Seminars and Colloquia by Series

The joint spectral radius of a set of matrices: theoretical and computational aspects.

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 31, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nicola Guglielmi – Università di L'Aquila –
In this talk I will address the problem of the computation of the jointspectral radius (j.s.r.) of a set of matrices.This tool is useful to determine uniform stability properties of non-autonomous discrete linear systems. After explaining how to extend the spectral radius from a single matrixto a set of matrices and illustrate some applications where such conceptplays an important role I will consider the problem of the computation ofthe j.s.r. and illustrate some possible strategies. A basic tool I willuse to this purpose consists of polytope norms, both real and complex.I will illustrate a possible algorithm for the computation of the j.s.r. ofa family of matrices which is based on the use of these classes of norms.Some examples will be shown to illustrate the behaviour of the algorithm.Finally I will address the problem of the finite computability of the j.s.r.and state some recent results, open problems and conjectures connected withthis issue.

Penalized orthogonal-components regression for large p small n data

Series
Stochastics Seminar
Time
Thursday, August 27, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dabao Zhang – Purdue University
We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data. This is an joint work with Yanzhu Lin and Min Zhang

Planar graphs and planar posets

Series
Graph Theory Seminar
Time
Thursday, August 27, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
William T. Trotter – Math, GT
Slightly modifying a quote of Paul Erdos: The problem for graphs we solve this week. The corresponding problem for posets will take longer. As one example, testing a graph to determine if it is planar is linear in the number of edges. Testing an order (Hasse) diagram to determine if it is planar is NP-complete. As a second example, it is NP-complete to determine whether a graph is a cover graph. With these remarks in mind, we present some results, mostly new but some classic, regarding posets with planar cover graphs and planar diagrams. The most recent result is that for every h, there is a constant c_h so that if P is a poset of height h and the cover graph of P is planar, then the dimension of P is at most c_h.

Big Bang and the Quantum

Series
School of Mathematics Colloquium
Time
Wednesday, August 26, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Chemistry and Biochemistry Boggs Building, Room B-6A
Speaker
Abhay Ashtekar – Department of Physics and Institute for Gravitational Physics and Geometry, Pennsylvania State University –

Please Note: Pre-reception at 2:30 in Room N201.  If you would like to meet with Prof. Ashtekar while he is on campus (at the Center for Relativistic Astrophysics - Boggs building), please contact lori.federico@physics.gatech.edu.

General relativity is based on a deep interplay between physics and mathematics: Gravity is encoded in geometry. It has had spectacular observational success and has also pushed forward the frontier of geometric analysis. But the theory is incomplete because it ignores quantum physics. It predicts that the space-time ends at singularities such as the big-bang. Physics then comes to a halt. Recent developments in loop quantum gravity show that these predictions arise because the theory has been pushed beyond the domain of its validity. With new inputs from mathematics, one can extend cosmology beyond the big-bang. The talk will provide an overview of this new and rich interplay between physics and mathematics.

On the interchange process on weighted graphs and other card shuffling models

Series
ACO Student Seminar
Time
Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
SyE Executive Classroom
Speaker
Ton Dieker – School of Industrial and Systems Engineering, Georgia Tech
A central question in the theory of card shuffling is how quickly a deck of cards becomes 'well-shuffled' given a shuffling rule. In this talk, I will discuss a probabilistic card shuffling model known as the 'interchange process'. A conjecture from 1992 about this model has recently been resolved and I will address how my work has been involved with this conjecture. I will also discuss other card shuffling models.

Two weight inequalities for singular integrals

Series
Analysis Seminar
Time
Wednesday, August 26, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael Lacey – Georgia Institute of Technology
We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals.  In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

Analyticity in time and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional, compressible flow

Series
PDE Seminar
Time
Tuesday, August 25, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
David Hoff – Indiana University, Bloomington
We prove that solutions of the Navier-Stokes equations of three-dimensional, compressible flow, restricted to fluid-particle trajectories, can be extended as analytic functions of complex time. One important corollary is backwards uniqueness: if two such solutions agree at a given time, then they must agree at all previous times. Additionally, analyticity yields sharp estimates for the time derivatives of arbitrary order of solutions along particle trajectories. I'm going to integrate into the talk something like a "pretalk" in an attempt to motivate the more technical material and to make things accessible to a general analysis audience.

Bendixson conditions for differential equations in Banach spaces

Series
CDSNS Colloquium
Time
Monday, August 24, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Qian Wang – School of Mathematics, Georgia Tech
The Bendixson conditions for general nonlinear differential equations in Banach spaces are developed in terms of stability of associated compound differential equations. The generalized Bendixson criterion states that, if some measure of 2-dimensional surface area tends to zero with time, then there are no closed curves that are left invariant by the dynamics. In particular, there are no nontrivial periodic orbits, homoclinic loops or heteroclinic loops. Concrete conditions that preclude the existence of periodic solutions for a parabolic PDE will be given. This is joint work with Professor James S. Muldowney at University of Alberta.

Submodular Function Approximation

Series
Combinatorics Seminar
Time
Friday, August 21, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Satoru Iwata – Kyoto University
In this lecture, I will explain the greedy approximation algorithm on submodular function maximization due to Nemhauser, Wolsey, and Fisher. Then I will apply this algorithm to the problem of approximating an monotone submodular functions by another submodular function with succinct representation. This approximation method is based on the maximum volume ellipsoid inscribed in a centrally symmetric convex body. This is joint work with Michel Goemans, Nick Harvey, and Vahab Mirrokni.

Submodular Function Minimization

Series
Combinatorics Seminar
Time
Wednesday, August 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Satoru Iwata – Kyoto University
In this lecture, I will review combinatorial algorithms for minimizing submodular functions. In particular, I will present a new combinatorial algorithm obtained in my recent joint work with Jim Orlin.

Pages