Seminars and Colloquia by Series

A Study of Discrepancy Results in Partially Ordered Sets

Series
Dissertation Defense
Time
Friday, March 19, 2010 - 09:00 for 3 hours
Location
Skiles 269
Speaker
David HowardSchool of Math, Georgia Tech
In 2001, Fishburn, Tanenbaum, and Trenk published a series of two papers that introduced the notions of linear and weak discrepancy of a partially ordered set or poset. Linear discrepancy for a poset is the least k such that for any ordering of the points in the poset there is a pair of incomparable points at least distance k away in the ordering. Weak discrepancy is similar to linear discrepancy except that the distance is observed over weak labelings (i.e. two points can have the same label if they are incomparable, but order is still preserved). My thesis gives a variety of results pertaining to these properties and other forms of discrepancy in posets.

Forbidden paths

Series
ACO Colloquium
Time
Thursday, March 18, 2010 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jaroslav NesetrilCharles University, Prague

Please Note: ***Refreshments at 4PM in Skiles 236.***

Forbidding (undirected or directed) paths in graphs, what can be easier? Yet we show that in the context of coloring problems (CSP) and structural graph theory, this is related to the notions tree depth, (restricted) dualities, bounded expansion and nowhere dense classes with applications both in and out of combinatorics.

From Soap Bubbles to the Poincare Conjecture

Series
School of Mathematics Colloquium
Time
Thursday, March 18, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Frank MorganDepartment of Mathematics and Statistics, Williams College

Please Note: Light refreshments will be available in Room 236 at 10:30 am.

A single round soap bubble provides the least-area way to enclose a given volume. How does the solution change if space is given some density like r^2 or e^{-r^2} that weights both area and volume? There has been much recent progress by undergraduates. Such densities appear prominently in Perelman's paper proving the Poincare Conjecture. No prerequisites, undergraduates welcome.

Interpolation in the Drury-Arveson Space

Series
Analysis Seminar
Time
Wednesday, March 17, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Brett WickGeorgia Tech
The Drury-Arveson space of functions on the unit ball in C^n has recently been intensively studied from the point of view function theory and operator theory. While much is known about this space of functions, a characterization of the interpolating sequences for the space has still remained elusive. In this talk, we will discuss the relevant background of the problem, and then I will discuss some work in progress and discuss a variant of the question for which we know the answer completely.

Joint DOS/ACO Seminar - The reflex algorithm - Convex optimization by random reflection

Series
Other Talks
Time
Wednesday, March 17, 2010 - 13:30 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom
Speaker
Merrick FurstCollege of Computing, Georgia Tech
Santosh Vempala and I have been exploring an intriguing new approach to convex optimization. Intuition about first-order interior point methods tells us that a main impediment to quickly finding an inside track to optimal is that a convex body's boundary can get in one's way in so many directions from so many places. If the surface of a convex body is made to be perfectly reflecting then from every interior vantage point it essentially disappears. Wondering about what this might mean for designing a new type of first-order interior point method, a preliminary analysis offers a surprising and suggestive result. Scale a convex body a sufficient amount in the direction of optimization. Mirror its surface and look directly upwards from anywhere. Then, in the distance, you will see a point that is as close as desired to optimal. We wouldn't recommend a direct implementation, since it doesn't work in practice. However, by trial and error we have developed a new algorithm for convex optimization, which we are calling Reflex. Reflex alternates greedy random reflecting steps, that can get stuck in narrow reflecting corridors, with simply-biased random reflecting steps that escape. We have early experimental experience using a first implementation of Reflex, implemented in Matlab, solving LP's (can be faster than Matlab's linprog), SDP's (dense with several thousand variables), quadratic cone problems, and some standard NETLIB problems.

The reflex algorithm - Convex optimization by random reflection

Series
ACO Student Seminar
Time
Wednesday, March 17, 2010 - 13:30 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom
Speaker
Prof. Merrick FurstComputer Science, Georgia Tech
Santosh Vempala and I have been exploring an intriguing newapproach to convex optimization. Intuition about first-order interiorpoint methods tells us that a main impediment to quickly finding aninside track to optimal is that a convex body's boundary can get inone's way in so many directions from so many places. If the surface ofa convex body is made to be perfectly reflecting then from everyinterior vantage point it essentially disappears. Wondering about whatthis might mean for designing a new type of first-order interior pointmethod, a preliminary analysis offers a surprising and suggestiveresult. Scale a convex body a sufficient amount in the direction ofoptimization. Mirror its surface and look directly upwards fromanywhere. Then, in the distance, you will see a point that is as closeas desired to optimal. We wouldn't recommend a direct implementation,since it doesn't work in practice. However, by trial and error we havedeveloped a new algorithm for convex optimization, which we arecalling Reflex. Reflex alternates greedy random reflecting steps, thatcan get stuck in narrow reflecting corridors, with simply-biasedrandom reflecting steps that escape. We have early experimentalexperience using a first implementation of Reflex, implemented inMatlab, solving LP's (can be faster than Matlab's linprog), SDP's(dense with several thousand variables), quadratic cone problems, andsome standard NETLIB problems.

Town Hall Meeting of the Graduate Students and Graduate Coordinator

Series
Research Horizons Seminar
Time
Tuesday, March 16, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Luca DieciProfessor and Graduate Coordinator, School of Mathematics

Please Note: Hosted by: Huy Huynh and Yao Li

We will have a chance to spend some time together to discuss issues of relevance to the Graduate Program. Sort of like a "Town Hall Meeting" of the graduate students and the graduate coordinator. There are some things that I need to communicate to all of you, but the format is otherwise unstructured, and I am seeking suggestions on things which you would like to see addressed. So, please send me comments on things which you would like to see discussed and I will do my best to get ready for them. Thanks, Luca Dieci.

On a parametrization of positive semidefinite matrices

Series
Algebra Seminar
Time
Monday, March 15, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Josephine YuGeorgia Tech
We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in the class is a polynomial map associated with a simplicial complex comprising cliques of the graph. The images of the maps are convex cones, and the maps can only be surjective onto the cone of zero-constrained positive semidefinite matrices when the associated graph is chordal. Our main result gives a semi-algebraic description of the image of the parametrizations for chordless cycles. The work is motivated by the fact that the considered maps correspond to Gaussian statistical models with hidden variables. This is joint work with Mathias Drton.

CANCELLED

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 15, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Maria CameronCourant Institute, NYU
The overdamped Langevin equation is often used as a model in molecular dynamics. At low temperatures, a system evolving according to such an SDE spends most of the time near the potential minima and performs rare transitions between them. A number of methods have been developed to study the most likely transition paths. I will focus on one of them: the MaxFlux functional.The MaxFlux functional has been around for almost thirty years but not widely used because it is challenging to minimize. Its minimizer provides a path along which the reactive flux is maximal at a given finite temperature. I will show two ways to derive it in the framework of transition path theory: the lower bound approach and the geometrical approach. I will present an efficient way to minimize the MaxFlux functional numerically. I will demonstrate its application to the problem of finding the most likely transition paths in the Lennard-Jones-38 cluster between the face-centered-cubic and icosahedral structures.

Pages