# Nir Gadish: The "generating function" of configuration spaces, as a source for explicit formulas and representation stability

**Time: **
Tue 2019-04-09 13.15 - 15.00

**Lecturer: **
Nir Gadish (University of Chicago)

**Location: ** Room 3418, Lindstedtsvägen 25, 4th floor, Department of Mathematics KTH

ABSTRACT: As countless examples show, sequences of complicated objects should be studied all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of (orbit-)configuration spaces, using the notion of twisted commutative algebras, which essentially categorify exponential generating functions. With this idea, originating from the work of Petersen, I will describe a factorization of the configuration space "generating function" into an infinite product, whose terms are surprisingly easy to understand. Beyond the intrinsic aesthetic of this decomposition and its quantitative consequences, it encodes all primary, secondary, and higher representation stability phenomena. This work is joint with Christin Bibby.