Seminars and Colloquia by Series

Hypergeometric functions - the GKZ-perspective

Series
Geometry Topology Seminar
Time
Monday, April 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Uli Walther – Purdue University
Starting with some classical hypergeometric functions, we explain how to derive their classical univariate differential equations. A severe change of coordinates transforms this ODE into a system of PDE's that has nice geometric aspects. This type of system, called A-hypergeometric, was introduced by Gelfand, Graev, Kapranov and Zelevinsky in about 1985. We explain some basic questions regarding these systems. These are addressed through homology, combinatorics, and toric geometry.

Numerical Methods for Total Variation and Besov Smoothing

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Stacey Levine – Duquesne University
We present new finite difference approximations for solving variational problems using the TV and Besov smoothness penalty functionals. The first approach reduces oversmoothing and anisotropy found in common discrete approximations of the TV functional. The second approach reduces the staircasing effect that arises from TV type smoothing. The algorithms converge and can be sped up using a multiscale algorithm. Numerical examples demonstrate both the qualitative and quantitative behavior of the solutions.

Polynomial hierarchy, Betti numbers and a real analogue of Toda's theorem

Series
ACO Seminar
Time
Friday, April 10, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Saugata Basu – School of Mathematics, Georgia Tech and Purdue University
Toda proved in 1989 that the (discrete) polynomial time hierarchy, {\bf PH}, is contained in the class {\bf P}^{#\bf P}, namely the class of languages that can be decided by a Turing machine in polynomial time given access to an oracle with the power to compute a function in the counting complexity class #{\bf P}. This result which illustrates the power of counting is considered to be a seminal result in computational complexity theory. An analogous result in the complexity theory over the reals (in the sense of Blum-Shub-Smale real Turing machines) has been missing so far. We formulate and prove a real analogue of Toda's theorem. Unlike Toda's proof in the discrete case, which relied on sophisticated combinatorial arguments, our proof is topological in nature. (Joint work with Thierry Zell.)

The Jones polynomial and quantum invariants

Series
Geometry Topology Working Seminar
Time
Friday, April 10, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Thang Le – School of Mathematics, Georgia Tech

Please Note: These are two hour talks.

We will develop general theory of quantum invariants based on sl_2 (the simplest Lie algebra): The Jones polynomials, the colored Jones polynomials, quantum sl_2 groups, operator invariants of tangles, and relations with the Alexander polynomial and the A-polynomials. Optional: Finite type invariants and the Kontsevich integral.

Linear algebra method in combinatorics

Series
SIAM Student Seminar
Time
Friday, April 10, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Tianjun Ye – School of Mathematics, Georgia Tech
Linear algebra method is a very useful method in combinatorics. Lovas Theorem (a very deep theorem about perfect graph) is proved by using this way. The idea is, if we want to come up with an upper bound on the size of a set of objects, associate them with elements in a vector space V of relatively low dimension, and show that these elements are linearly independent. Then we cannot have more objects in our set than the dimension of V. We will show we can use this way to solve some combinatorics problem, such as odd town problem and two-distance sets problem.

Cameron-Martin theorem for Complete Noncompact Riemannian Manifold

Series
Stochastics Seminar
Time
Thursday, April 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Elton Hsu – Department of Mathematics, Northwestern University
The Cameron-Martin theorem is one of the cornerstones of stochastic analysis. It asserts that the shifts of the Wiener measure along certain flows are equivalent. Driver and others have shown that this theorem, after an appropriate reformulation, can be extension to the Wiener measure on the path space over a compact Riemannian manifold. In this talk we will discuss this and other extensions of the Cameron-Martin theorem and show that it in fact holds for an arbitrary complete Riemannian manifold.

Quantum Computing: What is it?

Series
ACO Student Seminar
Time
Wednesday, April 8, 2009 - 13:30 for 2 hours
Location
ISyE Executive Classroom
Speaker
Jean Bellissard – Schools of Mathematics and Physics, Georgia Tech
This short introduction to the principles of Quantum Computation will give hints upon why quantum computers, if they are built, will revolutionize the realm of information technology. If Physicists and Engineers can produce such machines, all the security protocoles used today will become obsolete and complex computations called NP will become easy. From the example of trapped ion computation, the talk will explain how Quantum Mechanics helps encoding information. The notion of quantum gate, the elementary brick of computation, will be introduced and some example of elementary program will be described. Comments about the Fourier transformalgorithm, its potential speed and its application to code breaking will end this talk.

PDE Techniques in Wavelet Transforms and Applications Image Processing, Part II

Series
Research Horizons Seminar
Time
Wednesday, April 8, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Hao Min Zhou – School of Mathematics, Georgia Tech
This talk will be a continuation of the one I gave in this Seminar on March~11. I will present a brief introduction to use partial differential equations (PDE) and variational techniques (including techniques developed in computational fluid dynamics (CFD)) into wavelet transforms and Applications in Image Processing. Two different approaches are used as examples. One is PDE and variational frameworks for image reconstruction. The other one is an adaptive ENO wavelet transform designed by using ideas from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing.

Socially-induced Synchronization of Avian Ovulation Cycles

Series
Mathematical Biology Seminar
Time
Wednesday, April 8, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Shandelle Henson – Andrews University
Oscillator synchrony can occur through environmental forcing or as a phenomenon of spontaneous self-organization in which interacting oscillators adjust phase or period and begin to cycle together. Examples of spontaneous synchrony have been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women. Many colonial birds breed approximately synchronously within a time window set by photoperiod. Some studies have suggested that heightened social stimulation in denser colonies can lead to a tightened annual reproductive pulse (the “Fraser Darling effect”). It has been unknown, however, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We will discuss socially-stimulated egg-laying synchrony in a breeding colony of glaucous-winged gulls using Monte Carlo analysis and a discrete-time dynamical system model.

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