Seminars and Colloquia Schedule

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.

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.

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.

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

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

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.

Boundedness of matrix valued dyadic paraproducts on matrix weighted L^p

Series
Analysis Seminar
Time
Wednesday, January 16, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josh Isralowitz – SUNY Albany
Weighted norm inequalities for singular integral operators acting on scalar weighted L^p is a classical topic that goes back to the 70's with the seminal work of R. Hunt, B. Muckenhoupt, and R. Wheeden. On the other hand, weighted norm inequalities for singular integral operators with matrix valued kernels acting on matrix weighted L^p are poorly understood and results (obtained by F. Nazarov, S. Treil, and A. Volberg in the late 90's) are only known for the situation when the kernel is essentially scalar valued.In this talk, we discuss matrix weighted norm inequalities for matrix valued dyadic paraproducts and discuss the possibility of using our results and a recent result of T. Hytonen to obtain concrete weighted norm inequalities for singular integral operators with matrix kernels acting on matrix weighted L^p. This is joint work with Hyun-Kyoung Kwon and Sandra Pott.

Poisson-Dirichlet statistics for the extremes of log-correlated Gaussian fields

Series
Stochastics Seminar
Time
Thursday, January 17, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Louis-Pierre Arguin – Université de Montréal
Gaussian fields with logarithmically decaying correlations, such as branching Brownian motion and the 2D Gaussian free field, are conjectured to form a new universality class of extreme value statistics (notably in the work of Carpentier & Ledoussal and Fyodorov & Bouchaud). This class is the borderline case between the class of IID random variables, and models where correlations start to affect the statistics. In this talk, I will report on the recent rigorous progress in describing the new features of this class. In particular, I will describe the emergence of Poisson-Dirichlet statistics. This is joint work with Olivier Zindy.

Conormals and contact homology

Series
Geometry Topology Working Seminar
Time
Friday, January 18, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

This is the first of 4 or 5, 1.5 hour talks.

In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

INVERSE PROBLEMS WITH EXPERIMENTAL DATA

Series
Applied and Computational Mathematics Seminar
Time
Friday, January 18, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Klibanov – University of North Carolina, Charlotte
Coefficient Inverse Problems (CIPs) are the hardest ones to work with in the field of Inverse Problems. Indeed, they are both nonlinear and ill-posed. Conventional numerical methods for CIPs are based on the least squares minimization. Therefore, these methods suffer from the phenomenon of multiple local minima and ravines. This means in turn that those methods are locally convergent ones. In other words, their convergence is guaranteed only of their starting points of iterations are located in small neighborhoods of true solutions. In the past five years we have developed a new numerical method for CIPs for an important hyperbolic Partial Differential Equation, see, e.g. [1,2] and references cited there. This is a globally convergent method. In other words, there is a rigorous guarantee that this method delivers a good approximation for the exact solution without any advanced knowledge of a small neighborhood of this solution. In simple words, a good first guess is not necessary. This method is verified on many examples of computationally simulated data. In addition, it is verified on experimental data. In this talk we will outline this method and present many numerical examples with the focus on experimental data.REFERENCES [1] L. Beilina and M.V. Klibanov, Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, Springer, New York, 2012. [2] A.V. Kuzhuget, L. Beilina and M.V. Klibanov, A. Sullivan, L. Nguyen and M.A. Fiddy, Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm, Inverse Problems, 28, 095007, 2012.

Indexed Additive Energy

Series
Combinatorics Seminar
Time
Friday, January 18, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Albert Bush – Georgia Tech
The additive energy of a set of integers gives key information on the additive structure of the set. In this talk, we discuss a new, closely related statistic called the indexed additive energy. We will investigate the relationship between the indexed additive energy, the regular additive energy, and the size of the sumset.