Seminars and Colloquia by Series

Asymptotics of spectral projectors of sample covariance

Series
Stochastics Seminar
Time
Thursday, February 27, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vladimir Koltchinskii – Gatech
Several new results on asymptotic normality and other asymptotic properties of sample covariance operators for Gaussian observations in a high-dimensional setting will be discussed. Such asymptotics are of importance in various problems of high-dimensional statistics (in particular, related to principal component analysis). The proofs of these results rely on Gaussian concentration inequality. This is a joint work with Karim Lounici.

Packing disjoint A-paths with specified endpoints

Series
Graph Theory Seminar
Time
Thursday, February 27, 2014 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Paul Wollan – University of Rome "La Sapienza"
Consider a graph G and a specified subset A of vertices. An A-path is a path with both ends in A and no internal vertex in A. Gallai showed that there exists a min-max formula for the maximum number of pairwise disjoint A-paths. More recent work has extended this result, considering disjoint A-paths which satisfy various additional properties. We consider the following model. We are given a list of {(s_i, t_i): 0< i < k} of pairs of vertices in A, consider the question of whether there exist many pairwise disjoint A-paths P_1,..., P_t such that for all j, the ends of P_j are equal to s_i and t_i for some value i. This generalizes the disjoint paths problem and is NP-hard if k is not fixed. Thus, we cannot hope for an exact min-max theorem. We further restrict the question, and ask if there either exist t pairwise disjoint such A-paths or alternatively, a bounded set of f(t) vertices intersecting all such paths. In general, there exist examples where no such function f(t) exists; we present an exact characterization of when such a function exists. This is joint work with Daniel Marx.

Hypergeometric Functions, Representation Theory and Integrability

Series
Research Horizons Seminar
Time
Wednesday, February 26, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Plamen Iliev – School of Math
Hypergeometric functions have played an important role in mathematics and physics in the last centuries. Multivariate extensions of the classical hypergeometric functions have appeared recently in different applications. I will discuss research problems which relate these functions to the representation theory of Lie algebras and quantum superintegrable systems.

Recent progress on computing Groebner bases

Series
Algebra Seminar
Time
Monday, February 24, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shuhong Gao – Clemson University
Buchberger (1965) gave the first algorithm for computing Groebner bases and introduced some simple criterions for detecting useless S-pairs. Faugere (2002) presented the F5 algorithm which is significantly much faster than Buchberger's algorithm and can detect all useless S-pairs for regular sequences of homogeneous polynomials. In recent years, there has been extensive effort trying to simply F5 and to give a rigorous mathematical foundation for F5. In this talk, we present a simple new criterion for strong Groebner bases that contain Groebner bases for both ideals and the related syzygy modules. This criterion can detect all useless J-pairs (without performing any reduction) for any sequence of polynomials, thus yielding an efficient algorithm for computing Groebner bases and a simple proof of finite termination of the algorithm. This is a joint work with Frank Volny IV (National Security Agency) and Mingsheng Wang (Chinese Academy of Sciences).

Timing It Just Right: Learning and Optimization of High Dimensional Event Cascades

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 24, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Le Song – Georgia Tech CSE
Dynamical processes, such as information diffusion in social networks, gene regulation in biological systems and functional collaborations between brain regions, generate a large volume of high dimensional “asynchronous” and “interdependent” time-stamped event data. This type of timing information is rather different from traditional iid. data and discrete-time temporal data, which calls for new models and scalable algorithms for learning, analyzing and utilizing them. In this talk, I will present methods based on multivariate point processes, high dimensional sparse recovery, and randomized algorithms for addressing a sequence of problems arising from this context. As a concrete example, I will also present experimental results on learning and optimizing information cascades in web logs, including estimating hidden diffusion networks and influence maximization with the learned networks. With both careful model and algorithm design, the framework is able to handle millions of events and millions of networked entities.

Probabilistic global well-posedness and Gibbs measure evolution for radial nonlinear Schr\"odinger and wave equations on the unit ball.

Series
CDSNS Colloquium
Time
Monday, February 24, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Aynur Bulut – Univ. of Michigan
In this talk we will discuss recent work, obtained in collaboration with Jean Bourgain, on new global well-posedness results along Gibbs measure evolutions for the radial nonlinear wave and Schr\"odinger equations posed on the unit ball in two and three dimensional Euclidean space, with Dirichlet boundary conditions. We consider initial data chosen according to a Gaussian random process associated to the Gibbs measures which arise from the Hamiltonian structure of the equations, and results are obtained almost surely with respect to these probability measures. In particular, this renders the initial value problem supercritical in the sense that there is no suitable local well-posedness theory for the corresponding deterministic problem, and our results therefore rely essentially on the probabilistic structure of the problem. Our analysis is based on the study of convergence properties of solutions. Essential ingredients include probabilistic a priori bounds, delicate estimates on fine frequency interactions, as well as the use of invariance properties of the Gibbs measure to extend the relevant bounds to arbitrarily long time intervals.

Georgia Scientific Computing Symposium 2014

Series
Other Talks
Time
Saturday, February 22, 2014 - 09:00 for 8 hours (full day)
Location
Kennesaw State University
Speaker
Georgia Scientific Computing Symposium – Kennesaw State University

Please Note: Contact Yuliya Babenko, ybabenko@kennesaw.edu

The Georgia Scientific Computing Symposium 2014 will be held at Kennesaw State University (KSU) on Saturday, February 22. It is organized by KSU Departments of Mathematics and Statistics and Computer Science. There will be six plenary talks and a poster session. Graduate students, postdocs, and junior faculty are encouraged to present posters. For complete details and to register, see the symposium website

Optimizing Influenza Vaccine Allocation

Series
School of Mathematics Colloquium
Time
Thursday, February 20, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Jan Medlock – Oregon State University
The emergence of the 2009 H1N1 influenza A strain and delays in production of vaccine against it illustrate the importance of optimizing vaccine allocation. We have developed computational optimization models to determine optimal vaccination strategies with regard to multiple objective functions: e.g.~deaths, years of life lost, economic costs. Looking at single objectives, we have found that vaccinating children, who transmit most, is robustly selected as the optimal allocation. I will discuss ongoing extensions to this work to incorporate multiple objectives and uncertainty.

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