Seminars and Colloquia by Series

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.

Holomorphic curves in geometry and topology

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

Please Note: Recall this is a two hour seminar (running from 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).

Optimal aggregation of affine estimators

Series
Stochastics Seminar
Time
Thursday, September 1, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joseph Salmon – Electrical and Computer Engineering, Duke University –
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing onthe exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads tosharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression,kernel ridge regression, shrinking estimators and many other estimators used in the literatureon statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without neither discretizing the rangeof tuning parameters nor splitting the set of observations. We also illustrate numerically thegood performance achieved by the exponentially weighted aggregate. (This is a joint work with Arnak Dalalyan.)

Representation stability of the Torelli group

Series
Geometry Topology Seminar
Time
Monday, August 29, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stavros Garoufalidis – Georgia Tech –
I will discuss a computation of the lower central series of the Torelli group as a symplectic module, which depends on some conjectures and was performed 15 years ago in unpublished joint work with Ezra Getzler. Renewed interest in this computation comes from recent work of Benson Farb on representation stability.

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