Flavors of Cohomology

Schedule

  Wednesday, June 3 Thursday, June 4 Friday, June 5
9:00am Coffee Break Coffee Break Coffee Break
9:30am Urs Schreiber Eric Peterson Corbett Redden
10:30am Coffee Break Coffee Break Coffee Break
11:00am Corbett Redden Carl McTague Carl McTague
12:00pm Lunch Break Lunch Break Lunch Break
1:30pm Carl McTague Urs Schreiber Eric Peterson
2:30pm Coffee Break Coffee Break Coffee Break
3:00pm Eric Peterson Corbett Redden Urs Schreiber

 

Speakers:

  • Carl McTague, Johns Hopkins
    1. The Cayley Plane and String Bordism
    2. tmf Is Not a Ring Spectrum Quotient of String Bordism
    3. Towards Higher Genera: A Synergy Between Elliptic and Witten Genera
  • Eric Peterson, Berkeley
    An invitation to Morava E-theory
    Abstract for day 1: Starting from a review of the notion of a complex orientation, we will construct the cohomology theories referred to as "Morava E-theories" and uncover their most essential properties.
    Abstract for day 2: With Morava E-theories now in hand, we will get a sense of how they're used by exploring one of their main applications: the structure theorems of Devinatz, Hopkins, and Smith for finite spectra.
    Abstract for day 3: Having now seen a success story with Morava E-theory, we turn to less well-understood behaviors and open questions, selected so as to be of interest to other attendees.
  • Corbett Redden, Long Island University
    Applications of differential cohomology
    1. Introduction to differential cohomology
    Differential cohomology is a non-trivial hybrid of cohomology and differential forms.  It is the natural home for many geometric invariants, including a refinement of the Chern-Weil theory for principal bundles with connection.  It allows the language of algebraic topology to be used in geometric problems.  We will explain this history in more detail, and we will show the importance of cocycle models.
    2. Differential equivariant cohomology
    For a manifold acted on by a compact Lie group, we construct "differential equivariant cohomology” groups, refining Borel’s construction of equivariant cohomology and the Cartan-Weil complex of equivariant differential forms.  The Chern-Weil homomorphism for equivariant bundles with connection naturally factors through differential equivariant cohomology.
    3. Geometric string structures and trivializations
    String structures arise as a higher analog of spin structures.  Unfortunately, working with them explicitly must involve infinite-dimensional spaces or higher categories.  We explain how the language of trivializations in differential cohomology can be used to describe geometric string structures in a more elementary way.
  • Urs Schreiber, Charles University, Prague
    Structure theory for higher WZW terms
    I will present results characterizing the behaviour higher WZW terms, with some applications to string theory. Following sections 5.3.9-5.3.14 of this document. Lecture notes available here.

Organized by Hisham Sati and Jason DeBlois

Sponsored by the Mathematics Research Center

June 3, 2015 (All day) to June 5, 2015 (All day)

Location and Address

705 Thackeray Hall