Math Sciences Colloquia - Fall 2003

All Math Sciences colloquia take place at on Wednesdays at 12:30p.m. in 655 Rhodes Hall with pizza before the colloquium at 12:00 p.m in 657 Rhodes Hall.

• September 17 - Tara Small, CAM, "Where There's a Whale, There's a Way"
  Abstract: Base stations of cellular networks offer ubiquitous coverage to mobile nodes at low data rates. Infostations provide similar functionality; however they communicate with nodes at high data rates, at the expense of geographically intermittent coverage only. The Infostation model lends itself well to applications where nodes pass known locations. We propose to augment the Infostation model by replicating and diffusing information, and to apply the augmented model to one such application - radio-tagged whales. We refer to this augmented model as the Shared Wireless Infostation Model (SWIM).
• October 1 - Chris Maloney, IGERT, "How to elbow your way into the field of mathematical finance"
  Abstract: In this talk I will discuss a paper I wrote about a new calculation technique that I developed to extract risk-neutral densities from options prices (see http://www.physics.cornell.edu/~cmaloney/publications/pg.pdf for full details). I'll spend about half of my time talking about some of the interesting mathematical and computational features of this problem. Additionally, I'll discuss the nature of interdisciplinary research in finance with particular emphasis on data acquisition techniques.
• October 15 - Ariel Cintron-Arias, CAM, "A Mathematical Study for the Spread of Rumors"
  Abstract: A rumor is a piece of information that lacks authentication. Rumors have been studied by psychologists (Allport and Postman), sociologists(Buckner, DiFonzo and Bordia), physicists(Zanette), and mathematicians(Daley and Kendall) among others. We intend to study the dynamics of rumor propagation by proposing various caricature models. This study includes rumor spread on a different social networks topologies. We also propose a caricature model for rumor dissemination among chat room (instant messenger) users and non-users. Next, we consider populations whose demographic steady states can be fixed on a complex attractor, therefore enabling us to study rumors on complex attractors. Finally, dispersal of rumors is considered in two levels: in metapopulations, and in a continuum of patches.
• October 29 - Radu Haiduc, Math, "Horseshoes in the Forced van der Pol Equation"
  Abstract: The van der Pol oscillator has had a considerable influence in the development of the Dynamical Systems Theory. In return, the geometric methods from this field have been succesfully applied to a large class of singularly perturbed systems of differential equations, VDP included. In this talk I will show one way in which chaotic motions occur and givenumerical and analytical evidence for the existence of Smale horseshoes.
• November 12 - Ryan Gutenkunst, Physics, "A two-mode random-walk model for bluefin tuna movement"
  Abstract: Atlantic bluefin tuna are under intense fishing pressure, and quality models are important for conservation efforts. Data is, however, very limited. Here a small number of tuna tracks are analyzed for two distinct movement patterns, long-range directed and local undirected motion. Both patterns are modelled as random walks, and combining the two accounts for both the mean and variance in observed displacement. Loose bounds on prey species density are then derived by simulating movement in a simple model environment.
• December 3 - Dmitriy Leykekhman, Math, "Semigroups in Finite element method for parabolic PDEs"
  Abstract: As an example of parabolic PDEs, we consider the heat equation. Discreatizing in space by standard Galerkin finite element method, we obtain a semidiscrete approximation, which satisfies a certain initial boundary value problem. The solution operator generates a strongly continuous semigroup. Using semigroup theory, we show some important properties of semidiscrete solution, such as "maximum" principle, smoothness, and convergence in any $L_p$ norm.