Seminars and Colloquia by Series

Stochastic Differential Equations, Intermittent Diffusion, and Shortest Path

Series
Research Horizons Seminar
Time
Wednesday, January 16, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hao Min Zhou – Georgia Tech, School of Math
In this talk, I will use the shortest path problem as an example to illustrate how one can use optimization, stochastic differential equations and partial differential equations together to solve some challenging real world problems. On the other end, I will show what new and challenging mathematical problems can be raised from those applications. The talk is based on a joint work with Shui-Nee Chow and Jun Lu. And it is intended for graduate students.

Algebraic statistics reading seminar

Series
Other Talks
Time
Monday, January 14, 2013 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
organizational meeting – Georgia Tech

Please Note: From the publisher's website: "... The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models... "

This reading seminar may be of interest to both algebraists and statisticians; everyone is welcome to join. As the main text we will use "Lectures on algebraic statistics" by Drton, Sturmfels, and Sullivant: http://www.springer.com/birkhauser/applied+probability+and+statistics/bo...

Quasi-Periodic solutions for conformally symplectic dynamical systems

Series
CDSNS Colloquium
Time
Monday, January 14, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 06
Speaker
Renato Calleja – Georgia Tech and ITAM
Conformally symplectic systems send a symplectic form into a multiple of itself. They appear in mecanical systems with friction proportional to the velocity and as Euler-Lagrange equations of the time discounted actions common in economics. The conformaly symplectic structure provides identities that we use to prove "a-posteriori" theorems that show that if we have an approximate solution which satisfies some non-degeneracy conditions, we can obtain a true solution close to the approximate one. The identities used to prove the theorem, also lead to very efficient algorithms with small storage and operation counts. We will also present implementations of the algorithms.

Generators for the hyperelliptoc Torelli group and the kernel of the integral Burau representation

Series
Geometry Topology Seminar
Time
Monday, January 14, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Institute of Technology
We give a simple generating set for the following three closely related groups: the hypereliptic Torelli group, the kernel of the integral Burau representation, and the fundamental group of the branch locus of the period mapping. Our theorem confirms a conjecture of Hain. This is joint work with Tara Brendle and Andy Putman.

A Fast Global Optimization-Based Approach to Evolving Contours with Generic Shape Prior

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 14, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xue-Cheng Tai – University of Bergen, Department of Mathematics, Norway
In this talk, we present a new global optimization based approach to contour evolution, with or without the novel variational shape constraint that imposes a generic star shape using a continuous max-flow framework. In theory, the proposed continuous max-flow model provides a dual perspective to the reduced continuous min-cut formulation of the contour evolution at each discrete time frame, which proves the global optimality of the discrete time contour propagation. The variational analysis of the flow conservation condition of the continuous max-flow model shows that the proposed approach does provide a fully time implicit solver to the contour convection PDE, which allows a large time-step size to significantly speed up the contour evolution. For the contour evolution with a star shape prior, a novel variational representation of the star shape is integrated to the continuous max-flow based scheme by introducing an additional spatial flow. In numerics, the proposed continuous max-flow formulations lead to efficient duality-based algorithms using modern convex optimization theories. Our approach is implemented in a GPU, which significantly improves computing efficiency. We show the high performance of our approach in terms of speed and reliability to both poor initialization and large evolution step-size, using numerous experiments on synthetic, real-world and 2D/3D medical images.This talk is based in a joint work by: J. Yuan, E. Ukwatta, X.C. Tai, A. Fenster, and C. Schnorr.

Polynomial progressions in the primes

Series
Combinatorics Seminar
Time
Friday, January 11, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thai Hoang Le – U. Texas
The Green-Tao theorem says that the primes contain arithmetic progressions of arbitrary length. Tao and Ziegler extended it to polynomial progressions, showing that congurations {a+P_1(d), ..., a+P_k(d)} exist in the primes, where P_1, ..., P_k are polynomials in \mathbf{Z}[x] without constant terms (thus the Green-Tao theorem corresponds to the case where all the P_i are linear). We extend this result further, showing that we can add the extra requirement that d be of the form p-1 (or p + 1) where p is prime. This is joint work with Julia Wolf.

