Seminar Schedule
February 21- February 25, 2005

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

MONDAY, February 21, 2005

Algebra
2:30 – 3:30p.m., Room 410
Speaker: Dan Nakano, University of Georgia
Title of talk: Reductive groups, Frobenius kernels and Finite Chevalley Groups:
Representation theory and Cohomology, II
Abstract: The second of two talks. This talk will be on recent work with Z. Lin.

Probability Theory
2:45 - 4:00p.m., Room 222
Speaker: Lirong Yu, University of Georgia
Title of talk: Expansion of a probability vector associated with a Markov chains with weak and strong interactions

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

Lie Theory
3:30-4:30p.m., Room 303
No Meeting this week

Topology
3:30-4:30p.m., Room 326
Speaker: Ken Baker, University of Georgia
Title of talk: Ozsvath-Szabo Invariants

CATS
4:40-5:30p.m., Room 306
Speaker: Yinglei Song, Department of Computer Science, University of Georgia
Title of talk: Tree decomposition based optimization algorithms (1)
Abstract: For nearly two decades, the concepts of tree decomposition and tree width have profoundly affected the fields of both graph theory and algorithm research. In this talk, I will provide a survey on the impact of the tree decomposition and tree width on algorithm design and complexity study.

A widely known fact is that, on graphs with bounded tree width, many NP-hard optimization problems, such as maximum independent set, mininum dominating set etc, have linear time algorithms. Although finding the minimum tree width of a graph is also NP-hard, a parameterized linear time algorithm developed by Bodlaender can determine whether a graph has a tree decomposition with its tree width less than a given parameter k.

References:

1. N. Robertson and P. D. Seymour, "Graph Minors II. Algorithmic aspects of tree-width", Journal of Algorithms, vol 7, pp. 309-322, 1986.
2. S. Arngorg and A. Proskurowski, "Linear time algorithms for NP-hard problems restricted to partial k-trees", Discrete Applied Mathematics 23: pp11-24, 1989.
3. H. L. Bodlaender, "A linear time algorithm for finding tree-decompositions of small tree width", SIAM Journal on Computing, vol 25, pp. 1305-1317, 1996.
4. H. L. Bodlaender, "Discovering Treewidth", SOFSEM 2005, LNCS 3381, pp. 1-16, 2005.


TUESDAY, February 22, 2005

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Chad Mullikin, University of Georgia
Title of talk: The Algebra Dance
Abstract: The Banach-Tarski paradox is an example of the hypocrisy of intuition. It says, if we assume the axiom of choice, then given a ball in R^n for n>2 of finite nonzero radius r we can cut this ball into finitely many sets, move the sets around, glue them back together and have a ball of radius 2r. Even better, we only move the pieces by rotations (this is the Algebra Dance part).

Why does this mean our intuition is hypocritical you may ask? It's because of the axiom of choice. The axiom of choice says if C is any collection of nonempty sets, then we can choose a member from each set in that collection to form a new set B so that the intersection of B with any set in C is nonempty. The axiom of choice is equivalent to the following statements:

If A and B are any two sets then either |A| <= |B| or |B| <= |A|. Any vector space over a field F has a basis. Any product of compact topological spaces is compact.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
Speaker: Robert Rumely, University of Georgia
Title of talk: Benedetto's no wandering domains theorem

WEDNESDAY, February 23, 2005

Spline Analysis
1:30-2:30pm, Room 326
Speaker: V. Baramidze, University of Georgia
Title of talk: Markov's Inequality over Spherical Triangles, continued

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: Harry Tamvakis, Brandeis
Title of talk: "Gromov-Witten invariants on Grassmannians"
Abstract: Let G be a classical Lie group and P a maximal parabolic subgroup. The homogeneous space X = G/P is a Grassmannian parametrizing (isotropic) subspaces in a (symplectic or orthogonal) complex vector space. We show that
the three-point genus zero Gromov-Witten invariants on X are equal (or related) to classical intersection numbers other homogeneous spaces of the same Lie type as X. The main application is an explicit quantum Pieri rule which determines the structure of the small quantum cohomology ring of X. This is joint work with Anders Buch and Andrew Kresch.

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

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

VIGRE-Algebra
3:45-4:45pm, Room 303 (Please note change in time is for this week only.)
Organizers: Brian Boe, Daniel Nakano, University of Georgia
Title of talk: Proving conjectures beyond p^2

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

THURSDAY, February 24, 2005

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

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

Colloquium
3:30p.m., Room 304
Speaker: Harry Tamvakis, Brandeis
Title of talk: "From linear algebra and puzzles to quantum cohomology"
Abstract: The cohomology ring of the Grassmannian X=G(k,n) has been studied for well over 100 years, but the last decade has seen surprising new twists to the story. I will explain the beautiful puzzle rule of Knutson-Tao-Woodward for the triple intersection numbers on X, and an extension of this rule that conjecturally computes all 3-point, genus zero Gromov-Witten invariants on X. These numbers are the structure constants of the quantum cohomology ring of X. Only linear algebra is required to follow most of this talk.

Student Arithmetic/Algebraic Geometry Seminar
3:30p.m., Room 304
No Meeting this week

FRIDAY, February 25, 2005

Geometry
2:30p.m., Room 326
Speaker: Adam Fletcher, University of Georgia
Title of talk: Mathematicians Have Curves in All the Right Spaces
Abstract: It's back to the "basics" of differential and Riemannian geometry with a discussion of the ideas of curvature in the plane, in space, and on surfaces and manifolds. The talk will be aimed at first year graduate students and advanced undergraduates with some points of interest and refreshment for the seasoned geometer.

Special Algebra Seminar
2:30p.m., Room 222
Speaker: Brian Parshall, University of Virginia
Title of talk: Characters and cohomology

Joint Analysis
3:30p.m., Room 304
Speaker: Akos Magyar, University of Georgia
Title of talk: On a theorem of Katznelson-Weiss

VIGRE – Clifford Algebras
3:30-4:45p.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), continued