Seminars and Colloquia by Series

How likely is Buffon's needle to land near a 1-dimensional Sierspinski gasket? A power estimate via Fourier analysis.

Series
Analysis Seminar
Time
Wednesday, November 18, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Matt Bond – Michigan State University
It is well known that a needle thrown at random has zero probability of intersecting any given irregular planar set of finite 1-dimensional Hausdorff measure. Sharp quantitative estimates for fine open coverings of such sets are still not known, even for such sets as the Sierpinski gasket and the 4-corner Cantor set (with self-similarities 1/4 and 1/3). In 2008, Nazarov, Peres, and Volberg provided the sharpest known upper bound for the 4-corner Cantor set. Volberg and I have recently used the same ideas to get a similar estimate for the Sierpinski gasket. Namely, the probability that Buffon's needle will land in a 3^{-n}-neighborhood of the Sierpinski gasket is no more than C_p/n^p, where p is any small enough positive number.

Grothendieck Topologies

Series
Other Talks
Time
Wednesday, November 18, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Doug Ulmer – Ga Tech
In the 60s, Grothendieck had the remarkable idea of introducing a new kind of topology where open coverings of X are no longer collections of subsets of X, but rather certain maps from other spaces to X.  I will give some examples to show why this is reasonable and what one can do with it.

Panel Discussion with Students About the Hiring Process.

Series
Research Horizons Seminar
Time
Wednesday, November 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Drs. Ulmer, Harrell, and Wick – School of Mathematics, Georgia Tech
The Research Horizons seminar this week will be a panel discussion on the academic job market for mathematicians. The discussion will begin with an overview by Doug Ulmer of the hiring process, with a focus on the case of research-oriented universities. The panel will then take questions from the audience. Professor Wick was hired last year at Tech, so has recently been on the students' side of the process. Professor Harrell has been involved with hiring at Tech for many years and can provide a perspective on the university side of the process.

Virulence evolution in a naturally occurring parasite of monarch butterflies

Series
Mathematical Biology Seminar
Time
Wednesday, November 18, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jaap de Roode – Emory University

Please Note: Host: Meghan Duffy (School of Biology, Georgia Tech)

Why do parasites cause disease? Theory has shown that natural selection could select for virulent parasites if virulence is correlated with between-host parasite transmission. Because ecological conditions may affect virulence and transmission, theory further predicts that adaptive levels of virulence depend on the specific environment in which hosts and parasites interact. To test these predictions in a natural system, we study monarch butterflies (Danaus plexippus) and their protozoan parasite (Ophryocystis elektroscirrha). Our studies have shown that more virulent parasites obtain greater between-host transmission, and that parasites with intermediate levels of virulence obtain highest fitness. The average virulence of wild parasite isolates falls closely to this optimum level, providing additional support that virulence can evolve as a consequence of natural selection operating on parasite transmission. Our studies have also shown that parasites from geographically separated populations differ in their virulence, suggesting that population-specific ecological factors shape adaptive levels of virulence. One important ecological factor is the monarch larval host plants in the milkweed family. Monarch populations differ in the milkweed species they harbor, and experiments have shown that milkweeds can alter parasite virulence. Our running hypothesis is that plant availability shapes adaptive levels of parasite virulence in natural monarch populations. Testing this hypothesis will improve our understanding of why some parasites are more harmful than others, and will help with predicting the consequences of human actions on the evolution of disease.

Kinetic-Fluid Boundary Layers and Applications to Hydrodynamic Limits of Boltzmann Equation (canceled)

Series
PDE Seminar
Time
Tuesday, November 17, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ning Jiang – Courant Institute, New York University
In a bounded domain with smooth boundary (which can be considered as a smooth sub-manifold of R3), we consider the Boltzmann equation with general Maxwell boundary condition---linear combination of specular reflection and diffusive absorption. We analyze the kinetic (Knudsen layer) and fluid (viscous layer) coupled boundary layers in both acoustic and incompressible regimes, in which the boundary layers behave significantly different. The existence and damping properties of these kinetic-fluid layers depends on the relative size of accommodation number and Kundsen number, and the differential geometric property of the boundary (the second fundamental form.) As applications, first we justify the incompressible Navier-Stokes-Fourier limit of the Boltzmann equation with Dirichlet, Navier, and diffusive boundary conditions respectively, depending on the relative size of accommodation number and Kundsen number. Using the damping property of the boundary layer in acoustic regime, we proved the convergence is strong. The second application is that we derive and justified the higher order acoustic approximation of the Boltzmann equation. This is a joint work with Nader Masmoudi.

