Seminars and Colloquia by Series

Dynamics in eigendirections of pseudo-Anosov maps on certain doubly periodic flat surfaces

Series
Geometry Topology Seminar
Time
Monday, September 12, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin Schmoll – Clemson U
We consider particle dynamics in the (unfolded) Ehrenfest Windtree Model and theflow along straight lines on a certain folded complex plane. Fixing some parameters,it turns out that both doubly periodic models cover one and the same L-shaped surface.We look at the case for which that L-shaped surface has a (certain kind of) structure preservingpseudo-Anosov. The dynamics in the eigendirection(s) of the pseudo-Anosovon both periodic covers is very different:The orbit diverges on the Ehrenfest model, but is dense on the folded complex plane.We show relations between the two models and present constructions of folded complex planes.If there is time we sketch some of the arguments needed to show escaping & density of orbits.There will be some figures showing the trajectories in different settings.

Nonconvex splitting algorithms for information extraction

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 12, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rick Chartrand – Los Alamos National Laboratory, Theoretical Division
 There has been much recent work applying splitting algorithms to  optimization problems designed to produce sparse solutions. In this talk,  we'll look at extensions of these methods to the nonconvex case, motivated  by results in compressive sensing showing that nonconvex optimization can recover signals from many fewer measurements than convex optimization. Our examples of the application of these methods will include image reconstruction from few measurements, and the decomposition of high-dimensional datasets, most notably video, into low-dimensional and sparse components.  

Concave generalized flows with applications to market equilibria

Series
Combinatorics Seminar
Time
Friday, September 9, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Laszlo Vegh – School of Computer Science, Georgia Tech –
The generalized flow model is a classical and widely applicable extension of network flows, where on every arc, the flow leaving the arc is a linear function of the flow entering the arc. In the talk, I will investigate a nonlinear extension of this model, with the flow leaving an arc being a concave function of the entering flow. I exhibit the first combinatorial polynomial time algorithm for solving corresponding optimization problems. This model turns out to be a common framework for solving several market equilibrium problems, such as linear Fisher markets, and immediately enables to extend them to more general settings. I will also give a survey on generalized flow algorithms and previous nonlinear flow models.

Holomorphic curves in geometry and topology II

Series
Geometry Topology Working Seminar
Time
Friday, September 9, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Recall this is a two hour seminar (2-4).

This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Asymptotics for random Young diagrams, a.k.a. asymptotics for last passage percolation along thin rectangles and dependent weights.

Series
Stochastics Seminar
Time
Thursday, September 8, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Christian houdre – School of mathematics, Georgia institute of Technology
Given a random word of size n whose letters are drawn independently from an ordered alphabet of size m, the fluctuations of the shape of the associated random RSK Young tableaux are investigated, when n and m converge together to infinity. If m does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau, i.e. of the length of the longest increasing subsequence of the word, towards the Tracy?Widom distribution.

On the pullback equation for differential forms.

Series
PDE Seminar
Time
Tuesday, September 6, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bernard Dacorogna – Ecole Polytechnique Federale de Lausanne
An important question in geometry and analysis is to know when two $k$-forms $f$ and $g$ are equivalent. The problem is therefore to find a map $\varphi$ such that $\varphi^*(g) =f$. We will mostly discuss the symplectic case $k=2$ and the case of volume forms$k=n$. We will give some results on the more difficult case where $3\leq k\leq n-2$, the case $k=n-1$ will also be considered.

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