# Felix Klein Lectures

## Indecomposable objects and potentials

### Professor Victor Ginzburg (University of Chicago)

Date: June 27 - July 1, 2016

Venue: Mathematics Center

• Lipschitz hall, Endenicher Allee 60: June 27, 2016; Coffee 15:00; Lecture: 16:00 - 18:00
• Lipschitz hall, Endenicher Allee 60: June 28, 2016; 16:00 - 18:00
• Seminar room 1.007, Endenicher Allee 60: June 30, 2016; 14:00 - 16:00
• Zeichensaal, Wegelerstraße 10: July 1, 2016; 10:00 - 12:00

### Abstract

Given an additive Karoubian category such that the moduli space of its objects is a smooth Artin stack (and some additional conditions) we give a formula for an exponential sum over the set of absolutely indecomposable objects of the category in terms of the geometry of the cotangent bundle on the moduli stack of framed objects. Our formula, inspired by the work of Hausel, Letellier, and  Rodriguez-Villegas, provides a new approach for counting absolutely indecomposable quiver representations, parabolic bundles on a projective curve, and irreducible l-adic local systems (via a result of Deligne). Our approach is based on the formalism of factorization sheaves.