Seminar Schedule
March 21 - March 25, 2005

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

MONDAY, March 21, 2005

Algebra - Please see Wed., March 23, 2005
2:30 – 3:30p.m., Room 410

Probability Theory
2:45 - 4:00p.m., Room 222
Speaker: M. Pemy, University of Georgia
Title of talk: Proofs of 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, Dept. of Computer Science, University of Georgia
Title of talk: "Leaf Languages --complexity theory made easy (2)"

TUESDAY, March 22, 2005

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Pete Casazza, University of Missouri
Title of talk: An (Historical) Introduction to Weyl-Heisenberg Frames and Signal Processing
Abstract: Weyl-Heisenberg (Gabor) frames are at the center of a myriad of modern day applied problems in signal/image processing, data compression, biomedical engineering, optics and more. We will look at the development of this important area from a historical perspective. This will allow even non-specialists to appreciate the beauty and power of this subject. Along the way we will see some of the major applications, some of the open problems, and some of the important results in this area.

Algebraic Geometry
3:30-04:45p.m., Room 410
No Meeting this week

Geometry/Physics Seminar
2:00p.m., Room 326
Speaker: Dmitri Vassilevich, Leipzig University
Title of talk: Heat trace asymptotics
Abstract: Let D be an elliptic differential operator acting in a vector bundle over some manifold M. We define the heat trace of D by the formula Tr(exp(-tD)). The asymptotics t-->+0 of the heat trace define main geometric characteristics of the problem, and are important for the Index Theorem and for applications in physics. After a historical overwiev, I describe recent developments in the field: heat trace for the "brane-world" geometries and on non-commutative manifolds.

Dynamics on Berkovich Space
2:30 PM Room 326
No Meeting this week

Refreshments with Job Candidate
3:00p.m., Room 409

Job Candidate Talk
3:30p.m., Room 328
Speaker: Dr. Hemanshu Kaul, University of Illinois at Urbana-Champaign
Title of talk: Kauffman NK Model - A Stochastic Combinatorial Optimization Model for
Complex Systems
Abstract: Many scenarios in theoretical biology, physics, and management science can be modeled as discrete complex systems with several interacting components that can be in various states. The aim is to maximize a performance measure involving contributions from each component. This measure may depend on both the state of each component and on interactions between components. In 1987, Kauffman and Levin introduced a combinatorial optimization model for such systems, called the Kauffman NK model, where N is the number of components of the system and K measures the interaction between the components. This was proposed to model the evolution of genomes in theoretical biology but has since been applied in other areas as listed above.

Previous research on the NK model has emphasized simulations and analysis of local optima. Here we focus on rigorous results for global optima. We describe a computational setup using a stochastic network model, which leads to applicable strategies for computing bounds on global optima. Recent papers used tools from analysis and probability to obtain bounds on the expected value of the global optima for fixed K and N tending to infinity. We present bounds when K grows with N, for all N, using ideas from graph theory, probabilistic combinatorics and order statistics. These general ideas are then applied to the analysis of the cases when underlying distributions are uniform and normal distributions. The focus of the talk will be on how tools and ideas from various parts of mathematics and operations research come together in the analysis of this complex system model.


WEDNESDAY, March 23, 2005

Spline Analysis
1:30-2:30pm, Room 326
Speaker: Dr. Cheng Wang, Dept. of Math. Univ. of Tennessee, Knoxville, TN.
Title of talk: Numerical study for structural bifurcation of divergence-free vectors
Abstract: Structural stability and structural bifurcation for 2-D divergence-free vectors are analyzed, both theoretically and numerically. Boundary layer separation, symmetric stability and and interior structural transition are taken into consideration.

A driven cavity flow with Reynolds number Re=100,000, a strong shear flow induced by a temperature jump, and the secondary instability of a rising plume in Boussinesq convection, are chosen as numerical examples to verify the stability and bifurcation classifications.

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

Algebra
2:30p.m., Room 222
Speaker: Vyacheslav Futorny, University of Sao Paulo
Title: Representations of Affine Lie superalgebras
Abstract: Recent developments in the representation theory of Affine Lie superalgebras will be discussed, including a classification of irreducible modules with finite-dimensional weight spaces and integrability problem. The results will be compared with the situation for Affine and finite-dimensional Lie algebras. The talk is based on joint results with S.Eswara Rao.

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

VIGRE-Algebra
3:30-4:30pm, Room 303
Organizers: Daniel Nakano, Brian Boe, University of Georgia
Activity: Investigating restrictions of Specht modules to elementary abelians via MAGMA

Number Theory
3:45-5:15pm, Room 304
Speaker: TBA
Title of talk: TBA


THURSDAY, March 24, 2005

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

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

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

Colloquium
3:30p.m., Room 304
Speaker: Pete Casazza, University of Missouri
Title of talk: Applications of Hilbert space frames
Abstract: Hilbert space frames have traditionally been used in signal/image processing.
Recently, there have arisen a variety of new applications to wireless communication, internet coding, physics, Biomedical Engineering, speech recognition technology, and more. We will look at some of the new applications of frame theory and how frame theory has begun to impact some of the most famous unsolved problems in ``pure'' mathematics.

FRIDAY, March 25, 2005

Geometry
2:30p.m., Room 326
Speaker: Semyon Alesker, Tel Aviv University
Title of talk: Valuations on convex sets, pluripotential theory, and non-commutative determinants.

Joint Analysis
3:30p.m., Room 303
Speaker: Neil Lyall, University of Georgia
Title of talk: Sharp L^2 estimates for strongly singular integral operators on the Heisenberg group.
Abstract: I will most likely start by discussing a (translation invariant) model for strongly singular integrals in R^d and discuss two different approaches to analysing its L^2 behaviour. The first approach, which essentially restricts us to the model case, utilises the Fourier transform while the second approach frees us from this restriction.

With the "right" proof of the Euclidean result in hand it is then easy to see what one has to do to prove analogous sharp results in more general settings, for example on homogeneous groups. Easy to see - but not necessarily easy to do. I will try to indicate how this can done in the special case of the Heisenberg group, this is joint work with Norberto Laghi.

As in the Euclidean case one could also choose to analyse appropriate model operators on the Heisenberg group via Fourier transform methods, in this case using the group Fourier transform. I will also discuss partial results that have been obtained in this way.

The talk will not be overly technical and should be accessible to all graduate students.


VIGRE – Clifford Algebras
3:30-4:45p.m. Room 302

Wavelet Analysis
3:30-4:30p.m., Room 322
Speaker: Haipeng Liu, University of Georgia
Title of talk: Construction of Prewavelets in Sobolev spaces
Abstract: I will show how to construct compactly supported prewavelets in Sobolev space in the univariate setting.