Abstract: There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems, especially for young researchers. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, methods in linear and nonlinear partial differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes. Examples will consider both "bottom up'' and "top down'' approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.
Thursday, April 26, 2012
3:30pm, Boyd Grad Studies Bldg., Room 328
Swarming by Nature and by Design
Abstract: The cohesive movement of a biological population is a commonly observed natural phenomenon. With the advent of platforms of unmanned vehicles, such phenomena have attracted a renewed interest from the engineering community. This talk will cover a survey of the speaker's research and related work in this area ranging from aggregation models in nonlinear partial differential equations to control algorithms and robotic testbed experiments. We conclude with a discussion of some interesting problems
for the applied mathematics community.
Friday, April 27, 2012
3:30pm, Boyd Grad Studies Bldg., Room 328
Aggregation Equations and Fluid Dynamics
Abstract: Aggregation equations arise in many applications from materials science to biological interactions and design of consensus algorithms. This talk will focus on recent analysis results for kinematic aggregation equations and their connection to well-known problems in fluid dynamics. The main connection is the interaction kernel for the multidimensional aggregation problem as compared to the Biot-Savart law for the vorticity/velocity fields in fluids. Well-posedness of aggregation equations has been recently shown to have connection to the regularity of the kernel and we compare and contrast these results to the famous unsolved problem in fluid dynamics of global regularity of the 3D Navier-Stokes equations.
Refreshments will be served at 3:00pm, preceding each lecture.
There will be a banquet honoring Prof. Bertozzi on the evening of the first lecture. Details to be announced.
