Robert Ghrist	Departments of Mathematics & Electrical Engineering, University of Pennsylvania
Robert D. MacPherson	School of Mathematics, Institute for Advanced Study
Konstantin Mischaikow	Department of Mathematics, Rutgers University

This program is primarily for graduate students of IMA Participating Institutions. The hosting institution may provide support for a limited number of students at other US universities. In order to participate, students need to fill out the application form and provide a letter of nomination.

From Monday, July 25 through Friday, August 12, 2011, the University of Pennsylvania, Philadelphia will be the host of the Institute for Mathematics and its Applications (IMA) Summer Graduate Program in Mathematics. The course will concentrate on Topological Methods in Complex Systems.

Topological methods are generating a revolution in the understanding and management of data in large systems ranging from robotics, dynamics, sensors, materials, biology, communications, and vision. Such methods, inspired by a century’s worth of development in algebraic and geometric topology, have the virtue of being qualitative and robust under perturbations. Of particular utility is the local-to-global nature of topological invariants, a feature of increasing relevance in large systems with distributed or modular constraints.

The summer school will train students in topological methods (complexes, homology, index theory, Morse theory, etc.) by means of and in the context of applications. The applications will include dynamical systems, systems biology, materials science, sensor and communications networks, and robotics. Prerequisites will be limited to linear algebra and advanced calculus, with some prior exposure to dynamical systems, abstract algebra, and setbased topology.

Venue: Philadelphia is a vibrant, historical city, easily reached by air or rail. Excellent facilities and a wealth of living and dining arrangements are available. Summer school participants in the program will benefit from an arranged tour of the GRASP robotics & sensing lab, as well as seeing ENIAC on the 1^st floor of the Moore building.

Principal Lecturers:

• Robert Ghrist "Topological Methods in Networked Engineering Systems"
• Randall Kamien "Topological Methods in Materials Science"
• Robert MacPherson "Topological Methods in Materials Science"
• Konstantin Mischaikow "Topological Methods in Biological Dynamical Systems"

Guest lecturers:

• Gareth Alexander
• Yuliy Baryshnikov
• Brian Chen
• Michael Erdmann
• Sean Harker
• Matthew Kahle
• Bill Kalies
• Miro Karmer
• Daniel E. Koditschek
• Jeremy Mason
• Michael Robinson
• Robert Vandervorst

Blackboard: