Seminars and Colloquia by Series

Coupled diffusions and systemic risk

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, October 31, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
J.-P. Fouque – Department of Statistics and Applied Probability, University of California Santa Barbara,

Please Note: Hosted by Christian Houdre and Liang Peng

We present a simple model of diffusions coupled through their drifts in a way that each component mean-reverts to the mean of the ensemble. In particular, we are interested in the number of components reaching a "default" level in a given time. This coupling creates stability of the system in the sense that there is a large probability of "nearly no default". However, we show that this "swarming" behavior also creates a small probability that a large number of components default corresponding to a "systemic risk event". The goal is to illustrate systemic risk with a toy model of lending and borrowing banks, using mean-field limit and large deviation estimates for a simple linear model. In the last part of the talk we will show some recent work with Rene Carmona on a "Mean Field Game" version of the previous model and the effects of the game on stability and systemic risk.

Stein fillings of planar open books.

Series
Geometry Topology Student Seminar
Time
Wednesday, October 31, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech
The goal of this talk is to study geography and classification problem for Stein fillings of contact structures supported by planar open books. In the first part we will prove that for contact structures supported by planar open books Stein fillings have a finite geography. In the second part we will outline an approach to classify Stein fillings of manifolds supported by planar open books.

Curvature and (contact) topology

Series
Research Horizons Seminar
Time
Wednesday, October 31, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John Etnyre – Georgia Tech, School of Math
Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it.

Symplectic topology of rational blowdowns

Series
Geometry Topology Seminar
Time
Monday, October 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yankı Lekili – University of Cambridge & Simons Center
We study some finite quotients of the A_n Milnor fibre which coincide with the Stein surfaces that appear in Fintushel and Stern's rational blowdown construction. We show that these Stein surfaces have no exact Lagrangian submanifolds by using the already available and deep understanding of the Fukaya category of the A_n Milnor fibre coming from homological mirror symmetry. On the contrary, we find Floer theoretically essential monotone Lagrangian tori, finitely covered by the monotone tori that we studied in the A_n Milnor fibre. We conclude that these Stein surfaces have non-vanishing symplectic cohomology. This is joint work with M. Maydanskiy.

Variational method for speckle reduction in coherent imaging systems

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hyenkyun Woo – Georiga Tech CSE –
The fully developed speckle(multiplicative noise) naturally appears in coherent imaging systems, such as synthetic aperture radar imaging systems. Since the speckle is multiplicative, it makes difficult to interpret observed data. In this talk, we introduce total variation based variational model and convex optimization algorithm(linearized proximal alternating minimization algorithm) to efficiently remove speckle in synthetic aperture radar imaging systems. Numerical results show that our proposed methods outperform the augmented Lagrangian based state-of-the-art algorithms.

Hereditary Chip-Firing Models and Spanning Trees

Series
Combinatorics Seminar
Time
Friday, October 26, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Spencer Backman – School of Math, Georgia Tech –
A hereditary chip-firing model is a chip-firing game whose dynamics are induced by an abstract simplicial complex \Delta on the vertices of a graph, where \Delta may be interpreted as encoding graph gluing data. These models generalize two classical chip-firing games: The Abelian sandpile model, where \Delta is disjoint collection of points, and the cluster firing model, where \Delta is a single simplex. Two fundamental properties of these classical models extend to arbitrary hereditary chip-firing models: stabilization is independent of firings chosen (the Abelian property) and each chip-firing equivalence class contains a unique recurrent configuration. We will present an explicit bijection between the recurrent configurations of a hereditary chip-firing model on a graph G and the spanning trees of G and, if time permits, we will discuss chip-firing via gluing in the context of binomial ideals and metric graphs.

Large Deviations of Branching Random Walks

Series
ACO Student Seminar
Time
Friday, October 26, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Will Perkins – School of Math., Georgia Tech –
A branching random walk consists of a population of individuals each of whom perform a random walk step before giving birth to a random number of offspring and dying. The offspring then perform their own independent random steps and branching. I will present classic results on the convergence of the empirical particle measure to the Gaussian distribution, then present new results on large deviations of this empirical measure. The talk will be self-contained and can serve as an introduction to both the branching random walk and large deviation theory. The format will be 40 minutes of introduction and presentation, followed by a short break and then 20 minutes of discussion of open problems for those interested.

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