Seip's Interpolation Theorem in Weighted Bergman Spaces

Series
Analysis Working Seminar
Time
Monday, November 16, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Brett Wick – Georgia Tech
We are going to continue explaining the proof of Seip's Interpolation Theorem for the Bergman Space. We are going to demonstrate the sufficiency of these conditions for a certain example. We then will show how to deduce the full theorem with appropriate modifications of the example.

Multiscale modeling of granular flow

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Chris Rycroft – UC-Berkeley
Due to an incomplete picture of the underlying physics, the simulation of dense granular flow remains a difficult computational challenge. Currently, modeling in practical and industrial situations would typically be carried out by using the Discrete-Element Method (DEM), individually simulating particles according to Newton's Laws. The contact models in these simulations are stiff and require very small timesteps to integrate accurately, meaning that even relatively small problems require days or weeks to run on a parallel computer. These brute-force approaches often provide little insight into the relevant collective physics, and they are infeasible for applications in real-time process control, or in optimization, where there is a need to run many different configurations much more rapidly. Based upon a number of recent theoretical advances, a general multiscale simulation technique for dense granular flow will be presented, that couples a macroscopic continuum theory to a discrete microscopic mechanism for particle motion. The technique can be applied to arbitrary slow, dense granular flows, and can reproduce similar flow fields and microscopic packing structure estimates as in DEM. Since forces and stress are coarse-grained, the simulation technique runs two to three orders of magnitude faster than conventional DEM. A particular strength is the ability to capture particle diffusion, allowing for the optimization of granular mixing, by running an ensemble of different possible configurations.

Spectral methods in Hamiltonian PDE

Series
CDSNS Colloquium
Time
Monday, November 16, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Wei-Min Wang – Universite Paris-Sud, France
We present a new theory on Hamiltonian PDE. The linear theory solves an old spectral problem on boundedness of L infinity norm of the eigenfunctions of the Schroedinger operator on the 2-torus. The nonlinear theory develops Fourier geometry, eliminates the convexity condition on the (infinite dimension) Hamiltonian and is natural for PDE.

Stability methods and extremal graph theory

Series
Combinatorics Seminar
Time
Friday, November 13, 2009 - 15:05 for 2 hours
Location
Skiles 255
Speaker
Miklos Simonovits – Alfred Renyi Institute, Budapest, Hungary

Stability methods are often used in extremal graph theory, Ramsey theory and similar areas, where an extremal problem is to be solved and

  1. we have a conjecture about the structure of the conjectured extremal configurations and according to our conjecture, it has some given property \mathcal P;
  2. we can prove that all the almost extremal structures are near to the property \mathcal P, in some sense;
  3. if we knew that if a structure is near to the property \mathcal P and is extremal, then it is already the conjectured structure.

Of course, stability methods can also be used in other cases, but we restrict ourselves to the above two areas.

In my lecture I will give an introduction to the applications of the stability methods in extremal graph theory, describe cases in extremal graph theory, extremal hypergraph theory, in the Erdos-Frankl-Rold (= generalized Erdos-Kleitman-Rothschild theory) ...

In the second part of my lecture I shall describe the application of this method to the Erdos-Sos conjecture. This is part of our work with Ajtai, Komlos and Szemeredi.

From Gibbs free energy to the dynamical system with random perturbation

Series
SIAM Student Seminar
Time
Friday, November 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao Li – School of Mathematics, Georgia Tech
Gibbs free energy plays an important role in thermodynamics and has strong connection with PDE, Dynamical system. The results about Gibbsfree energy in 2-Wasserstein metric space are known recently.First I will introduce some basic things, so the background knowledge isnot required. I will begin from the classic definition of Gibbs freeenergy functional and then move to the connection between Gibbs freeenergy and the Fokker-Planck equation, random perturbation of gradientsystems. Second, I will go reversely: from a dynamical system to thegeneralized Gibbs free energy functional. I will also talk about animportant property of the Gibbs free energy functional: TheFokker-Planck equation is the gradient flux of Gibbs free energyfunctional in 2-Wasserstein metric.So it is natural to consider a question: In topological dynamical systemand lattice dynamical system, could we give the similar definition ofGibbs free energy, Fokker-Planck equation and so on? If time allowed, Iwill basicly introduce some of my results in these topics.

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