University of Georgia
Department of Mathematics

Seminar Schedule
August 29 - September 2, 2005
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, August 29, 2005

Algebra
2:30p.m., Room 410
Speaker: Emilie Wiesner, University of Georgia
Title of talk: The Shapovalov determinant and Translation Functors for the Virasoro Algebra (Day 1).
Abstract: Lie algebras with triangular decomposition generalize finite dimensional simple Lie algebras, and much of the representation theory still works in the more general setting. In particular, we can still define the category of modules $\mathcal{O}$ and obtain a decomposition of this category by blocks. Therefore we can consider translation between blocks (that is, translation functors). The Virasoro algebra is a concrete example of a Lie algebra with triangular decomposition. In my thesis, I considered translation functors for the Virasoro algebra, using the Shapovalov determinant as my primary tool. On Day One of my talk, I will introduce the Virasoro algebra along with some of its representation theory and try to motivate using the Shapovalov determinant as a useful tool for studying translation functors. On Day Two, I'll talk about some of my results.

Topology/Geometry
2:30pm, Room 303
Speaker: Ken Baker, University of Georgia
Title of talk: 3-string braids and once-punctured torus bundles
Abstract: The double branched cover of a closed 3-string braid in a solid torus is a once-punctured torus bundle. If the closed 3-string braid is in S^3, then in the double branched cover the braid axis becomes a genus one fibered knot. We will demonstrate how one may visualize these relationships. Using these techiniques we will put forth a classification of genus one fibered knots in lens spaces. This is a work in progress.

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

TUESDAY, August 30, 2005

VIGRE-Graduate Student Seminar
2:00p.m., Room 303
Speaker: Robert Rumely, University of Georgia
Title of talk: VIGRE group introduction (number theory)

WEDNESDAY, August 31, 2005

Algebraic Geometry
2:30-3:45pm, Room 410
Speaker: Carel Faber, Johns Hopkins University
Title of talk: Complete subvarieties and the Prym map.
Abstract: I will report on joint work with Gerard van der Geer, in which we attempt to construct a complete subvariety of M_g of dimension g-2 in positive characteristic. The attempt as such was unsuccessful, but some results obtained along the way appear to be of independent interest.

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

Number Theory
3:30-5:00pm, Room 304
Speaker: Clayton Petsche, University of Georgia
Title of talk: Torsion points on elliptic curves over number fields of large degree.
Abstract: Let k be a number field of degree d=[k:Q], and let E/k be an elliptic curve. I will discuss the problem of giving bounds on the number of k-rational torsion points that depend explicitly on: (i) both k and E, (ii) k only, or (iii) d only. For example, a very deep theorem of Merel settled case (iii), showing that a bound exists that depends on d only. It is still an interesting open problem, however, to decide how the optimal bound should depend on d; and in particular, to decide whether the optimal bound should grow polynomially with d. I will discuss recent work that relates these questions to a well-known conjecture of Szpiro concerning the conductor and discriminant of E/k.

VIGRE-Algebra
3:45p.m. , Room 326
Speakers: Daniel Nakano and Brian Boe, University of Georgia
Title of talk: Lie algebra cohomology and semisimple Lie algebras

VIGRE Algebraic Geometry Group
3:45 pm in room 303
Speaker: Maxim Arap, University of Georgia
Title of talk: Definition and first properties of complex projective spaces

THURSDAY, September 1, 2005

VIGRE-Graduate Student Seminar
2:00p.m., Room 303
Speaker: Ken Baker, University of Georgia
Title of talk: Braiding in lens spaces
Abstract: A classical theorem of Alexander states that every oriented link in S^3 can be represented as a the closure of a braid. Observe how this suggests the decomposition of S^3 as a union of two solid tori along their boundaries. Viewing one of these solid tori as a neighborhood of the braid axis, Alexander's theorem says that any oriented link may be made to lie in the other solid torus in a well-groomed fashion. Lens spaces are also unions of two solid tori along their boundaries. In this VIGRE group our main goal is to study to what extent an analogue of Alexander's theorem holds for links in lens spaces. To this end we will address various topics in classical (i.e. S^3) knot theory and braid theory, some techniques of 3-manifold topology, and of course lens spaces.

FRIDAY, September 2, 2005

Probability Theory
2:30pm, Room 303
Speaker: Q. Zhang, University of Georgia
Title of talk: Pricing Bond with Regime Switching

Grant Writing Workshop
3:30-4:30pm, Room 323
Valery Alexeev, Dan Nakano, and Bill Graham will discuss grant writing, including how to write a good proposal, and what NSF panels are looking for. Postdocs are especially encouraged to attend, but we hope other faculty members and graduate students will show up to offer suggestions, comments, and questions.