Seminar Schedule
January 8 - 12, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, January 8, 2007
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Talk
3:30pm, Room 304
Speaker: Christian Haesemeyer, University of Illinois
Title of talk: On the algebraic K-theory of singularities
Abstract: Algebric K-theory is a highly complicated invariant of algebraic
varieties that encodes arithmetic, geometric and algebraic information. In this
talk, I will try to make this distinction somwhat less vague and explain how
to isolate some of the algebraic and geometric information K-theory provides
about singularities, leading to proofs of various longstanding conjectures in
the subject.
TUESDAY, January 9, 2007
VIGRE-Graduate Student Seminar
2:00pm, Room 302
Speakers: TBA
Title of talk: TBA
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Talk
3:30pm, Room 304
Speaker: Jonathan Hanke, Duke University
Title of talk: The Arithmetic of Quadratic Forms and Modular
Forms
Abstract: This talk will describe some recent results
about the arithmetic of quadratic forms, and their relationship to the theory
of modular forms. Through a combination of local and global methods, this connection
allows one to answer questions like:
- Exactly what numbers are represented by a given positive
definite integer-valued quadratic form in 4 or more variables?
- How can one characterize positive definite quadratic forms
which represent all positive integers?
The main obstruction to answering these is explicitly understanding:
- How close do congruence conditions come to describing what
numbers are represented by a quadratic form?
We will discuss the arithmetic and analytic nature of this question, which
depends crucially on the number of variables of the quadratic form.
WEDNESDAY, January 10, 2007
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Talk
3:30pm, Room 304
Speaker: Daniel Groves, Caltech
Title of talk: Isoperimetric functions and non-positive
curvature in group theory
Abstract: I will introduce isoperimetric functions and discuss
their relation to classical decision problems in group theory. Next, various
notions of `negative curvature' and `non-positive curvature' for discrete groups
will be discussed, particularly in relation to isoperimetric functions. Finally,
joint work with Martin Bridson about isoperimetric functions for free-by-cyclic
groups will be discussed.
THURSDAY, January 11, 2007
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Talk
3:30pm, Room 304
Speaker: Huiqiang Jiang, University of Minnesota
Title of talk: Analysis of an activator-inhibitor system: global
solutions and steady states
Abstract:
FRIDAY, January 12, 2007
Geometry
2:30pm, Room 410
Speaker: Rob Kusner
Title of talk: Nondegeneracy and Moduli Space Theory for
CMC Surfaces
Abstract: Properly embedded constant mean curvature (CMC) surfaces
-- the model for complete noncompact soap bubbles or equilibrium fluid droplets
-- have a particularly nice asymptotic behavior. This leads to a pair of natural
questions:
1) How well do these asymptotic data determine the surface?
2) Can one describe the moduli space of all CMC surfaces with a given (finite) topology, using these asymptotic data as natural parameters?
The key to answering these questions is the nondegeneracy of the linearized mean curvature, namely, the Jacobi (or second variation of area) operator.
We will report on recent joint work with K. Grosse-Brauckmann, N. Korevaar, J. Ratzkin and J. Sullivan, in which we have found good estimates for the (tempered) nullity of the Jacobi operator. For the special class of coplanar CMC surfaces, we have also proven that the natural classifying homeomorhism is, in fact, a diffeomorphism. It follows that all 3-ended CMC surfaces of genus 0 are nondegenerate, and we hope to use this to show the same is true for an number of ends k > 3, at least in the coplanar case. Some applications to CMC gluing constructions and implications for the structure of CMC moduli space will also be discussed.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Job Talk
3:30pm, Room 304
Speaker: Michael Usher, Princeton
Title: The topology of symplectic four-manifolds
Abstract: Much has been learned over the past twenty years
about the global properties of symplectic manifolds (i.e., manifolds equipped
with a closed, nondegenerate two-form), with some of the most striking results
appearing in dimension four. I'll give a brief general overview of the subject,
mentioning in particular how certain coarse symplectic properties of a symplectic
four-manifold, such as the existence of certain spheres and the "symplectic
Kodaira dimension," can tell us interesting things about the differential
topology of the manifold. I'll then discuss some recent results showing how
these properties behave with respect to an important surgery operation called
the symplectic sum. Time permitting, I'll end with some interesting open questions.