Time and place: Thursdays 3:30-4:30 in REC 116

Organizer: Ralph Kaufmann. Contact organizer.

01/24:James McClure:A Convenient Category of C^{infty} Manifolds.

Abstract: This is joint with Gerd Laures. We show that by expanding the

category of manifolds with corners one obtains a category in which gluing is

canonical.

01/31:Ben Walter:Rational Hopf Invariants via coLie Coalgebras.

Abstract: This is joint work with Dev Sinha. Using colie coalgebras of

graphs, we define natural, rational functionals on homotopy

groups using cochain data. Our work extends work of Sullivan,

Chen and Hain, and overlaps with work of Boardman and Steer.

Proofs are simple and the underlying geometric picture is

compelling.

02/07:Matthew Ando(UIUC).A quasicategory approach to units of ring spectra and Thom spectra.

Abstract: May-Quinn-Ray-Tornehave developed the obstruction theory for E_\infty

orientations of E_\infty Thom spectra. Initially we set out to develop

the A_\infty analogue. In both cases, the complications arise from the

fact that the Thom isomorphism arises from trivializing ahomotopy

sheaf of module spectra. Quasicategories are designed to provide a natural

setting for such sheaves, and so we should have been merely pleased

rather than pleasantly surprised that in this setting the obstruction

theory simplifies a great deal.

02/21:Philip Hackney(Purdue):Coproducts, Smith Chains, and Hochschild Cohomology.Abstract: The Gerstenhaber algebra structure on the Hochschild cohomology of an

algebra A is naturally defined at the cochain level. The cup product is

actually the dual of the cut coproduct on the Hochschild chains if A is

commutative. When A is a complete intersection, Larry Smith developed a

small resolution of A; we introduce a coproduct in this setting which

plays the role of the cut coproduct.

03/06:Anatoly Libgober(UIC).Higher genera in algebraic geometry.

Abstract: I will discuss elliptic genus and Hirzebruch's chi_y genus generalizations

of Novikov's higher signatures. Applications to multiplicativity of chi_y

in for locally trivial fibrations and birational analogs of Novikov's conjecture

will be given.

03/27:Javier Zuniga(Purdue).The Master Equation of Open-closed String Theory.

Abstract: I will set up a Quantum Master Equation for open-closed string theory and construct a

solution using a compactified version of moduli space of bordered Riemann Surfaces.

04/03:Alastair Hamilton(UConn).Noncommutative geometry and

compactifications fo the moduli space of curves.

Abstract: There is a theorem, due to Kontsevich, which states that the homology

of the moduli space of curves can be expressed as the homology of a

certain Lie algebra. In this talk I will explain how the homology of a

certain compactification of the moduli space, introduced by Kontsevich

in his study of Witten's conjectures, can be expressed as the homology

of a certain differential graded Lie algebra by deforming Kontsevich's

original Lie algebra using a Lie bialgebra structure considered by many authors.

04/10:Jinhyun Park(Purdue).Hochschild and cyclic homologies as additive K-theories

This talk is introductory: we recall the Lie algebra homology, Leibniz homology

and discuss how they are related to cyclic homology and Hochschild homology.

Then we argue why cyclic homology and Hochschild homology are additive K-theories.

We will talk about the aim of the second talk as well.

04/17:Jinhyun Park(Purdue).Commutative differential graded algebras of additive Chow cycles

We first mention the relationship between Quillen K-theory and higher Chow groups.

Then, we discuss briefly the additive higher Chow cycles and what it aims to achieve

in connection with additive K-theory. We will define motivic analogues of Connes'

boundary map and the shuffle product whose traditional place of discussion

is Hochschild complex. Using them, we discuss how to give the structure of CDGA on

additive higher Chow groups.