Emil Grosswald Lectures 2012
Andrea Bertozzi, University of California Los Angeles
Mathematics in the Real World
- Tuesday April 10, 4:00 PM, Shusterman Hall:
Andrea Bertozzi,
University of California Los Angeles,
Mathematics of Crime
- Wednesday April 11, 4:00 PM, Tuttleman Hall 105:
Andrea Bertozzi,
University of California Los Angeles,
Swarming by Nature and by Design
- Thursday April 12, 4:00 PM, Wachman Hall 617:
Andrea Bertozzi,
University of California Los Angeles,
Geometric methods for image processing and data analysis
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Refreshments will be served before the lectures at 3:30pm. All lectures take place on the main campus of Temple University in Philadelphia, Pennsylvania. Links:
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Abstracts
- Mathematics of Crime:
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. 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.
- Swarming by Nature and by Design:
The cohesive movement of a biological population is a commonly observed
natural phenomenon. With the advent of platforms of unmanned vehicles, this
occurrence is attracting renewed interest from the engineering community.
This talk will review recent research results on both modeling and analysis
of biological swarms and also design ideas for efficient algorithms to control
groups of autonomous agents. For biological models we consider two kinds of
systems: driven particle systems based on force laws and continuum models based
on kinematic rules. Both models involve long-rage social attraction and short
range dispersal and yield patterns involving clumping, mill vortices, and
surfacetension-like effects. For artificial platforms we consider the problem
of boundary tracking of an environmental material and consider both computer
models and demonstrations on real platforms of robotic vehicles. We also
consider the motion of vehicles using artificial potentials.
- Geometric methods for image processing and data analysis: This talk will be an overview of geometric methods in image processing developed by my research group. Applications include hyperspectral imaging, image inpainting, pan sharpening, deblurring, and statistical density estimation. Mathematical methods include the fast solution of higher order PDEs, methods that combine wavelet based methods with nonlinear geometric models, dictionary based methods, and graph based methods.
Photos
All photos by Benjamin Seibold.