Seminar Schedule
March 7 - March 11, 2005

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

MONDAY, March 7, 2005

Algebra
2:30 – 3:30p.m., Room 410
Joint seminar with VIGRE-Algebra this week, please see Wednesday schedule.

Probability Theory
2:45 - 4:00p.m., Room 222
Speaker: M. Pemy, University of Georgia
Title of talk: Structural properties of 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, continued

CATS
4:40-5:30p.m., Room 306
Speaker: Gregory Baramidze, Department of Computer Science, University of Georgia
Title of talk: Leaf languages -- "complexity theory made easy"
Abstract: Papadimitriou [1] calls this "an amusing and instructive way of looking at ... diverse complexity classes ... from a unified point of view". The concept of leaf languages was apparently first developed by Papadimitriou and Sipser around 1979 as a teaching tool for their complexity classes. It was later rediscovered and published independently by Bovet, Creszenzi, and Silvestry in 1992 [2], and Vereshchagin in 1993 [3]. The concept of leaf languages arises from generalized acceptance criteria for nondeterministic computation models. Here the input word is said to be accepted if the leaf word of the computation (the word made of the leaves of the computation tree) belongs to a certain language. It can be shown that any language A (the leaf language) determines a complexity class C(A).

A number of interesting facts and insights were discovered with relation to leaf languages. The talk will survey some of the results in this area. It is based mostly on the survey paper by Heribert Vollmer [4].

References:

1. C. H. Papadimitriou, Computational Complexity (Addison-Wesley, Reading, MA, 1994).
2. D. P. Bovet, P. Crescenzi, and R. Silvestri, A uniform approach to define complexity classes. Theoret. Comp. Sci. 104, 263 -- 283 (1992).
3. N. K. Vereshchagin, Relativizable and non-relativizable theorems in the polynomial theory of algorithms. Izvestija Rossijskoj Akademii Nauk 57, 51 -- 90 (1993). In Russian.
4. H. Vollmer, Complexity Theory Made Easy. The Formal Language Approach to the definition of Complexity Classes. Proc. 7th Developments in Language Theory Vol. 2710, 95 --110, 2003. Springer-Verlag.
5. M. Galota, S. Kosub, and H. Vollmer. Generic separations and leaf languages. Mathematical Logic Quarterly , 49, No. 4, 353 -- 362 (2003).


TUESDAY, March 8, 2005

VIGRE Graduate Student Seminar
2:00p.m., Forestry Bldg., Room 304
Speaker: Greg Warrington, Wake Forest University
Title of talk: Juggling Probabilities
Abstract: There is a natural way to view a person juggling as a Markov process by assuming that the juggler throws to random heights. I make this association for the simplest reasonable model of random juggling and compute the steady state probabilities in terms of the Stirling numbers of the second kind. I also explore several alternate models of juggling. The mathematics will be illustrated with juggling demonstrations.

Algebraic Geometry
03:30-04:45p.m., Room 410
Speaker: Dino Lorenzini, University of Georgia
Title of talk: Wild cyclic quotient singularities of surfaces.
Abstract: I will give a brief overview of several important problems in the
subject, and present some new results (joint with M. Raynaud).

WEDNESDAY, March 9, 2005

Spline Analysis
1:30-2:30pm, Room 326
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

VIGRE-Algebra joint with Algebra
3:30-4:30pm, Room 303
Speaker: David Hemmer, University of Toledo
Title: An introduction to Scopes' block equivalence for the symmetric group.

Number Theory
3:45-5:15pm, Room 304
Speaker: Dino Lorenzini, University of Georgia
Title of talk: Neron models and wild ramification
Abstract: I will first review these notions in the context of elliptic curves, and then present some new results (joint with M. Raynaud). My talk in the algebraic geometry seminar is related, but not necessarily a prerequisite.


THURSDAY, March 10, 2005

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

Dynamics on Berkovich Space
2:30 PM Room 326
Speaker: Robert Rumely, University of Georgia
Title of talk: Benedetto's no wandering domains theorem

Student Arithmetic/Algebraic Geometry Seminar
3:30p.m., Room 304
Speaker: TBA
Title of talk: TBA

Special Number Theory Seminar
3:30pm, Room 326
Speaker: Tom Tucker, University of Rochester
Title of talk: TBA

FRIDAY, March 11, 2005

Geometry
2:30p.m., Room 326
No meeting this week, due to the Southeast Geometry Conference at U. of
South Carolina on March 11-12.

Joint Analysis
3:30p.m., Room 303
Speaker: Mihalis Koluntzakis, Univ. of Crete and Ga Tech
Title of talk: The Fuglede Conjecture
Abstract: Fuglede conjectured in the 70s that a domain D in Euclidean space admits an orthogonal basis of exponentials e^{2 pi i k x} (for some set K of frequencies k; K is called a spectrum of D and D is then called spectral) if and only if D can tile Euclidean space by translation.

After a long series of results supporting the conjecture, in the 90s mostly, the direction "spectral -> tile" was disproved by Tao (2003) in dimension 5. He gave a simple example using Hadamard matrices. Kolountzakis and Matolcsi disproved the direction "tile -> spectral" in 2004, also in dimension 5. The dimension of counterexamples in both directions has since come down to 3. In all cases counterexamples are first constructed in some appropriate finite group, for subsets of which the conjecture also makes sense.

In this talk I will describe the problem and its history and will sketch some results including the counterexamples.

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: Factorization of Multivariate Positive Polynomials
Abstract: This talk is based on a joint work with J. Geronimo at Georgia Tech. We give a new proof to a recent result of Dritschel about the factorization of multivariate positive polynomials. That is, if a Laurent polynomial P is strictly positive on the multi-torus, it can be factorized into a finitely many polynomals p_i such that P= sum_i |p_i|^2. We finally show how to compute such a factorization numerically.