SPRING 2013
SATURDAY MAY 11  SUNDAY MAY 12
Continuing the now decadeslong tradition, the Spring 2013 Midwest Topology Seminar was held May 11 and 12, 2013 at the University of Kentucky.
Speakers
Mohammed Abouzaid  Columbia University
Lagrangian immersions and the Floer homotopy type
A conjecture of Arnold would imply that every exact Lagrangian in a cotangent bundle is isotopic to the zero section through Lagrangian embeddings. We now know that every such Lagrangian is homotopy equivalent to the zero section. I will explain how, combining the hprinciple with the spectrumvalued invariants introduced by T. Kragh, one can hope to show that such Lagrangians are in fact isotopic to the zero section through Lagrangian immersions. I will discuss partial results obtained with Kragh, constraining the Lagrangian isotopy class of Lagrangians embeddings.
Michael Ching  Amherst College
Some examples of homotopic descent
I will describe a collection of theorems that exemplify homotopic descent. Each of these theorems says that a certain Quillen adjunction is `comonadic' in a homotopical sense: that is, it identifies the homotopy theory on one side of the adjunction with the homotopy theory of coalgebras over a certain comonad that acts on the other side. I will say what I mean by the homotopy theory of such coalgebras and give a BarrBeck comonadicity condition.
The examples I am interested in concern operad theory and Goodwillie calculus. One result identifies the homotopy theory of 0connected algebras over an operad of spectra with that of 0connected divided power coalgebras over the Koszul dual operad. (This is joint work with John E. Harper.) Another describes the homotopy theory of nexcisive homotopy functors (between categories of spaces and/or spectra) in terms of appropriate comonads. (This is joint work with Greg Arone.) In the case of functors from spaces to spectra, and algebras over the commutative operad, there is a close connection between these two examples, which I shall describe.
John Lind  Johns Hopkins University
Equivariantly Twisted Cohomology Theories
Twisted Ktheory is a cohomology theory whose cocycles are like vector bundles but with locally twisted transition functions. If we instead consider twisted vector bundles with a symmetry encoded by the action of a compact Lie group, the resulting theory is equivariant twisted Ktheory. This subject has garnered much attention for its connections to conformal field theory and representations of loop groups. While twisted Ktheory can be defined entirely in terms of the geometry of vector bundles, there is a homotopytheoretic formulation using the language of parametrized spectra. In fact, from this point of view we can define twists of any multiplicative generalized cohomology theory, not just Ktheory. The aim of this talk is to explain how this works, and then to propose a definition of equivariant twisted cohomology theories using a similar framework. The main ingredient is a structured approach to multiplicative homotopy theory that allows for the notion of a Gtorsor where G is a grouplike A∞ space.
Charles Rezk  University of Illinois at UrbanaChampaign
pisogeny modules, and calculations in multiplicative stable homotopy at height 2
I will describe two calculations, obtained using the theory power options for Morava E theory at height 2: (1) The E theory of the BousfieldKuhn spectrum (joint work with Mark Behrens) and (2) Twists of Ecohomology.
Kirsten Wickelgren  Harvard University
Massey products in Galois cohomology via étale homotopy types
The Milnor conjecture identifies the cohomology ring H*(Gal(k/k), Z/2) with the tensor algebra of k× mod the ideal generated by x⊗(1x) for x in k  {0,1} mod 2. In particular, x∪(1x) vanishes, where x in k× is identified with an element of H1. We show that order n Massey products of n1 factors of x and one factor of 1x vanish by embedding P1  {0,1,∞} into its Picard scheme, and applying obstruction theory to the resulting map on étale homotopy types. This also identifies Massey products of the form <1x, x, … , x , 1x> with f ∪(1x), where f is a certain cohomology class which arises in the description of the action of Gal(k/k) on π1et(P1  {0,1,∞}).
Bruce Williams  University of Notre Dame
Ktheory of Endomorphisms
Schedule
SATURDAY 


9:009:30  Coffee 
9:3010:30  Mohammed Abouzaid 
10:3011:00  Coffee Break 
11:0012:00  Charles Rezk 
2:003:00  John Lind 
3:003:30  Coffee Break 
3:304:30  Kirsten Wickelgren 
SUNDAY 

9:009:30  Coffee 
9:3010:30  Bruce Williams 
10:3011:00  Coffee Break 
11:0012:00  Michael Ching 
Participants
Name 
Institution 

Scott Bailey 
Clayton State University 
Philip Egger 
Northwestern University 
Tony Elmendorf 
Purdue University Calumet 
Robert Bruner 
Wayne State University 
Martin Frankland 
University of Illinois at UrbanaChampaign 
Zhen Huan 
University of Illinois at Urbana and Champaign 
Rolf Hoyer 
University of Chicago 
Angelica Osorno 
University of Chicago 
Peter Nelson 
University of Illinois at UrbanaChampaign 
JIBLAL UPADHYA 
NEW MEXICO STATE UNIVERSITY, LAS CRUCES, NEW MEXICO 
Jonathan Thompson 
University of Kentucky 
Bill Robinson 
University of Kentucky 
Marzieh Bayeh 
University of Regina 
Sarah Yeakel 
UIUC 
Inna Zakharevich 
University of Chicago 
Jim McClure 
Purdue 
Mona Merling 
UChicago 
Xiaoguang Jiang 
St. John's University 
Henry YiWei Chan 
The University of Chicago 
Niles Johnson 
Ohio State Newark 
Peter May 
University of Chicago 
Robert Bruner 
Wayne State University 
Anna Marie Bohmann 
Northwestern University 
David Copeland Johnson 
University of Kentucky (retired) 
Arnav Tripathy 
Stanford 
Sean Tilson 
Wayne State University 
Michael Catanzaro 
Wayne State University 
Cary Malkiewich 
Stanford University 
Amelia Tebbe 
University of Illinois UrbanaChampaign 
Andrew Wilfong 
University of Kentucky 
Howard Marcum 
Ohio State University at Newark 
Peter Ulrickson 
Notre Dame 
Augusto Stoffel 
University of Notre Dame 
Jialin Chen 
University of Illinois at Chicago 
Serge Ochanine 
University of Kentucky 
John Mosley 
University of Kentucky 
John Mack 
Univ of Kentucky 
Ryan Curry 
University of Kentucky 
John E. Harper 
Purdue University 
Funding for this meeting comes from the University of Kentucky College of Arts and Sciences, Vice President for Research, and Department of Mathematics.
MIDWEST TOPOLOGY SEMINAR
114 White Hall Classroom Building
140 Patterson Drive
Lexington, KY 405060025
CONTACT INFORMATION
Kate Ponto
kate.ponto@uky.edu
Department of Mathematics
University of Kentucky
Bert Guillou
bertguillou@uky.edu
Department of Mathematics
University of Kentucky