2004 IMA New Directions Short Course

Computational Topology

July 6-16, 2004

Principal Speakers

Herbert Edelsbrunner
Computer Science Department
Duke University
edels@cs.duke.edu
http://www.cs.duke.edu/~edels/

John L. Harer
Department of Mathematics
Duke University
john.harer@duke.edu
http://www.math.duke.edu/~harer/

Schedule	Participants
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From July 6-16, 2004 the IMA will host an intensive short course designed to efficiently provide mathematicians the basic knowledge prerequisite to understand "Computational Topology." The course will be taught by Herbert Edelsbrunner, Professor of Computer Science and Mathematics at Duke University and John L. Harer, Professor and Vice Provost for Academic Affairs, Department of Mathematics, Duke University. Participants will receive full travel and lodging support during the workshop.

Content and philosophy. We understand Computational Topology as the development of algorithmic tools implementing topological concepts for use in the sciences and engineering. This is different from using the computer to study topological questions although there is the potential for a beneficial symbiosis between the two efforts. The history of Computational Topology is short. It grew out of Computational Geometry as researchers expanded into applications where significant topological issues arise. The two such areas discussed in this course are structural molecular biology and geometric modeling. Both have connections to industries of substantial economical size.

A primary goal in this course is to develop a broad picture in which algorithmic tools connect pure mathematics with scientific applications. Our utilitarian view is that the application should drive the mathematics, the algorithms and the software development.

Organization. A typical day during the two weeks course consists of two general lectures by the principal speakers in the morning, each one-and-a-half hours in duration. There will be a more specialized one hour topical lecture after lunch. The speakers will vary and we will occasionally have introductions to topic related software packages. In the later afternoon there will be a loosely organized two hour brain-storming session.

Necessary background. The main requirements are mathematical maturity and an open mind toward connecting mathematics to the world around it in new ways. No specialized knowledge in the two application areas will be assumed. Some background in algorithmic thinking and using computers will be helpful. We recommend the following texts for background reading.

Carl Brandon John Tooze. Introduction to Protein Structure. Garland, 1991.

Mark de Berg, Otfried Schwarzkopf, Marc van Kreveld, and Mark Overmars. Computational Geometry. Algorithms and Applications. Springer-Verlag, 1997.

Herbert Edelsbrunner. Geometry and Topology for Mesh Generation. Cambridge Univ. Press, 2001.

Yukio Matsumoto. An Introduction to Morse Theory. AMS, 2002.

James Munkres. Elements of Algebraic Topology. Addison Wesley, 1984.

Robert Tarjan. Data Structures and Network Algorithms. SIAM, 1983.

Local arrangements. The participants of the short course and the instructors will be housed at one of the University of Minnesota's dormitories. Meals will be served at the the dormitory dining facility. Each participant will be provided with shared office space including an individual computer workstation. Lectures and problem-solving sessions will use the IMA's classroom, multimedia, and computer facilities. There are expected to be visits to relevant laboratories on the University of Minnesota campus.

Application and selection procedure. The IMA New Directions Short Courses will be limited to 25 participants. All successful applicants will be funded for travel and local expenses. Please see the IMA reimbursement policy for details about airfare. Applicants are required to submit a curriculum vita and a statement about their interest in the course, its place in their future research plans, and its expected impact on their research and teaching. A committee consisting of the course instructors and IMA directors will select the participants from among the applicants.

Short Course Schedule and Talk Materials

WEEK 1

TUESDAY, JULY 6
All lectures will be held in 409 Lind Hall

TIME

LECTURE