Seminars and Colloquia by Series

Stochastic Control Approach to KPZ equation

Series
Stochastics Seminar
Time
Thursday, April 25, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sergio Almada – UNC Chapel Hill
The Kardar-Parisi-Zhang(KPZ) equation is a non-linear stochastic partial di fferential equation proposed as the scaling limit for random growth models in physics. This equation is, in standard terms, ill posed and the notion of solution has attracted considerable attention in recent years. The purpose of this talk is two fold; on one side, an introduction to the KPZ equation and the so called KPZ universality classes is given. On the other side, we give recent results that generalize the notion of viscosity solutions from deterministic PDE to the stochastic case and apply these results to the KPZ equation. The main technical tool for this program to go through is a non-linear version of Feyman-Kac's formula that uses Doubly Backward Stochastic Differential Equations (Stochastic Differential Equations with times flowing backwards and forwards at the same time) as a basis for the representation.

Fractional calculus and Lévy statistics in non-diffusive transport modeling and option pricing in finance

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, April 24, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Diego del-Castillo-Negrete – Oak Ridge National Laboratory

Please Note: Hosts Christian Houdre and Liang Peng

Fractional calculus (FC) provides a powerful formalism for the modeling of systems whose underlying dynamics is governed by Lévy stochastic processes. In this talk we focus on two applications of FC: (1) non-diffusive transport, and (2) option pricing in finance. Regarding (1), starting from the continuous time random walk model for general Lévy jump distribution functions with memory, we construct effective non-diffusive transport models for the spatiotemporal evolution of the probability density function of particle displacements in the long-wavelength, time-asymptotic limit. Of particular interest is the development of models in finite-size-domains and those incorporating tempered Lévy processes. For the second application, we discuss fractional models of option prices in markets with jumps. Financial instruments that derive their value from assets following FMLS, CGMY, and KoBoL Lévy processes satisfy fractional diffusion equations (FDEs). We discuss accurate, efficient methods for the numerical integration of these FDEs, and apply them to price barrier options. The numerical methods are based on the finite difference discretization of the regularized fractional derivatives in the Grunwald-Letnikov representation.

ACO/Theory Seminar: A Polynomial Time Algorithm for Rank-1 Bimatrix Games (Despite Disconnected Solutions)

Series
Other Talks
Time
Wednesday, April 24, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Klaus 1456
Speaker
Ruta Mehta – Indian Institute of Technology, Bombay
The rank of a bimatrix game (A, B) is defined as the rank of (A+B). For zero-sum games, i.e., rank 0, Nash equilibrium computation reduces to solving a linear program. We solve the open question of Kannan and Theobald (2005) of designing an efficient algorithm for rank-1 games. The main difficulty is that the set of equilibria can be disconnected. We circumvent this by moving to a space of rank-1 games which contains our game (A, B), and defining a quadratic program whose optimal solutions are Nash equilibria of all games in this space. We then isolate the Nash equilibrium of (A, B) as the fixed point of a single variable function which can be found in polynomial time via an easy binary search. Based on a joint work with Bharat Adsul, Jugal Garg and Milind Sohoni.

Using semigroups to study coupled cell networks

Series
Mathematical Biology Seminar
Time
Wednesday, April 24, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
B.W. Rink – Vrije Univ. Amsterdam
Abstract: Dynamical systems with a coupled cell network structure arise in applications that range from statistical mechanics and electrical circuits to neural networks, systems biology, power grids and the world wide web. A network structure can have a strong impact on the behaviour of a dynamical system. For example, it has been observed that networks can robustly exhibit (partial) synchronisation, multiple eigenvalues and degenerate bifurcations. In this talk I will explain how semigroups and their representations can be used to understand and predict these phenomena. As an application of our theory, I will discuss how a simple feed-forward motif can act as an amplifier. This is joint work with Jan Sanders.

On well-posedness for a class of first order Hamilton-Jacobi equation in metric spaces

Series
PDE Seminar
Time
Tuesday, April 23, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jin Feng – University of Kansas
Using metric derivative and local Lipschitz constant, we define action integral and Hamiltonian operator for a class of optimal control problem on curves in metric spaces. Main requirement on the space is a geodesic property (or more generally, length space property). Examples of such space includes space of probability measures in R^d, general Banach spaces, among others. A well-posedness theory is developed for first order Hamilton-Jacobi equation in this context. The main motivation for considering the above problem comes from variational formulation of compressible Euler type equations. Value function of the variation problem is described through a Hamilton-Jacobi equation in space of probability measures. Through the use of geometric tangent cone and other properties of mass transportation theory, we illustrate how the current approach uniquely describes the problem (and also why previous approaches missed). This is joint work with Luigi Ambrosio at Scuola Normale Superiore di Pisa.

Riemann, Boltzmann and Kantorovich go to a party

Series
Stelson Lecture Series
Time
Monday, April 22, 2013 - 16:00 for 1.5 hours (actually 80 minutes)
Location
Klaus 1116
Speaker
Cedric Villani – Institut Henri Poincare, CNRS/UPMC

Please Note: General Audience Lecture. Reception to follow in Klaus Atrium.

This talk is the story of an encounter of three distinct fields: non-Euclidean geometry, gas dynamics and economics. Some of the most fundamental mathematical tools behind these theories appear to have a close connection, which was revealed around the turn of the 21st century, and has developed strikingly since then.

p-adic heights and integral points on hyperelliptic curves

Series
Algebra Seminar
Time
Monday, April 22, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jennifer Balakrishnan – Harvard University
We give a Chabauty-like method for finding p-adic approximations to integral points on hyperelliptic curves when the Mordell-Weil rank of the Jacobian equals the genus. The method uses an interpretation ofthe component at p of the p-adic height pairing in terms of iterated Coleman integrals. This is joint work with Amnon Besser and Steffen Mueller.

Shifting Paradigm: Agent-Based Modelling and its Application to Disease Dynamics

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 22, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Seyed Moghadas – York University
Modelling and computational approaches provide powerful tools in the study of disease dynamics at both the micro- and macro-levels. Recent advances in information and communications technologies have opened up novel vistas and presented new challenges in mathematical epidemiology. These challenges are central to the understanding of the collective dynamics of heterogeneous ensembles of individuals, and analyzing pertinent data that are less coarse and more complex. The evolution of dynamic modelling is typified by the agent-based modelling (ABM) as a shifting paradigm, a lattice-distributed collection of autonomous decision-making entities (i.e., agents), the interactions of which unveil the dynamics and emergent properties of a real-life problem, such as an infectious disease outbreak. In this talk, we show a general framework for developing an ABM that can be used to computationally optimize intervention strategies for novel influenza viruses with pandemic potential. Our findings contrast previous results !

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