University of Georgia
Department of Mathematics
Seminar Schedule
January 22, 2007 - January 26, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, January 22, 2007

Algebra
2:30pm, Room 328
Speaker: Jon Kujawa, University of Georgia
Title of talk: Support Varieties for Lie Superalgebras
Abstract: Support varieties are geometric objects which were first introduced to study the representation theory of finite groups over a field of positive characteristic. They have since become an essential tool. Because of their importance, much effort has gone into developing such theories for other objects (e.g. finite group schemes and quantum groups).

In recent work with Brian Boe and Daniel Nakano, we develop a support variety theory for Lie superalgebras over the complex numbers. In this talk we will discuss what is currently known and conjectured about these geometric objects. In particular, we will see that they give new insights into the representation theory and combinatorics of Lie superalgebras.

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies

Geometry-Topology Seminar
Joint Seminar - UGA-Georgia Tech Geometry-Topology Seminar, this time held at Georgia Tech

3:00 pm, Skiles 269
Speaker: Terry Fuller (Cal State, Northridge)
Title of talk: Realizing 4-manifolds as achiral Lefschetz fibrations
Abstract: Work of Donaldson and Gompf in the late 90s characterized symplectic 4-dimensional manifolds as those admitting a particular sort of fibration by surfaces known as a Lefschetz fibration. Following this, it was natural to ask to what extent arbitrary smooth 4-manifolds admit similar structures. In this talk, I will discuss joint work with John Etnyre which demonstrates that any smooth 4- manifold contains an embedded curve such that the manifold obtained by surgery along that curve admits an achiral Lefschetz fibration.

4:05 pm, Skiles 269
Speaker: Dan Margalit (University of Utah)
Title of talk: A topological proof of Mess’s theorem
Abstract: The Torelli group is the subgroup of the mapping class group consisting of elements which act trivially on the homology of the surface. In his 1989 thesis Geoff Mess proved the celebrated theorem that the Torelli group in genus 2 is an infinitely generated free group. While his proof is algebro-geometric, we give a new, topological, approach, with a view towards the higher genus cases.

5:10 pm, Skiles 269
Speaker: Brendan Owens (LSU)
Title of talk: Crossing changes and slice knots
Abstract: The slicing number of a knot is the minimum number of crossing changes required to convert to a slice knot. I will show that for many knots, previous bounds on unknotting number obtained by Ozsvath and Szabo and the speaker are in fact bounds on slicing number. I will also discuss a refined slicing invariant due to Livingston and exhibit an infinite family of knots for which Livingston's invariant is strictly greater than the slice genus.

TUESDAY, January 23, 2007

VIGRE-Graduate Student Seminar
2:00p.m., Room 304
Speaker: Dan Margalit, University of Utah
Title of talk: Introduction to moduli space
Abstract: In topology, the surface of a donut is called a "torus". We can have a thick torus, like an inner tube, or a thin torus, like a hula hoop. In a sense, the most symmetric torus is very different from both of these. What does this space of donuts look like and what does it mean? We will give a gentle introduction and answer some of the basic questions, indicating directions for further study.

WEDNESDAY, January 24, 2007

Algebraic Geometry
2:30pm, Room 410
Speaker: Elham Izadi, University of Georgia
Title of talk: An inductive approach to the Hodge conjecture for abelian varieties
Abstract: After some preliminaries and background, I will describe an inductive approach most appropriate for abelian varieties with an action of an imaginary quadratic field.

Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea

Number Theory/Arithmetic Geometry
3:30pm, Room 304
No Meeting this week

VIGRE – Quantum Mechanics
4:45pm, Room 302

THURSDAY, January 25, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Moduli spaces
2:00pm, Room 304

VIGRE-Geometry
2:00pm, Room 410

FRIDAY, January 26, 2007

Geometry
2:30pm, Room 410
Speaker: Aaron Abrams, Emory University
Title of talk: Dissecting a square
Abstract: I will talk about the following (old and solved) problem: if you want to cut a square into triangles of equal area, how many triangles can you use? I will discuss the old solution and a new approach. (Organizer's note: Aaron's new approach will involve algebraic geometry in a nontrivial way and may be of interest to algebraic geometers as well as the usual audience for geometry seminar.)

VIGRE – Algebra
2:30pm, Room 304

VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 410