of the conference is to discuss the results, applications, and future directions of these ideas. In addition to research talks, there will be short courses aimed at graduate students and mathematicians new to the area.

#### Registration Form

#### All talks will be held in 245 Altgeld Hall -- click here for Lecture Schedule

#### Conference Instructions and Reimbursement Information

#### Short courses

**Emanuel Diaconescu, Generalized Donaldson-Thomas Invariants and Wallcrossing**

This course is an introduction to the theory of generalized Donaldson-Thomas invariants developed by Joyce and Song. Earlier work of Joyce on stack functions and wallcrossing in abelian categories will also be reviewed. Concrete examples and applications, including local Pandharipande-Thomas theory, will be provided.**Markus Reineke, Quiver moduli and wall-crossing**

We start with an introduction to quiver representations, their moduli spaces, and Hall algebras. Several classes of examples will be discussed. We derive formulas for the cohomology of quiver moduli via Hall algebras and counting over finite fields. A map between part of the Hall algebra of a quiver and a group of Poisson automorphisms allows us to interpret wall-crossing formulas in terms of quiver moduli. Integrality properties of the wall-crossing DT-invariants will be derived. If time allows, we will discuss relations to the tropical vertex group and to wall-crossing formulas of Gaiotto-Moore-Neitzke.

#### Speakers

Kai Behrend, University of British Columbia

Jim Bryan, University of British Columbia

Emanuel Diaconescu, Rutgers University

Sergei Gukov, University of California at Santa Barbara

Davesh Maulik, MIT

Andy Neitzke, University of Texas

Alexei Oblomkov, University of Massachusetts-Amherst

Rahul Pandharipande, Princeton University

Markus Reineke, University of Wuppertal

Vivek Shende, Princeton University

Jacopo Stoppa, University of Cambridge

Balázs Szendrői, University of Oxford

Yukinobu Toda, University of Tokyo

#### Accommodations

Blocks of rooms have been reserved at the following hotels.

#### Travel

At http://illinois.edu/resourcesfor/visitors/directions.html the University maintains a web page giving some travel information, especially about driving to Urbana-Champaign.

#### Scientific Organizing Committee

Emanuel Diaconescu, Rutgers University

Sheldon Katz, University of Illinois at Urbana-Champaign

Rahul Pandharipande, Princeton University

#### Local Organizing Committee

Sheldon Katz, University of Illinois at Urbana-Champaign

Thomas Nevins, University of Illinois at Urbana-Champaign

The workshop is supported by the National Science Foundation and the University of Illinois.