Seminars and Colloquia by Series

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 HsuDepartment 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 BellissardSchools 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 ZhouSchool 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 HensonAndrews 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.

Quasi-linear Stokes phenomenon for the Painleve first equation

Series
Analysis Seminar
Time
Tuesday, April 7, 2009 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Andrei KapaevIndiana University-Purdue University Indianapolis
Solutions of the simplest of the Painleve equations, PI, y'' = 6y^2+x, exhibit surprisingly rich asymptotic properties as x is large. Using the Riemann-Hilbert problem approach, we find an exponentially small addition to an algebraically large background admitting a power series asymptotic expansion and explain how this "beyond of all orders" term helps us to compute the coefficient asymptotics in the preceding series.

Global Weak Solutions for an Incompressible Charged Fluid with Multi-Scale Couplings - Initial-Boundary Value Problem

Series
PDE Seminar
Time
Tuesday, April 7, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Joseph Jerome Northwestern University, Evanston
The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this talk, the existence of a global distribution solution is proved to hold for the model, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is discussed. The solution obtained is quite rudimentary, and further progress would be expected in resolving issues of regularity.

Entropy and Sumsets

Series
Combinatorics Seminar
Time
Tuesday, April 7, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Adam MarcusYale University
The entropy function has a number of nice properties that make it a useful counting tool, especially when one wants to bound a set with respect to the set's projections. In this talk, I will show a method developed by Mokshay Madiman, Prasad Tetali, and myself that builds on the work of Gyarmati, Matolcsi and Ruzsa as well as the work of Ballister and Bollobas. The goal will be to give a black-box method for generating projection bounds and to show some applications by giving new bounds on the sizes of Abelian and non-Abelian sumsets.

Dispersive properties of surface water waves

Series
CDSNS Colloquium
Time
Monday, April 6, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Vera Mikyoung HurMIT
I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a precise account of the formulation of the surface water-wave problem and discussion of its distinct features. They include the dispersion relation, its severe nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing effect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some open questions regarding long-time behavior and stability.

Density of isoperimetric spectra

Series
Geometry Topology Seminar
Time
Monday, April 6, 2009 - 16:00 for 1 hour (actually 50 minutes)
Location
Emory, W306 MSC (Math and Science Center)
Speaker
Noel BradyUniversity of Oklahoma

Please Note: Joint meeting at Emory

A k--dimensional Dehn function of a group gives bounds on the volumes of (k+1)-balls which fill k--spheres in a geometric model for the group. For example, the 1-dimensional Dehn function of the group Z^2 is quadratic. This corresponds to the fact that loops in the euclidean plane R^2 (which is a geometric model for Z^2) have quadratic area disk fillings. In this talk we will consider the countable sets IP^{(k)} of numbers a for which x^a is a k-dimensional Dehn function of some group. The situation k \geq 2 is very different from the case k=1.

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