Seminar Schedule
February 25 - February 29, 2008
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, February 25, 2008
VIGRE – Algebraic Geometry
2:15pm, Room 222
Topology
2:30pm, Room 303
Speaker: Shea Vick, University of Pennsylvania
Title of talk: Higher-dimensional linking integrals
Abstract: In 1833, Carl Friedrich Gauss published a half-page paper containing an integral expression which computes the linking number of two closed curves in Euclidean 3-space. The integral defined by Gauss has two important properties. On one hand, it's topological in nature, since it's purpose is to compute linking numbers. On the other hand, it's also a geometric gadget, since the its integrand is invariant under orientation-preserving isometries of Euclidean 3-space. In 2004, Dennis DeTurck and Herman Gluck defined generalizations of Gauss's geometric linking integral for closed curves in the 3-sphere and hyperbolic 3-space. In this talk, I'll present a method for computing geometric linking integrals for closed submanifolds of the n-sphere. The method is very intuitive and can easily be used to derive linking integrals in any manifold which appears as a sufficiently nice hypersurface in some Euclidean space. This is joint work with Clay Shonkwiler
Algebra
2:30pm, Room 410
No meeting this week
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, February 26, 2008
WEDNESDAY, February 27, 2008
Algebraic Geometry
2:30pm, Room 410
Speaker: Elham Izadi, University of Georgia
Title of talk: Unirationality and rationality of moduli spaces of curves, abelian varieties and related structures
Abstract: I will give an overview of known and unknown results on the rationality and unirationality of moduli spaces of curves and abelian varieties with extra structures. Then I will sketch a proof of the unirationality of the moduli space of curves of genus 5 with a non-trivial double cover.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
Colloquium
3:30pm, Room 304
Speaker: Carl Pomerance, Dartmouth College
Title of talk: Euler's function
Abstract: A familiar concept in elementary number theory and algebra, Euler's function at $n$ is the order of the unit group in the ring of integers mod $n$. It is a surprisingly rich source of interesting problems, some of them still unsolved. For example, is it always at least 2 to 1 as a mapping from the natural numbers to themselves? What is the computational complexity of computing Euler's function? Is there an asymptotic formula for the distribution of its range? These, and many more problems and results (some with UGA connections) will be discussed.
Math Club Talk
5:30-6:30pm, Room 304
Speaker: Carl Pomerance, Darmouth College
Title of talk: The covering congruences of Paul Erdos.
Abstract: Note that every integer is either even or odd. That is, the residue classes 0 mod 2 (the even numbers) and 1 mod 2 (the odd numbers) cover all of the integers. Can this be done where the moduli are all different and larger than 1? Sure, but it's harder: try 0 mod 2, 0 mod 3, 1 mod 4, 1 mod 6, and 11 mod 12. Over 50 years ago, Paul Erdos asked if one can cover with a finite collection of residue classes with distinct moduli, where the least modulus is arbitrarily large. He later wrote that this was perhaps his favorite problem. It's not so difficult to find examples with least modulus 3 or 4 or so, but no one knows any examples with least modulus greater than 36. Can you find one? This talk will give an introduction to this thorny, yet accessible research problem, discussing its origins in antiquity, some new results, and some related problems.
THURSDAY, February 28, 2008
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
2:00pm, Room 326
VIGRE – Number Theory
3:30pm, Room 303
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
FRIDAY, February 29, 2008
VIGRE-Algebra
2:30pm, Room 322
Applied Math
2:30pm, Room 302
Speaker: Kun Zhao, Georgia Tech
Title of talk: Initial Boundary Value Problem for 2D Viscous Boussinesq System
Abstract: The 2D Boussinesq systems share similar vortex stretching effects as that of 3D incompressible Euler or Navier-Stokes equations. In this talk, I will present some recent result on 2D viscous Boussinesq equations in bounded domains. The global existence of smooth solutions is obtained by the method of energy estimate. Also, the kinetic energy is found to be uniformly bounded. This is a joint work with Mingjun Lai and Ronghua Pan.
Geometry
2:30pm, Room 410
Speaker: Gordana Stojanovic, Georgia Tech
Title of talk: TBA