Seminars and Colloquia by Series

Thrifty approximations of convex bodies by polytopes

Series
School of Mathematics Colloquium
Time
Thursday, March 7, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Barvinok – University of Michigan
Given a d-dimensional convex body C containing the origin in its interior and a real t>1, we seek to construct a polytope P with as few vertices as possible such that P is contained in C and C is contained in tP. I plan to present a construction which breaks some long-held records and is nearly optimal for a wide range of parameters d and t. The construction uses the maximum volume ellipsoid, the John decomposition of the identity and its recent sparsification by Batson, Spielman and Srivastava, Chebyshev polynomials, and some tensor algebra.

The Spectrum and Essential Spectrum of Toeplitz Operators

Series
Analysis Seminar
Time
Wednesday, March 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dechao Zheng – Vanderbilt University
On the Hardy space, by means of an elegant and ingenious argument, Widom showed that the spectrum of a bounded Toeplitz operator is always connected and Douglas showed that the essential spectrum of a bounded Toeplitz operator is also connected. On the Bergman space, in 1979, G. McDonald and the C. Sundberg showed that the essential spectrum of a Toeplitz operator with bounded harmonic symbol is connected if the symbol is either real or piecewise continuous on the boundary. They asked whether the essential spectrum of a Toeplitz operator on the Bergman space with bounded harmonic symbol is connected. In this talk, we will show an example that the spectrum and the essential spectrum of a Toeplitz operator with bounded harmonic symbol is disconnected. This is a joint work with Carl Sundberg.

"Transverse knots and Khovanov homology"

Series
Geometry Topology Student Seminar
Time
Wednesday, March 6, 2013 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alan Diaz – Georgia Tech
I'll discuss Plamenevskaya's invariant of transverse knots, how it can be used to determine tightness of contact structures on some 3-manifolds, and efforts to understand more about this invariant. This is an Oral Comprehensive Exam; the talk will last about 40 minutes.

Algebraic Certificates in Optimization and Beyond

Series
Research Horizons Seminar
Time
Wednesday, March 6, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg Blekherman – Georgia Tech, School of Math
I will discuss algebraic (sums of squares based) certificates for nonnegativity of polynomials and their use in optimization. Then I will discuss some recent results on degree bounds and state some open questions.

Oral Examination: "Invariant Densities for Dynamical Systems with Random Switching"

Series
Other Talks
Time
Tuesday, March 5, 2013 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tobias Hurth – Georgia Institute of Technology, School of Mathematics –
On a smooth manifold, we consider a non-autonomous ordinary differential equation whose right side switches between finitely many smooth vector fields at random times. These switching times are exponentially distributed to guarantee that the resulting random dynamical system has the Markov property. A Hoermander-type hypoellipticity condition on a recurrent subset of the manifold is then sufficient for uniqueness and absolute continuity of the invariant measure of the Markov semigroup. The talk is based on a paper with my advisor Yuri Bakhtin.

Courtesy Listing - Health and Wealth

Series
Other Talks
Time
Monday, March 4, 2013 - 17:00 for 1 hour (actually 50 minutes)
Location
Scheller College of Business, LeCraw Auditorium
Speaker
Ken Arrow – Stanford University, Emeritus

Please Note: Hosted by the College of Computing Light refreshments served at 4:30 PM

You are cordially invited to "Health and Wealth," a distinguished lecture by Nobel Laureate Ken Arrow that will provide a policy guide for matters of health, public and private. Professor Arrow, Joan Kenney Professor of Economics and Professor of Operations, Emeritus, at Stanford University, will address longevity and other aspects of health as commodities, as well as their trade-off with more usual goods as important measures of the well-being of nations. Register: http://www.formdesk.com/collegeofcomputing/KenArrow

A Tale of Two Theorems

Series
Algebra Seminar
Time
Monday, March 4, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg Blekherman – Georgia Tech
I will explain and draw connections between the following two theorems: (1) Classification of varieties of minimal degree by Del Pezzo and Bertini and (2) Hilbert's theorem on nonnegative polynomials and sums of squares. This will result in the classification of all varieties on which nonnegative polynomials are equal to sums of squares. (Joint work with Greg Smith and Mauricio Velasco)

Fokker-Planck Equation Method for Predicting Viral Signal Propagation in Social Networks

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 4, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xiaojing Ye – Georgia Tech, School of Math –
We consider the modeling and computations of random dynamical processes of viral signals propagating over time in social networks. The viral signals of interests can be popular tweets on trendy topics in social media, or computer malware on the Internet, or infectious diseases spreading between human or animal hosts. The viral signal propagations can be modeled as diffusion processes with various dynamical properties on graphs or networks, which are essentially different from the classical diffusions carried out in continuous spaces. We address a critical computational problem in predicting influences of such signal propagations, and develop a discrete Fokker-Planck equation method to solve this problem in an efficient and effective manner. We show that the solution can be integrated to search for the optimal source node set that maximizes the influences in any prescribed time period. This is a joint work with Profs. Shui-Nee Chow (GT-MATH), Hongyuan Zha (GT-CSE), and Haomin Zhou (GT-MATH).

A double exponential bound on Folkman numbers

Series
Combinatorics Seminar
Time
Friday, March 1, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Andrzej Rucinski – Poznan and Emory
For two graphs, G and F, we write G\longrightarrow F if every 2-coloring of the edges of G results in a monochromatic copy of F. A graph G is k-Folkman if G\longrightarrow K_k and G\not\supset K_{k+1}. We show that there is a constant c > 0 such that for every k \ge 2 there exists a k-Folkman graph on at most 2^{k^{ck^2}} vertices. Our probabilistic proof is based on a careful analysis of the growth of constants in a modified proof of the result by Rodl and the speaker from 1995 establishing a threshold for the Ramsey property of a binomial random graph G(n,p). Thus, at the same time, we provide a new proof of that result (for two colors) which avoids the use of regularity lemma. This is joint work with Vojta Rodl and Mathias Schacht.

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