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Mississippi State University, Starkville
Lead Organizer:
Kevin P. Knudson
Department of Mathematics and Statistics
Mississippi State University
http://www2.msstate.edu/~kk116/
Speakers:
Gunnar Carlsson
Department
of Mathematics
Stanford University
http://math.stanford.edu/~gunnar/
John Harer
Department of Mathematics
Duke University
http://fds.duke.edu/db/aas/math/faculty/harer/
Konstantin Mischaikow
School of Mathematics
Georgia Institute of Technology
http://www.math.gatech.edu/~mischaik/
During July 10-28, 2006 , Mississippi State University, Starkville will be the host of the Institute for Mathematics and its Applications (IMA) summer graduate program in mathematics. The course will concentrate on Topology and its Applications.
This program is open to graduate students from IMA Participating Institutions. Students are nominated by their department head. Participating institution department heads nominate graduate students from their institution by an e-mail to with the students' names and e-mail addresses.
Those students may then register by filling out the application form. Places are guaranteed for two graduate students from each participating institution, with additional students accommodated as space allows.
Course Description:
In a number of diverse areas, topological issues have begun to surface. In molecular biology, for example, the geometric features of the surface of a molecule have been shown to influence certain protein docking processes. Knot theory is becoming increasingly important in the study of DNA. Computer scientists encounter topological problems in attempts to reconstruct surfaces from sampled data. Topology in phase space can help overcome the inherent sensitivity in longtime simulations of dynamical systems. During the three-week meeting in the period July 9-29, 2006, there will be three week-long courses in the following areas:
Konstantin Mischaikow (School of Mathematics, Georgia Institute of Technology)
Applications to Dynamical Systems (Week 1)
We will discuss computational homology and its use in the study
of
nonlinear dynamical systems. The lectures will survey five
topics:
(1) Algorithms for computing the homology of spaces.
(2) The use of homology in investigating and classifying
nonlinear
systems based on the patterns observed in experiments or
numerical
simulations.
(3) Algorithms for computing the homology of maps.
(4) Conley index theory and associated algorithms.
(5) Computer assisted proofs in dynamics.
The associated projects will involve the application of these
tools to
specific problems.
Gunnar Carlsson (Department of Mathematics, Stanford University)
Topological Approximation and Surface (Week 2) Reconstruction
High dimensional data is now being generated at a very rapid rate in many different disciplines. Further, the data is frequently noisy, and is not equipped with any theoretical model. Rather, the data analysis needs to be used to discover the model. Since there is frequently no model, and therefore no preferred coordinate system, it is important to study those properties which don't change under continuous coordinate changes, which are called topological. The goal of this course is to provide an introduction to a recently developed computational version of algebraic topology, called persistent homology, which allows one to infer topological properties of geometric objects from "point clouds" sampled from them. We will introduce algebraic topology itself, the theory of persistent homology, software which permits its computation, and demonstrate how it is used in several real world examples.
John Harer (Department of Mathematics, Duke University)
Applications to Molecular Biology (Week 3)
The typical day's schedule will consist of two lectures in the morning, one after lunch, and informal problem sessions in the late afternoon as shown below.
9:00—10:00 lecture
10:00—10:30 break
10:30—11:30 lecture
11:30—1:30 lunch
1:30 until ? computer demos/problem sessions
Organizer is also trying to work out some Saturday excursions. Perhaps a day trip to Memphis one weekend, and a canoe trip in Noxubee wildlife refuge another. More details to follow.
Lecture room: Swalm Hall, Room 140. Please meet here 9:00 Monday morning
Dorm info: single rooms, shared bathroom at Cresswell Hall (http://www.msstate.edu/dept/housing/creswell.htm)
Abstracts, reading materials, etc. will be posted as it is received.
More information about the Department of Mathematics and Statistics at Mississippi State may be found at our website http://www.msstate.edu/dept/math. We look forward to hosting this event. If you need further information, please contact the organizer.
NAME | DEPARTMENT | AFFILIATION |
---|---|---|
Paul Bendich | Department of Mathematics | Duke University |
Gunnar Carlsson | Department of Mathematics | Stanford University |
Jer-Chin (Luke) Chuang | Department of Mathematics | Rice University |
Vin de Silva | Department of Mathematics and Computer Science | Pomona College |
Ali Elgindi | Department of Mathematics | University of Chicago |
Cecilia Gonzalez Tokman | Department of Mathematics | University of Maryland |
John Harer | Department of Mathematics | Duke University |
William Kalies | Department of Mathematical Sciences | Florida State University |
Mary Kloc | Department of Biophysics | University of Wisconsin, Madison |
Kevin Knudson | Department of Mathematics & Statistics | Mississippi State University |
Eun Joo Lee | Department of Mathematical Sciences | Seoul National University |
Juhyun Lee | School of Mathematical Sciences | Seoul National University |
Ram Medikonduri | Department of Applied Mathematics and Computer Science | The University of Iowa |
Jason Mireles-James | Department of Mathematics | University of Texas, Austin |
Konstantin Mischaikow | School of Mathematics | Georgia Institute of Technology |
Son Nguyen | Department of Mathematics | Wayne State University |
Neil Nicholson | Department of Mathematics | The University of Iowa |
Juan Ortiz-Navarro | Department of Mathematics | The University of Iowa |
Madhulika Pannuri | Department of Electrical and Computer Engineering | Mississippi State University |
Kyung Bae Park | Department of Mathematical Sciences | Seoul National University |
Lance Pittman | bad address | University of Illinois at Urbana-Champaign |
Reza Rezazadegan | Department of Mathematics | Rutgers, The State University Of New Jersey |
Joshua Roberts | Department of Mathematics | University of Kentucky |
Sundararajan Srinivasan | Department of Electrical and Computer Engineering | Mississippi State University |
Nathaniel Strawn | Department of Mathematics | Texas A & M University |
Courtney Taylor | Department of Mathematics | Purdue University |
Jonathan Whitehouse | Department of Mathematics | University of Minnesota, Twin Cities |
Xuefeng Zhang | Department of Mechanical Engineering | Mississippi State University |
Alexander Zorach | Department of Mathematics | University of Delaware |