03/09/10 Dennis Borisov (Yale). 3:30
REC 313. Higher dimensional
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.
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
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
of Gerstenhaber's original bracket on the Hochschild cochains of an
04/15/10 David Gepner (UIC)A nonconnective version of
the units of ring spectrum
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
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.
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.