University of Georgia
Department of Mathematics

Seminar Schedule
January 29 – February 2, 2007

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, January 29, 2007

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

Topology
2:30pm, Room 304
Speaker: Valerie Hower, University of Georgia
Title of talk: Comparing the topology of real and complex toric varieties
Abstract: By definition, a real algebraic variety X is maximal if the sum of the mod 2 Betti numbers of the real points X(R) is equal to the sum of the mod 2 Betti numbers of the complex points X(C). In 2004 Bihan, Franz, McCrory, and van Hamel conjectured that every toric variety is maximal. I will discuss this conjecture for the case of projective toric varieties and give some beginning examples. I will state sufficient (but definitely not necessary) conditions for a projective toric variety to be maximal, and I will present a counterexample to the conjecture.

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

TUESDAY, January 30, 2007

VIGRE-Graduate Student Seminar
2:00pm, Room 304
Speaker: Jerry Hower, University of Georgia
Title of talk: An Introduction to Modular Forms and Maeda's Conjecture
Abstract: I will first introduce modular forms and then discuss Maeda's conjecture. The latter states that certain polynomials associated to modular forms are in fact irreducible.

WEDNESDAY, January 31, 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, continued

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

Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Robert Rumely, University of Georgia
Title of talk: Applications of the Fekete-Szego Theorem with Splitting Conditions
Abstract: The Fekete-Szego theoreom with splitting conditions is a general existence theorem for algebraic points on curves defined over number fields, whose conjugates satisfy geometric constraints at each place. This talk will illustrate the theorem for the Fermat Curves $F_p$ and the modular curves $X_0(p)$, for $p$ a prime.

VIGRE – Quantum Mechanics
4:45pm, Room 302


THURSDAY, February 1, 2007

VIGRE – ODE
2:00pm, Room 326

VIGRE – Moduli spaces
2:00pm, Room 304

VIGRE – Geometry
2:00pm, Room 410

FRIDAY, February 2, 2007

Applied Math
12:20-1:10pm, Room 326
Speaker: Ming-Jun Lai, University of Georgia
Talk of title: Multivariate Splines for Numerical Solution of PDE
Abstract: I will explain how to use multivariate splines (smooth piecewise polynomial functions) to solve some linear and nonlinear partial differential equations. A special iteration for the associated linear systems will be presented to show that our method converges. Some numerical examples in MATLAB will be demonstrated.

Geometry
2:30pm, Room 410
Speaker: Svetlana Krat, Georgia Tech
Title of talk: On surfaces with small variation of Gaussian curvature
Abstract: Consider a surface whose total Gaussian curvature is small, where the total curvature is defined to be the integral of the absolute value of Gaussian curvature. Of course, such a surface can arise as a small perturbation of a developing surface (that is, of a surface of zero curvature). One now asks if every surface with small total curvature is actually a small perturbation of a developing surface (as opposed to the situation where there is no developing surface close to the original one). Establishing relations between intrinsic geometry of a surface and properties of this surface as a subset of the ambient space is one of the most classic areas of differential geometry. Most of the deep results in this area involve a condition that the curvature of the surface in question is non-positive or non-negative. On the other hand, there are much fewer results about the immersion of 2-dimensional smooth surfaces, whose Gaussian curvature changes sign. One such result concerns the immersion of tubes. It is known due to D. Burago, that if a complete boundary-free surface diffeomorphic to a cylinder with bounded total curvature is isometrically immersed in R3, then the image is not contained in a compact set. D. Burago suggested that the tools he developed to prove this result can also be applied to other problems related to surfaces with small total curvature. The argument we used is indeed based on these tools. Consider a simply connected, compact two dimensional surface with small total curvature in R3. The surface has a boundary, which is convex from the outside with respect to the interior metric. We proved that such a surface always lies near a smooth developing surface with almost the same boundary.

VIGRE – Algebra
3:30pm, Room 304

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