Math Sciences Colloquia - Fall 2006

The Center for Applied Mathematics and the IGERT Nonlinear Systems program are sponsoring the Mathematical Sciences Graduate Student Seminar Series. We hope that this seminar series will become a fixture of Cornell's interdisciplinary programs. As part of these seminars in the mathematical sciences, Cornell graduate students will give informal one-hour talks about their research to fellow graduate students as well as professors.

The idea behind these seminars is twofold: (1) To foster interactions between graduate students in various disciplines for both academic and social purposes. (2) To allow students the opportunity to present and discuss their work with a broad group of their peers in a manner that is not currently available at Cornell. No one is going to demand or expect a polished presentation. The seminar is intended for work in progress. Students should not feel shy about presenting their work, as there are many people who will be interested in hearing about it. It's a chance for graduate students to get to know each other, practice their speaking ability, offer constructive criticism, etc.

This seminar series is a natural extension of the interdiscplinary efforts of CAM and the IGERT program. We hope you'll inform your students and colleagues of this seminar series, and we also invite you to provide suggestions for student speakers. These suggestions or expressions of interest to give a presentation should be e-mailed to Megan Owen (mao29cornell.edu).

All Math Sciences colloquia take place on Thursdays from 12:15 pm to 1pm in 657 Rhodes Hall. Pizza will be served before the talk.

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• Thursday, September 28 - Megan Owen, CAM
  Time: 12:15-1pm, with pizza at 12pm.
  Place: 657 Rhodes Hall, conference room
  
  Title: What is the distance between two phylogenetic (evolutionary) trees and how can we efficiently compute it?
  Abstract: In a 2001 paper, Billera, Holmes and Vogtmann constructed a space containing all binary phylogenetic trees, and showed the distance between the points corresponding to trees in their space was a reasonable inter-tree distance measure. Unfortunately, the obvious algorithm to compute this distance is not polynomial. I will be presenting preliminary results on my research to find a polynomial time algorithm and explaining the challenges that lie ahead.

This talk is in preparation for my A exam, so comments and suggestions will be greatly appreciated.

• Thursday, November 2
  Time: 11:30am - 12pm - Mateo Restrepo, CAM
  12pm - pizza
  12:15pm - 12:45pm - Jamie Barrera CAM.
  Place: 657 Rhodes Hall, conference room
  
  Mateo Restrepo
  Title: Towards Ambulance Relocation via Approximate Dynamic Programming
  Abstract: We consider a stylized version of the ambulance relocation problem. The goal is to minimize a function of the response times of all calls arriving within a finite horizon. We focus on obtaining good policies for the relocation of idle ambulances that allow the system to anticipate future calls. After presenting a dynamic programming formulation for this problem, we report on the implementation and experimental performance of approximate dynamic programming algorithms.
  
  Jamie Barrera
  Abstract: The porous media equation is a nonlinear heat equation that exhibits many cool features, like finite speed of propagation of disturbances and conservation of mass; and has applications in plasma physics and population dynamics, to name just two. I will describe a novel spectral numerical method developed by Professor Stephen Vavasis and myself that attempts to determine the solution as well as the (unknown) free boundary at any given time. I will also talk about properties of our method that match the behavior of the true solution and give initial convergence results.

• Wednesday, November 8
  Time: 1 p.m.- Michael Robinson, CAM
  Pizza at 12:45 p.m.
  Place: 657 Rhodes Hall, conference room
  
  Michael Robinson
  Title: "Towards a characterization of the dynamics of a semilinear parabolic
  differential equation"
  Abstract: One of the neat ways one can look certain parabolic differential equations
  is through the lens of dynamical systems. Essentially, one thinks of it as an ordinary differential equation on a Banach space. Many of the familiar features of dynamical systems arise, such as equilibria, stable manifolds, and bifurcations. However, finding these things is much harder! And also, extremely tame ordinary differential equations
  become much more exciting when allowed infinitely more dimensions.
  
  In this talk, I will describe a particular parabolic equation, and examine some of its dynamics. Since at present, its characterization is an open question, I can only hint at what might be lurking behind some very puzzling features of what we do know. (This talk is a dry run for my A exam, so I'll be happy to answer questions as we go!)

• Thursday, November 30
  Time: 1:15 p.m.- Anael Verdugo, CAM
  Pizza at 1 p.m.
  Place: 657 Rhodes Hall, conference room
  
  Aneal Verdugo
  Title: " Dynamics of a gene expression model with time delay"
  Abstract: Delays play a significant role in the dynamics of gene transcription and protein synthesis models. In principle, the influence of such delays can result in oscillatory mRNA and protein expressions. I will describe the biological model and its dynamical behavior close to a Hopf bifurcation. This will be accomplished by using Lindstedt's perturbation method and a center manifold reduction on the system. The final outcome results in closed form expressions for the limit cycle amplitude and
  frequency of oscillation. (This talk is in preparation for my A-exam, so comments and suggestions will be greatly appreciated.)