Seminars and Colloquia by Series

Stein fillings on Lens spaces II

Series
Geometry Topology Student Seminar
Time
Wednesday, October 19, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amey Kaloti – Georgia Tech
In this talk we will outline proof due to Plameneveskaya and Van-Horn Morris that every virtually overtwisted contact structure on L(p,1) has a unique Stein filling. We will give a much simplified proof of this result. In addition, we will talk about classifying Stein fillings of ($L(p,q), \xi_{std})$ using only mapping class group basics.

“What’s Eating You?” Quantifying Proteolytic Activity in Health and Disease with Novel Assays and Computational Models

Series
Mathematical Biology Seminar
Time
Wednesday, October 19, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Manu O. Platt – Coulter Department of Biomedical Engineering, Georgia Institute of Technology & Emory University
Cathepsins are enzymes that can cleave collagen and elastin, major structural proteins of tissue and organs, and participate in tissue-destructive disease progression seen in osteoporosis, arthritis, atherosclerosis, and cancer metastasis. Detection of mature cathepsins and quantification of specific activity have proven difficult due to instability of the mature, active enzyme extracellularly, which has led to them being overlooked in a number of diseases. During this seminar, Dr. Platt will discuss the important development of a reliable, sensitive method to detect the activity of mature cathepsins K, L, S, and V. Then he will focus on their progress towards developing a comprehensive computational model of cathepsin-mediated degradation of extracellular matrix, based on systems of ordinary differential equations. From the computational model and experimental results, a general assumption of inertness between familial enzymes was shown to be invalid as it failed to account for the interaction of these proteases among themselves and within their microenvironment. A consequence of this was significant overestimation of total degradative potential in multiple cathepsin reaction systems. After refining the system to capture the cathepsin interactive dynamics and match the experimental degradation results, novel mechanisms of cathepsin degradation and inactivation were revealed and suggest new ways to inhibit their activity for therapeutic benefit.

Restricted Ramsey theorems and Combinatorial Games

Series
Combinatorics Seminar
Time
Friday, October 14, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thomas Valla – Charles University, Prague
Ramsey theory studies the internal homogenity of mathematical structures (i.e. graphs, number sets), parts of which (subgraphs, number subsets) are arbitrarily coloured. Often, the sufficient object size implies the existence of a monochromatic sub-object. Combinatorial games are 2-player games of skill with perfect information. The theory of combinatorial games studies mostly the questions of existence of winning or drawing strategies. Let us consider an object that is studied by a particular Ramsey-type theorem. Assume two players alternately colour parts of this object by two colours and their goal is to create certain monochromatic sub-object. Then this is a combinatorial game. We focus on the minimum object size such that the appropriate Ramsey-type theorem holds, called "Ramsey number", and on the minimum object size such that the first player has a winning strategy in the corresponding combinatorial game, called "game number". In this talk, we investigate the "restricted Ramsey-type theorems". This means, we show the existence of first player's winning strategies, and we show that game numbers are surprisingly small, compared to Ramsey numbers. (This is joint work with Jarek Nesetril.)

Tangent lines, inflection points, and vertices of closed space curves

Series
Geometry Topology Working Seminar
Time
Friday, October 14, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
Mohammad Ghomi – Ga Tech
We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V>5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or points of vanishing torsion) of C. The proof, which employs curve shortening flow, is based on a corresponding inequality for the numbers of double points, singularites, and inflections of closed contractible curves in the real projective plane which intersect every closed geodesic. In the process we will also obtain some generalizations of classical theorems due to Mobius, Fenchel, and Segre (which includes Arnold's ``tennis ball theorem'').

Ruin Problems under Model Uncertainties

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, October 12, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jin Ma – School of Mathematics, University of Southern California

Please Note: Hosted by Christian Houdre and Liang Peng

In this work we study the ruin problem for a generalized Cramer-Lundberg reserve model with investments, under the modeling (volatility and claim intensity) uncertainty. We formulate the problem in terms of the newly developed theory on G-Expectation, initiated by S. Peng (2005). More precisely, we recast the problem as to determine the ruin probability under a G-expectation for a reserve process with a G-Compound Poisson type claim process, and perturbed by a G-Brownian motion. We show that the Lundberg bounds for a finite time ruin probability can still be obtained by an exponential $G$-martingale approach, and that the asymptotic behavior of the ruin, as the initial endowment tends to infinity, can be analyzed by the sample path large deviation approach in a G-expectation framework, with respect to the corresponding storage process. This is a joint work with Xin Wang.

