Title: "Math of Crime"
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.
Andrea Bertozzi is an applied mathematician whose work has impacted many fields: the theory and applications of nonlinear partial differential equations, fluid dynamics, geometric methods for image processing, crime modeling and analysis, and swarming/cooperative dynamics. Among her many honors are: SIAM's Kovalevsky Prize (2009), election to the American Academy of Arts and Sciences (2010), and Fellow of both Society of Industrial and Applied Mathematics and the American Mathematical Society (2010). Professor Bertozzi currently serves as Chair of the Science Board of the NSF Institute for Computational and Experimental Research in Mathematics at Brown University and serves on the Science Boards for the Banff International Research Station and the Mathematical Sciences Research Institute at Berkeley.
Title: 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 will show how pair wise potential models are used to study biological movement and how to develop a systematic theory of such models. We also discuss how to use "designer potentials" to orchestrate cooperative movement in specific patterns, many of which may not be observed in nature but could be desirable for artificial swarms. Finally we conclude with some recent related work on emotional contagion in crowds.
Title: Geometric graph-based methods for high dimensional data
Abstract:We present new methods for segmentation of large datasets with graph based structure. The method combines ideas from classical nonlinear PDE-based image segmentation with fast and accessible linear algebra methods for computing information about the spectrum of the graph Laplacian. The goal of the algorithms is to solve semi-supervised and unsupervised graph cut optimization problems. We discuss results for image processing applications such as image labeling and hyperspectral video segmentation, and results from machine learning and community detection in social networks, including modularity optimization posed as a graph total variation minimization problem.
The lectures are supported by the Arne Magnus Lecture Fund and the Albert C. Yates Endowment in Mathematics.
Contributions to the Magnus Fund are greatly appreciated and may be made through the Department of Mathematics. Please contact Sheri Hofeling (firstname.lastname@example.org) at at (970)-491-7047 for specific information.
All lectures are free and open to the public.