Seminars and Colloquia by Series

Near optimality in covering games by exposing global information

Series
ACO Student Seminar
Time
Friday, November 30, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sara Krehbiel – College of Computing, Georgia Tech
Mechanism design for distributed systems is fundamentally concerned with aligning individual incentives with social welfare to avoid socially inefficient outcomes that can arise from agents acting autonomously. One simple and natural approach is to centrally broadcast non-binding advice intended to guide the system to a socially near-optimal state while still harnessing the incentives of individual agents. The analytical challenge is proving fast convergence to near optimal states, and we present the first results that carefully constructed advice vectors yield stronger guarantees. We apply this approach to a broad family of potential games modeling vertex cover and set cover optimization problems in a distributed setting. This class of problems is interesting because finding exact solutions to their optimization problems is NP-hard yet highly inefficient equilibria exist, so a solution in which agents simply locally optimize is not satisfactory. We show that with an arbitrary advice vector, a set cover game quickly converges to an equilibrium with cost of the same order as the square of the social cost of the advice vector. More interestingly, we show how to efficiently construct an advice vector with a particular structure with cost $O(\log n)$ times the optimal social cost, and we prove that the system quickly converges to an equilibrium with social cost of this same order.

Smoothness properties for some infinite-dimensional heat kernel measures

Series
Stochastics Seminar
Time
Thursday, November 29, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tai Melcher – University of Virginia
Smoothness is a fundamental principle in the study of measures on infinite-dimensional spaces, where an obvious obstruction to overcome is the lack of an infinite-dimensional Lebesgue or volume measure. Canonical examples of smooth measures include those induced by a Brownian motion, both its end point distribution and as a real-valued path. More generally, any Gaussian measure on a Banach space is smooth. Heat kernel measure is the law of a Brownian motion on a curved space, and as such is the natural analogue of Gaussian measure there. We will discuss some recent smoothness results for these measures on certain classes of infinite-dimensional groups, including in some degenerate settings. This is joint work with Fabrice Baudoin, Daniel Dobbs, and Masha Gordina.

The Mathematics of Criminal Behavior: Modeling and Experiments

Series
Job Candidate Talk
Time
Thursday, November 29, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Martin Short – UCLA
In this era of "big data", Mathematics as it applies to human behavior is becoming a much more relevant and penetrable topic of research. This holds true even for some of the less desirable forms of human behavior, such as crime. In this talk, I will discuss the mathematical modeling of crime on various "scales" and using many different mathematical techniques, as well as the results of experiments that are being performed to test the usefulness and accuracy of these models. This will include: models of crime hotspots at the scale of neighborhoods -- in the form of systems of PDEs and also statistical models adapted from literature on earthquake predictions -- along with the results of the model's application within the LAPD; a model for gang retaliatory violence on the scale of social networks, and its use in the solution of an inverse problem to help solve gang crimes; and a game-theoretic model of crime and punishment at the scale of a society, with comparisons of the model to results of lab-based economic experiments performed by myself and collaborators.

Robust optimization and quadratic BSDEs

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, November 28, 2012 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Hernandez – CIMAT, Mexico

Please Note: Hosts: Christian Houdre and Liang Peng

The relation between robust utility maximization problems and quadratic backward stochastic differential equations will be explored in this talk. Motivated by the solution of the dual formulation of the robust hedging problem for semi-martingales, when the model adopted is a diffusion it is possible to describe more completely the solution using the dynamic programming intuition, as well as some results of BSDEs.

A parametrix construction for the wave equation with low regularity coefficients using a frame of gaussians

Series
Analysis Seminar
Time
Wednesday, November 28, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alden Waters – Jyvaskyla University
We show how to construct frames for square integrable functionsout of modulated Gaussians. Using the frame representation of the Cauchydata, we show that we can build a suitable approximation to the solutionfor low regularity, time dependent wave equations. The talk will highlightthe relationship of the construction to harmonic analysis and will explorethe differences of the new construction to the standard Gaussian beamansatz.

Mathematical models of heterogeneous solids

Series
Research Horizons Seminar
Time
Wednesday, November 28, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guillermo Goldsztein – Georgia Tech, School of Math
I will describe a class of mathematical models of composites and polycrystals. The problems I will describe two research projects that are well suited for graduate student interested in learning more about this area of research.

Time-varying dynamical networks

Series
Mathematical Biology Seminar
Time
Wednesday, November 28, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles Bldg Rm.005
Speaker
Igor Belykh – Georgia State –
This talk focuses on mathematical analysis and modeling of dynamical systems and networks whose coupling or internal parameters stochastically evolve over time. We study networks that are composed of oscillatory dynamical systems with connections that switch on and off randomly, and the switching time is fast, with respect to the characteristic time of the individual node dynamics. If the stochastic switching is fast enough, we expect the switching system to follow the averaged system where the dynamical law is given by the expectation of the stochastic variables. There are four distinct classes of switching dynamical networks. Two properties differentiate them: single or multiple attractors of the averaged system and their invariance or non-invariance under the dynamics of the switching system. In the case of invariance, we prove that the trajectories of the switching system converge to the attractor(s) of the averaged system with high probability. In the non-invariant single attractor case, the trajectories rapidly reach a ghost attractor and remain close most of the time with high probability. In the non-invariant multiple attractor case, the trajectory may escape to another ghost attractor with small probability. Using the Lyapunov function method, we derive explicit bounds for these probabilities. Each of the four cases is illustrated by a specific technological or biological network.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Tuesday, November 27, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Christine Heitsch – Georgia Tech
A discussion of the paper "Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data" by Segal et al (2003).

Arithmetic of Abelian Varieties

Series
Algebra Seminar
Time
Monday, November 26, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Saikat Biswas – Georgia Tech
We introduce a new invariant of an abelian variety defined over a number field, and study its arithmetic properties. We then show how an extended version of Mazur's visibility theorem yields non-trivial elements in this invariant and explain how such a construction provides theoretical evidence for the Birch and Swinnerton-Dyer Conjecture.

The topology of a subspace of the Legendrian curves in a closed contact 3-manifold

Series
Geometry Topology Seminar
Time
Monday, November 26, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ali Maalaoui – Rutgers University
In this talk we are going to present a theorem that can be seen as related to S. Smale's theorem on the topology of the space of Legendrian loops. The framework will be slightly different and the space of Legendrian curves will be replaced by a smaller space $C_{\beta}$, that appears to be convenient in some variational problems in contact form geometry. We will also talk about the applications and the possible extensions of this result. This is a joint work with V. Martino.

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