Math Institutes

Modern Math Workshop

September 29-30, 2010

In conjunction with the

2010 Society for Advancement of Chicanos and Native Americans in Science (SACNAS)Conference
on Sep 29-30 at Anaheim, California

Organizers:
Ivelisse Rubio Canabal Computer Science, University of Puerto Rico at Rio Piedras
Herbert A. Medina Mathematics, Loyola Marymount University
Chehrzad Shakiban IMA and University of Saint Thomas
Mariel Vazquez Mathematics, San Francisco State University
Christian Ratsch Associate Director of IPAM

Sponsored Institutes: AIM, ICERM, IMA, IPAM, MBI, MSRI, NIMBioS, PIMS, SAMSI

Supported by National Science Foundation: DMS-1038424.
and National Geospatial-Intelligence Agency.

Online Application

Application is only available to undergraduate students after August 15, 2010.
Application is only available to students receiving SACNAS travel funds after August 15, 2010.

Description:

The 2010 workshop on contemporary research in mathematics is sponsored by all the US-based Math Institutes. The topics of the workshop are related to programs that will occur in the Institutes during the academic year 2011-2012. All presentations will be expository, intended for mathematical scientists and students not necessarily working in these areas, but interested in learning about new developments and the possibility of spending some time at one of the Math Institutes.

This year we will have two 'mini courses' for the undergraduate students on Wednesday, September 29, 2010. This year's key note address will be given by Dr. Guillermo Saprio, University of Minnesota. All students and postdocs encouraged to apply. For additional information, please contact Cheri Shakiban at shakiban@ima.umn.edu shakiban(at)ima.umn.edu.

The tentative schedule for the 2010 workshop

Wednesday, September 29, 2010,
Session 1: Presentations:

12:30-1:30  Registration/Pick up Lunch boxes

1:30-2:00  Speakers: National Science Foundation program directors

2:10-2:40  IMA Speaker: Oscar Fernandez, IMA. Title: Developing geometric integrators for Hamiltonizable nonholonomic systems

2:50-3:20  PCMI Speaker: Richard Hain, Duke University. Title: Topology and symmetries of surfaces

3:30-4:00  Break/mentoring

4:00-4:50  Keynote Address: Guillermo Sapiro, University of Minnesota. Title: Image processing: Math travels to Hollywood, the hospital, and Mars

5:00-5:30  MBI Speaker: Suzanne Robertson, MBI. Title: Modeling spatial patterns in structured populations with an application to Tribolium

5:40-6:10  MSRI Speaker: Richard Kenyon, Brown University. Title: Dimers and determinants

6:20-6:30  break

6:30-8:00  Reception/ Math Institute Presentations

Session 2:  Mini-course. Presented by Juan Restrepo, University of Arizona, Title: Introduction to Deterministic and Stochastic Time Dependent Inverse Problems

1:30-3:10  Part 1

3:20-4:00  Break/mentoring

4:00-4:50  All students will join the keynote Address by Dr. Guillermo Sapiro.

5:00-6:10  Part 2

Thursday, September 30, 2010.

Session 1: Presentations:

8:30-9:00  NIMBIOS  Speaker: Suzanne Lenhart, University of Tennessee. Title: Optimal control for managing natural resources

9:10-9:40  IPAM Speaker: Matteo Pellegrini, UCLA. Title: Mathematical and Computational Approaches in High-Throughput Genomics

9:50-10:20  SAMSI Speaker: Ariel Cintron-Arias, East Tennessee State University. Title: Network Epidemic Models.

10:30-10:50  Break/mentoring

10:50-12:30  Panel of all the Institute representatives

Session 2:  Mini-course. Presented by Reinhard Laubenbacher, Virginia Bioinformatics Institute. Title: Mathematics and the Systems Biology of Cancer.

9:00-10:30  Part 1

10:30-11:00  Break/mentoring

11:00-12:15  Part 2

Abstracts:

Ariel Cintron-Arias. Title: Network Epidemic Models

Abstract: Structure among human populations is a relevant aspect in the study of infectious disease transmission. Analysis of epidemics on structured human populations is aided with techniques ranging from statistical physics to graph theory to theoretical epidemiology. In this talk, we revisit the definitions of random graph models, degree distributions, clustering, and basic network epidemic models, and we discuss the role played by structure in epidemic dynamics.

