September 1 
Bob Oliver 
(In the algebra seminar) 
September 9 
Nick Kuhn (UVA) 
On a new nonrealization theorem of Gaudens and Schwartz 
September 16 
Nick Kuhn (UVA) 
On a new nonrealization theorem of Gaudens and Schwartz II 
September 23 
Calder Wishne 
The moduli space of Riemann surfaces, mapping class groups, and the Mumford conjecture 
September 30 
TBA 
TBA 
October 7 
Rebecca Field (JMU) 
BSO(2n) as an extension of BO(2n) by BSp(2n) 
October 14 
Peter Bubenik (Cleveland State U) 
Persistent homology and statistical estimation
I will give a tutorial on some aspects of the persistent homology machinery. Next I will give an application to analyzing data obtained from sampling from a realvalued function on a manifold. If there is interest, I will discuss a particular application to brain imaging data. 
October 21 
TBA 
TBA 
October 28 
John Harper 
On a homotopy completion tower for algebras over operads in symmetric spectra
In Haynes Miller's proof of the Sullivan conjecture on maps from classifying spaces, Quillen's derived functor notion of homology (in the case of commutative algebras) is a critical ingredient. This suggests that homology for the larger class of algebraic structures parametrized by an operad O will also provide interesting and useful invariants. Working in the context of symmetric spectra, we introduce a completion tower for algebras over operads and prove that under appropriate connectivity conditions this tower interpolates between topological Quillen homology and the identity functor. This is part of a larger goal to attack the problem: how much of an Oalgebra can be recovered from its topological Quillen homology? We also prove analogous results for algebras over operads in unbounded chain complexes. This talk is an introduction to these results (joint with K. Hess) with an emphasis on several of the motivating ideas.

November 4 
Rekha Santhanam (Johns Hopkins) 
Equivariant Gamma Spaces and Equivariant BarrattPriddy Theorem
We describe equivariant \Gamma spaces as defined by Shimakawa and explain how they model equivariant infinite loop spaces.
We construct a veryspecial equivariant \Gammaspace from a symmetric monoidal Gcategory for a finite group G. We outline a proof of the equivariant version of the BarrattPriddy theorem in the finite group case using these ideas.

November 11 
Niles Johnson (UGA) 
Complex Orientations and ptypicality
This talk will describe computational results related to the structure of power operations on complex oriented cohomology theories (localized at a prime p). After introducing the relevant concepts, we will describe results from joint work with Justin Noel showing that, for primes p less than or equal to 13, a number of wellknown MU_(p)rings do not admit the structure of commutative MU_(p)algebras.
These spectra have complex orientations which factor through the BrownPeterson spectrum and correspond to ptypical formal group laws; our computations show that such a factorization is incompatible with the power operations on complex cobordism and thus the complex orientations cannot carry MU_(p)algebra structure. This implies, for example, that if E is a Landweber exact MU_(p)ring whose associated formal group law is ptypical of positive height, then the canonical map MU_(p) >E is not a map of H_infty ring spectra. It immediately follows that the standard ptypical orientations on BP, E(n), and E_n do not rigidify to maps of E_infty ring spectra. We conjecture that similar results hold for all primes.

November 18 
TBA 
TBA 
November 25 
No Seminar 
Thanksgiving 
December 2 
Andrew Salch (Johns Hopkins) 
Some recent developments in the stable homotopy groups of spheres
We will describe the current state of an ongoing project which attempts to describe the stable homotopy groups of spheres using the arithmetic of Lfunctions. This is sometimes called a "topological Langlands program." This project is happening on two fronts, a conceptual front and a computational front; we will spend some time describing progress made on both fronts. On the conceptual front, we will give a crash course in the constructions used in the proof of the local Langlands correspondences, and we describe efforts (including some successful ones!) to lift these constructions from commutative rings to E_\inftyring spectra; and on the computational front, we describe the appearance of the same unit groups in padic division algebras in both the JacquetLanglands correpondences and in chromatic stable homotopy theory (as Morava stabilizer groups), and we describe a systematic method of attack on the cohomology of these profinite groups, as well as some new computations that this systematic computational attack has resulted in.
