Purdue University

Department of Mathematics
Topology Seminar


Spring 2010
Time and place: Thursdays 3:30-4:30 in REC 303

Organizer: Ralph Kaufmann. Contact organizer.


03/09/10 Dennis Borisov (Yale). 3:30 REC 313. Higher dimensional operads.
I will discuss several approaches to define higher dimensional operads and the corresponding definitions of weak higher categories, and in particular contractible operads and the relation to Deligne conjecture. I will present a unifying framework for higher dimensional operadic algebra.

03/25/10 Javier Zuniga (Purdue). A bracket for Moduli chains.
    Abstract: I will give a detailed account of the construction of the BV-algebra structure on the (geometric) chains of the moduli space of bordered Riemann Surfaces. This leads to a Lie Bracket that is part of the Quantum Master Equation.

04/01/10 Ben Ward (Purdue). BV Structures and Modular Operads
    Abstract: We associate a BV operator to a suitable type of Modular Operad, whose failure to be a derivation gives an odd lie bracket associated to the underlying Cyclic Operad.  This bracket is a cyclic generalization of Gerstenhaber's original bracket on the Hochschild cochains of an associative algebra

04/15/10 David Gepner (UIC)A nonconnective version of the units of ring spectrum
    Abstract: A commutative S-algebra R has a spectrum of units gl_1(R),
usually defined via the observation that its space of units GL_1(R) is an
infinite loop space. In this talk, we discuss a more canonical method of
delooping GL_1(R), yielding a spectrum of units with nontrivial negative
homotopy groups, and whose connective cover is the usual gl_1(R).

04/22/10 Greg Friedman (TCU). Additivity and Non-additivity of Perverse Signatures.
    Abstract: The Novikov Additivity and Wall Non-additivity theorems relate the signature of a manifold, respectively a manifold with boundary, to the signatures of the pieces when the manifold is cut in two. I will discuss joint work with Eugenie Hunsicker in which we extend these results to a signature of stratified spaces that is defined using intersection homology. We will review all relevant background concerning both signatures and intersection homology, so the only prerequisites are basic graduate student algebraic topology.