Oscar Fernandez Title: Developing geometric integrators for Hamiltonizable nonholonomic systems

Abstract: Although it is well known that nonholonomic mechanical systems are not Hamiltonian, recent research has uncovered a variety of techniques which allow one to express the reduced, constrained dynamics of certain classes of nonholonomic systems as Hamiltonian. In this talk I will discuss the application of these methods to develop alternative geometric integrators for nonholonomic systems with perhaps more efficiency than the known nonholonomic integrators.

Richard Kenyon. Title: Dimers and determinants

Abstract: We study the set of perfectmatchings ("dimer coverings") of a planar graph, for example the tilings of an n-by-n chessboard with 2-by-1 rectangles. Starting from the basic result that this number can be counted with a determinant, we obtain a rich theory of random dimer coverings and random interfaces.

Suzanne Lenhart. Title: Optimal control for managing natural resources

Abstract: We model harvesting of natural resources with spatial and temporal features using partial differential equations. The illustrative example is management of fishery resources to maximize yield. Our work is motivated by the justification for marines reserves (areas of no harvest) in a fishing region.

Matteo Pellegrini Title: Mathematical and Computational Approaches in High-Throughput Genomics.

Abstract: Biological sciences have been transformed over the past couple of decades by the development of instruments that permit large-scale measurements of cellular states. Among these, sequencing technologies have undergone an extraordinary increase in efficiency during the past few years, and are currently revolutionizing genomic studies. As a result of this innovation the cost to sequence billions of bases has decreased by many orders of magnitude during the last decade. This extraordinary increase in efficiency is creating an enormous need and opportunity to develop mathematical and computational infrastructures to meet the challenges emerging from the assembly and downstream analysis of the data. To name just a few, these involve, for example, the reconstruction of RNA transcript populations, the identification of sequence polymorphisms or copy number variations, as well as locating the sites of protein-DNA interactions. Additional types of analyses include the generation of statistical frameworks for whole genome association studies or reconstruction of population structures, and the reconstruction of microbial communities that colonize hosts or particular environmental niches. I will present the a program to be held in the fall of 2011 in the Institute for Pure and Applied mathematics (IPAM) at UCLA that will be to bring together mathematical and computational scientists, sequencing technology developers both in industry and academia, and the biologists who ultimately use the instruments to carry out genomic research. This long program presents a unique opportunity to bring together these three communities over an extended period to foster their interactions and ultimately advance the mathematical foundations of this exciting field.

Suzanne Robertson Title: Modeling spatial patterns in structured populations with an application to Tribolium

Abstract: Spatial segregation among life cycle stages has been observed in many stage-structured species, both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation by using stage-structured, integrodifference equation models that incorporate density dependent dispersal kernels as well as partial dispersal. We construct a spatial model to describe the population dynamics of the flour beetle species Tribolium brevicornis and use it to assess density dependent dispersal mechanisms that are able to explain spatial formations observed in this species.

Guillermo Sapiro Title: Image processing: Math travels to Hollywood, the hospital, and Mars.

Abstract: In this talk I will cover some of our recent results on image and video analysis, with applications covering numerous areas of our daily life. I will illustrate the underlying mathematical tools we exploit and develop, and show how image processing is a clear example of applied mathematics.

Abstract for the Mini-courses:

Reinhard Laubenbacher. Title: Mathematics and the Systems Biology of Cancer.

Abstract for the Mini-course: The goal of this mini-course is to illustrate the approach of systems biology and its utility for our understanding of cancer. After an introduction to cancer systems biology, the course will describe several case studies of successful mathematical approaches. The course will end with hands-on modeling activities.

Juan Restrepo. Title: Introduction to Deterministic and Stochastic Time Dependent Inverse Problems

Abstract for the Mini-course: Part 1: Statement of the problem, The least squares problem, Singular value decomposition, Regularization, Sequential and global estimation

Part 2: Sequential and global estimation, cont'd, Sampling basics, Parameter estimation using sampling, Image cleaning using sampling.

Reinhard Laubenbacher. Title: Mathematics and the Systems Biology of Cancer.

Abstract for the Mini-course: The goal of this mini-course is to illustrate the approach of systems biology and its utility for our understanding of cancer. After an introduction to cancer systems biology, the course will describe several case studies of successful mathematical approaches. The course will end with hands-on modeling activities.