How to categorify quantum sl(2) and its finite dimensional representations?

Series
Geometry Topology Seminar
Time
Wednesday, October 12, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
A. Beliakova – University of Zurich
I will explain in details starting with the basics, how the bimodules over some polynomial rings (cohomology of grasmanians) categorify the irreducible representations of sl(2) or U_q(sl(2).The main goal is to give an introduction to categorification theory. The talk will be accessible to graduate students.

Nonnegative Polynomials and Sums of Squares

Series
Research Horizons Seminar
Time
Wednesday, October 12, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg Blekherman – Georgia Tech
A multivariate real polynomial p(x) is nonnegative if p(x) is at least 0 for all x in R^n. I will review the history and motivation behind the problem of representing nonnegative polynomials as sums of squares. Such representations are of interest for both theoretical and practical computational reasons, with many applications some of which I will present. I will explain how the problem of describing nonnegative polynomials fits into convex algebraic geometry: the study of convex sets with underlying algebraic structure, that brings together ideas of optimization, convex geometry and algebraic geometry. I will end by presenting current research problems in this area.

Modeling and measuring different interferon resistance of HCV quasispecies (Math Biology)

Series
Mathematical Biology Seminar
Time
Wednesday, October 12, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel Skums – CDC
Hepatitis C virus (HCV) infects 2.2% of the world's population and is a major cause of liver disease worldwide. There is no vaccine against HCV and current interferon and ribavirin (IFN/RBV) therapy is effective in 50%-60% of patients. Since the interferon therapy is the expansive and painful for the patient process, it is very important to predict its outcome before starting full course of treatment. HCV exists in infected patients as a large viral population of intra-host variants (quasispecies), which form the certain topological structure (sequence space) and may be differentially resistant to interferon treatment. We present a method for measuring differential interferon resistance of HCV quasispecies based on the mathematical modeling and analysis of HCV population dynamics during the first hours of interferon therapy. The analysis of the model allowed us to accurately predict the long-term outcome of the interferon therapy on the test group of patients.

The Subtour LP for the Traveling Salesman Problem

Series
ACO Colloquium
Time
Tuesday, October 11, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David P. Williamson – Cornell University and TU Berlin –

Please Note: Refreshments at 10:30am in the atrium outside Skiles 006

The traveling salesman problem (TSP) is the most famous problem in discrete optimization. Given $n$ cities and the costs $c_{ij}$ for traveling from city $i$ to city $j$ for all $i,j$, the goal of the problem is to find the least expensive tour that visits each city exactly once and returns to its starting point. We consider cases in which the costs are symmetric and obey the triangle inequality. In 1954, Dantzig, Fulkerson, and Johnson introduced a linear programming relaxation of the TSP now known as the subtour LP, and used it to find the optimal solution to a 48-city instance. Ever since then, the subtour LP has been used extensively to find optimal solutions to TSP instances, and it is known to give extremely good lower bounds on the length of an optimal tour. Nevertheless, the quality of the subtour LP bound is poorly understood from a theoretical point of view. For 30 years it has been known that it is at least 2/3 times the length of an optimal tour for all instances of the problem, and it is known that there are instances such that it is at most 3/4 times the length of an optimal tour, but no progress has been made in 30 years in tightening these bounds. In this talk we will review some of the results that are known about the subtour LP, and give some new results that refine our understanding in some cases. In particular, we resolve a conjecture of Boyd and Carr about the ratio of an optimal 2-matching to the subtour LP bound in the worst case. We also begin a study of the subtour LP bound for the extremely simple case in which all costs $c_{ij}$ are either 1 or 2. For these instances we can show that the subtour LP is always strictly better than 3/4 times the length of an optimal tour. These results are joint work with Jiawei Qian, Frans Schalekamp, and Anke van Zuylen.

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