The 2015 Magnus Lecture Series was recently held March 23 & 24, 2015, hosted by the Department of Mathematics. This year’s guest speaker was Professor Andrea Bertozzi from UCLA. While visiting, Professor Bertozzi gave three impressive talks:
Public Lecture March 23, 2015
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.
Colloquium – Open to Faculty and Graduate Students
March 24, 2015
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.
Research Seminar March 24, 2015
Title: Geometric graphbased 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 PDEbased 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 semisupervised 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.
Brief Biography
Andrea Bertozzi is an applied mathematician with expertise in nonlinear partial differential equations and fluid dynamics. She also works in the areas of geometric methods for image processing, crime modeling and analysis, and swarming/cooperative dynamics. Bertozzi completed all her degrees in Mathematics at Princeton. She was an L. E. Dickson Instructor and NSF Postdoctoral Fellow at the University of Chicago from 19911995. She was the Maria GeoppertMayer Distinguished Scholar at Argonne National Laboratory from 19956. She was on the faculty at Duke University from 19952004 first as Associate Professor of Mathematics and then as Professor of Mathematics and Physics. She has served as the Director of the Center for Nonlinear and Complex Systems while at Duke. Bertozzi moved to UCLA in 2003 as a Professor of Mathematics. Since 2005 she has served as Director of Applied Mathematics, overseeing the graduate and undergraduate research training programs at UCLA. In 2012 she was appointed the Betsy Wood Knapp Chair for Innovation and Creativity. Bertozzi's honors include the Sloan Research Fellowship in 1995, the Presidential Early Career Award for Scientists and Engineers in 1996, and SIAM's Kovalevsky Prize in 2009. She was elected to the American Academy of Arts and Sciences in 2010 and to the Fellows of the Society of Industrial and Applied Mathematics in 2010. She became a Fellow of the American Mathematical Society in 2013. Bertozzi serves on the editorial boards of twelve journals: SIAM J. Math. Anal., SIAM's Multiscale Modeling and Simulation, Interfaces and Free Boundaries, Applied Mathematics Research Express (Oxford Press), Applied Mathematics Letters, Mathematical Models and Methods in the Applied Sciences (M3AS), Communications in Mathematical Sciences, Nonlinearity, and Advances in Differential Equations, Journal of Nonlinear Science, Journal of Statistical Physics, and Nonlinear Analysis Real World Applications.
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. To date she has graduated 25 PhD students and has mentored 39 postdoctoral scholars.
Her current mathematical cv can be viewed at: http://www.math.ucla.edu/~bertozzi/vita/vita.html
The Arne Magnus Lectures are given annually in the Department of Mathematics at Colorado State University in honor of Dr. Arne Magnus, our friend and colleague for 25 years. The 2013 lectures were 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 CSU Foundation. Please donate online: https://advancing.colostate.edu/CNS/MATH/GIVE] or contact Jennifer Pedneau at 9704915711 or jennifer.pedneau@colostate.edu.
