Seminars and Colloquia Schedule

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.

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.

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

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).

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.