University of Georgia
Department of Mathematics

Seminar Schedule
January 31 – February 4, 2005

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

MONDAY, January 31, 2005

Algebra
2:30 – 3:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title of talk: An introduction to the cohomology of groups
Abstract: My intention is to go over the basic algebraic and topological definitions of group cohomology, say why they give the
same answer, give a few examples, and talk a little bit about duality. This talk is intended for Graduate Students.

Probability Theory
2:45-4:00p.m., Room 222
Speaker: Q. Zhang, University of Georgia
Title of talk: Two-time scale Markov chains (cont.)

Faculty and Graduate Social
3:00p.m., Room 409
Coffee, Cookies, Tea

Topology
3:30-4:30p.m., Room 326
Speaker: Will Kazez, University of Georgia
Title of talk: Computing Ozsvath-Szabo invariants, continued

CATS
4:40-5:30p.m., Room 306
Speaker: Ananda Chowdbury, Dept. of Computer Science, University of Georgia
Title of talk: Solving Jigsaw Puzzles by a Computer
Abstract: The jigsaw puzzle assembly problem is regarded as a classical problem in pattern recognition and was first addressed by Freeman et al. as early as 1964. After 24 years in 1988, Wolfson et al. proposed a novel algorithm for assembling large jigsaw puzzles (with many almost similar pieces) using curve matching and combinatorial optimization techniques. The algorithm by Wolfson et al. could successfully handle a puzzle assembly of 104 pieces. Even the algorithm could be extended to solve an
intermixed puzzle of 208 pieces which is an assembly of two intermixed 104-piece puzzles. I will briefly touch upon the curve matching part and mainly focus on the combinatorial optimization issues of this very interesting puzzle assembly algorithm (by Wolfson et al.).

TUESDAY, February 1, 2005

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Clay Petsche, University of Georgia
Title of talk: The p-adic Numbers
Abstract: This will be a gentle introduction to the field of p-adic numbers. Although this number theoretic object shares many properties in common with the field of real numbers, the p-adic field can be rather bizarre in some respects as well. For example, in this field the closed unit ball forms a ring, every triangle is isosceles, and in any open ball, every point is the center! We'll discuss these oddities and more.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
Speaker: Robert Rumely, University of Georgia
Title of talk: Wandering Domains

WEDNESDAY, February 2, 2005

Spline Analysis
1:30-2:30pm, Room 326
Speaker: V. Baramidze, University of Georgia
Title of talk: Markov's Inequality over Spherical Triangles
Abstract: I will show how to prove Markov's inequality over spherical triangles using the radial projection method introduced in a previous week.

Algebraic Geometry
2:30-3:45 p.m., Room 410
No Meeting this week

VIGRE – Cardiac Physiology
2:30p.m., Room 640

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Colloquium
3:30p.m., Room 304
Speaker: David Savitt, McGill University
Title of talk: Modular Galois representations
Abstract: The study of Galois representations (representations of Galois groups) plays a fundamental role in number theory today. By a celebrated theorem of Deligne, one can associate to every modular form a two-dimensional (p-adic) representation of the automorphism group of the field of algebraic numbers. To what extent is the converse true? The first breakthrough in this direction was Wiles's work proving Fermat's last theorem, in which Galois representations played an intermediary role between elliptic curves and modular forms. We will describe recent progress in this area, with an emphasis on p-adic aspects of the theory.

VIGRE – Algebra
2:30-3:30p.m., Room 222*
*Please note the change of time and room are for this week only
Speakers: Daniel Nakano, Brian Boe, University of Georgia
Title of activity: Beyond p^2 continued

Student Arithmetic/Algebraic Geometry Seminar
3:30-4:45p.m., Room 326
Speaker: TBA
Title of talk: TBA

Number Theory
3:45-5:15pm, Room 304
No Meeting this week


THURSDAY, February 3, 2005

VIGRE – Algebraic Geometry
2:00p.m., Room 304

FRIDAY, February 4, 2005

Geometry
2:30p.m., Room 326
Speaker: Jason Cantarella, U. of Georgia
Title of talk: How hard is it to find the self-contacts of a tube or necklace? (part II)
Abstract: Suppose you are given a necklace of N tangent unit-radius spheres in 3-space, and you want to figure out whether or not any of these two spheres overlap. One obvious algorithm is to calculate the distances between each pair of sphere centers. Since there are N spheres, there are O(N^2) pairs, and this algorithm takes time O(N^2). Various computational-geometric methods have been proposed to accomplish this task faster-- for instance in (expected) time O(N log N) (but worst-case time O(N^2)). In this talk, we'll prove that for "well-behaved" necklaces, a class of partitioning methods is guaranteed to solve the problem in time O(N^{4/3}). (This is an expository talk.)

VIGRE – Clifford Algebras
3:30-4:30p.m. Room 302

Wavelet Analysis
3:30-4:30p.m., Room 322
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: The reversed polynomials (Christoffel-Darboux formula)