Antoine

 

PRINCIPAL SPEAKER
The principal speaker is Professor Benson Farb of the University of Chicago. He will give a series of three talks.

Clicking on the titles will take you to a video of the talk. Abstracts are below

Title: Permutations and polynomiality in algebra and topology

Title: Surface bundles, mapping class groups, moduli spaces, and cohomology

Title: Reconstruction problems in geometry and topology

Abstracts:

Title: Permutations and polynomiality in algebra and topology

Abstract: Tom Church, Jordan Ellenberg and I recently discovered that each Betti number
of the space of configurations on n points on any manifold is a polynomial in n. Similarly
for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces
of homogeneous polynomials arising in algebraic combinatorics. Why? What do these
disparate examples have in common? The goal of this talk will be to answer this question by
explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.

Title: Surface bundles, mapping class groups, moduli spaces, and cohomology

Abstract: In this talk I will try to explain the beautiful circle of ideas relating the terms in
the title. We'll see how the cohomology of mapping class groups (= of the moduli space of Riemann surfaces)
can be thought of as the characteristic classes of surface bundles. What are these classes? What is their
geometric meaning? We'll see that there are very few answers to these questions. Indeed, a main goal of this
talk will be to present a number of (completely) open problems on this subject that I find to be fundamental and
compelling. This is joint work with Tom Church and Andy Putman (in various linear combinations).

Title: Reconstruction problems in geometry and topology

Abstract: The Fundamental Theorem of Affine Geometry (FTAG) states that for n>2, any bijection of subspaces
of R^n preserving inclusion of subspaces must be affine. In addition to its applications (e.g. to Mostow Rigidity in higher rank),
I like to think of this theorem as an answer to the question: ``What is an affine map?''
In this talk I'll explain a research program that seeks to find topological versions of FTAG.
For example we will, in the spirit of FTAG, address questions of the form: ``What is a homeomorphism of a manifold?
What is an embedding? a finite cover?'' This is joint with Dan Margalit. I will also explain some geometric variations on FTAG.

REGISTRATION, ADDITIONAL DETAILS:
Details on how to register and request funding are provided in the registration link at that left.
There will be a registration/refreshment fee on a sliding scale ($20 for graduate students and $30 for faculty) to cover expenses that can not be covered with NSF or university funds.

FUNDING:
Funding is partially provided by the National Science Foundation and by Oregon State University.
Limited funds will be available to support travel and living expenses of participants. Priority will be
given to graduate students and those without other funding sources.

Location of Conference:
The conference will be held at Oregon State University. More details will be posted here once the room location is fixed.

TALKS:
Time periods of 20 minutes will be allotted for participants to give talks. 

CONFERENCE HOSTS
Dennis Garity , William Bogley, Ren Guo, Mark Walsh
Department of Mathematics 
Oregon State University 

 

ORGANIZERS:
Fredric Ancel, University of Wisconsin-Milwaukee, ancel at uwm dot edu
Dennis Garity, Oregon State University, garity at math dot oregonstate dot edu
Craig Guilbault, University of Wisconsin-Milwaukee, craigg at uwm dot edu
Eric Swenson, Brigham Young University, eric@math.byu.edu
Frederick Tinsley, Colorado College, ftinsley at ColoradoCollege dot edu
Gerard Venema, Calvin College, venema at calvin dot edu
David Wright, Brigham Young University, wright at math dot byu dot edu