Hamilton-Jacobi-Bellman equations for the optimal control of dynamical systems with delay

Series
PDE Seminar
Time
Tuesday, January 8, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Fausto Gozzi – LUISS University, Rome, Italy
In this talk we first present some applied examples (coming from Economics and Finance) of Optimal Control Problems for Dynamical Systems with Delay (deterministic and stochastic). To treat such problems with the so called Dynamic Programming Approach one has to study a class of infinite dimensional HJB equations for which the existing theory does not apply due to their specific features (presence of state constraints, presence of first order differential operators in the state equation, possible unboundedness of the control operator). We will present some results on the existence of regular solutions for such equations and on existence of optimal control in feedback form.

Linear isoperimetric bounds for graph coloring

Series
Graph Theory Seminar
Time
Tuesday, January 8, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luke Postle – Emory University
We will discuss how linear isoperimetric bounds in graph coloring lead to new and interesting results. To that end, we say a family of graphs embedded in surfaces is hyperbolic if for every graph in the family the number of vertices inside an open disk is linear in the number of vertices on the boundary of that disk. Similarly we say that a family is strongly hyperbolic if the same holds for every annulus. The concept of hyperbolicity unifies and simplifies a number of known results about coloring graphs on surfaces while resolving some open conjectures. For instance: we have shown that the number of 6-list-critical graphs embeddable on a fixed surface is finite, resolving a conjecture of Thomassen from 1997; that there exists a linear time algorithm for deciding 5-choosability on a fixed surface; that locally planar graphs with distant precolored vertices are 5-choosable (which was conjectured for planar graphs by Albertson in 1999 and recently resolved by Dvorak, Lidicky, Mohar and Postle); that for every fixed surface, the number of 5-list-colorings of a 5-choosable graph is exponential in the number of vertices. We may also adapt the theory to 3-coloring graphs of girth at least five on surface to show that: the number of 4-list-critical graphs of girth at least five on a fixed surface is finite; there exists a linear time algorithm for deciding 3-choosability of graph of girth at least five on a fixed surface; locally planar graphs of girth at least five whose cycles of size four are far apart are 3-choosable (proved for the plane by Dvorak and related to the recently settled Havel's conjecture for triangle-free graphs in the plane). This is joint work with Robin Thomas.

Polymers in Probability: Bridges, Brownian Motion, and Disorder on an Intermediate Scale

Series
Job Candidate Talk
Time
Tuesday, December 11, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tom Alberts – Caltech
Chemical polymers are long chains of molecules built up from many individual monomers. Examples are plastics (like polyester and PVC), biopolymers (like cellulose, DNA, and starch) and rubber. By some estimates over 60% of research in the chemical industry is related to polymers. The complex shapes and seemingly random dynamics inherent in polymer chains make them natural candidates for mathematical modelling. The probability and statistical physics literature abounds with polymer models, and while most are simple to understand they are notoriously difficult to analyze. In this talk I will describe the general flavor of polymer models and then speak more in depth on my own recent results for two specific models. The first is the self-avoiding walk in two dimensions, which has recently become amenable to study thanks to the invention of the Schramm-Loewner Evolution. Joint work with Hugo-Duminil Copin shows that a specific feature of the self-avoiding walk, called the bridge decomposition, carries over to its conjectured scaling limit, the SLE(8/3) process. The second model is for directed polymers in dimension 1+1. Recent joint work with Kostya Khanin and Jeremy Quastel shows that this model can be fully understood when one considers the polymer in the previously undetected "intermediate" disorder regime. This work ultimately leads to the construction of a new type of diffusion process, similar to but actually very different from Brownian motion.

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