University of Georgia
Department of Mathematics
Seminar Schedule
January 23, 2006 - January 27, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, January 23, 2006

Topology/Geometry
3:15pm - 5:30pm, GA Tech, Skiles 269

3:15 pm Monday, January 23, 2006
Algebra-Geometry-Topology Seminar: Existence of Engel structures
by Thomas Vogel (University of Pennsylvania and IAS) in Skiles 269
Engel structures are non-integrable plane fields on 4-manifolds who share many properties with contact structures. The existence of an Engel structure on a manifolds leads to strong restrictions on the topology of the manifold: Under certain orientation assumptions the tangent bundle of the manifold is trivial. In this talk we develop a construction which shows that the converse is also true: Every 4-manifold with trivial tangent bundle admits an Engel structure.

4:30 pm Monday, January 23, 2006
Algebra-Geometry-Topology Seminar: A survey of some smooth concordance invariants by Matthew Hedden (Princeton) in Skiles 269
In the past few years, several powerful smooth knot concordance invariants have been discovered. Perhaps most notable are the invariants $\tau(K)$ and $s(K)$, both of whose values for the $(p,q)$ torus knots provide new proofs of Milnor's famous conjecture on the unknotting number of these knots. $\tau(K)$ was discovered by Ozsv{\'a}th-Szab{\'o}, and independently by Rasmussen, and its definition relies on the analytically defined knot Floer homology theory developed by these authors. $s(K)$, on the other hand, was discovered by Rasmussen and its definition is in terms of the combinatorial knot homology theory of Khovanov. Though quite different in their definition, the two invariants share several formal properties, and agree for many knots. Indeed, it was conjectured by Rasmussen that the two invariants are equal, up to normalization. In this talk I will survey what is known about the two invariants, and discuss some of my recent results regarding the invariant $\tau$. I will conclude by presenting the first known examples where the invariants disagree, discovered jointly with Philip Ording of Columbia University.

Algebra
2:30pm, Room 410
No Meeting this week

Ed Azoff Tea Social
3:00pm, Room 409
Coffee, Cookies, Tea

Arithmetic Geometry/Number Theory
3:30pm, Room 302
Speaker: Ambrus Pal (IHES)
Title of talk: The torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves.

TUESDAY, January 24, 2006

VIGRE-Graduate Student Seminar
2:00p.m., Room 304
Speaker: Matt Hedden, Princeton University
Title: Introduction to knot theory and knot invariants
Abstract: I'll begin the talk by introducing what a knot is mathematically, and trying to motivate why someone (probably a topologist) might study them. I'll then discuss how one could go about studying knots through the use of invariants, and introduce two of the most famous invariants, the Alexander and Jones polynomials. I'll may try to conclude by speaking roughly about some beautiful modern generalizations of these polynomials which go by the names of Ozsvath-Szabo and Khovanov homology, respectively. The talk will be aimed at beginning graduate students or advanced undergraduates.

Ed Azoff Tea Social
3:00pm, Room 409
Coffee, Cookies, Tea

Colloquium
3:30pm, Room 302
Speaker: Ambrus Pal (IHES, France)
Title of talk: K_2 of elliptic surfaces and the rigid analytic regulator
Abstract: Milnor K-groups of algebraic varieties play a significant role in algebra, geometry, number theory and even in mathematical logic. In spite of some spectacular results, such as the work of Voevodsky on the Bloch-Kato conjecture, some fundamental finiteness conjectures remain open about these objects. In this talk I will explain how a refined form of the Langlands correspondence over function fields were used to make progress in this problem.

WEDNESDAY, January 25, 2006

Geometry in the Curriculum Seminar
1:25pm, Aderhold Room 111
Speaker: Brad Findell, University of Georgia
Title: Geometry in the new Georgia Performance Standards
Abstract: What and where are the geometry ideas in the new Georgia Performance
Standards (especially grades 6-12)?

Algebraic Geometry
2:30pm, Room 410
No Meeting this week

VIGRE- Algebra
2:30pm, Room 303
Speaker: Brian Boe, University of Georgia
Title of talk: Proof of Kostant's Theorem, continued

THURSDAY, January 26, 2006

VIGRE – Feynman Diagrams
2:00pm, Room 326

VIGRE – Cardiac Physiology
2:00pm, Room 640

VIGRE- Zeta Functions
2:15pm, Room 302

VIGRE-Algebraic Geometry
3:30pm, Room 324

Ed Azoff Tea Social
3:00pm, Room 409
Coffee, Cookies, Tea

Colloquium
3:30pm, Room 302
Speaker: Alexander Iosevich, Univ. of Missouri-Columbia
Title of talk: "Analysis, combinatorics and number theory of distance sets".
Abstract: The Erdos distance conjecture says that $N$ points in "d"-dimensional Euclidean space determine at least $CN^{\frac{2}{d}}$ distinct distances. The continuous analog of this conjecture, introduced by Falconer says that if the Hausdorff dimension of a set in Euclian space exceeds $d/2$ than the Lebesgue measure of the set of distances is positive. We shall discuss these conjectures and connections between them. We shall also describe the finite field analog of these problems where Gauss and Kloosterman sums play a crucial role.

FRIDAY, January 27, 2006

Probability Theory
2:30-3:30pm, Room 303
Speaker: Qing Zhang, University of Georgia
Title of talk: Nonlinear filtering