Workshop:
GEOMETRIC COMBINATORICS

Monday June 6 through Thursday June 9, 2005
at the Mathematical Sciences Research Institute, Berkeley, CA

GENERAL INFORMATION

The Mathematical Association of America (MAA) and the Mathematical Sciences Research Institute are hosting a workshop through PREP (the Professional Enhancement Program of the MAA) on the topic of Geometric Combinatorics. The organizer is Francis Su.

Geometric Combinatorics refers to a growing body of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Polytopes (which are bounded polyhedra) and complexes built up form them are primary examples. Other examples include arrangements of points, lines, planes, convex sets, and their intersectin patterns. There are many connections to linear algebra, discrete mathematics, analysis, and topology, and there are exciting applications to game theory, computer science, and biology. The beautiful yet accessible ideas in geometric combinatorics are perfect for enriching courses in these areas.

The target audience is professors who desire to learn about this exciting field, enrich a variety of courses with new examples and applications, or teach a stand-alone course in geometric combinatorics.

Some of the topics we will cover include the geometry and combinatorics of polytopes, triangulations, combinatorial fixed point theorems, set intersection theorems, combinatorial convexity, lattice point counting, and tropical geometry. We will also explore applications to other fields such as the social sciences (e.g., fair division problems) and biology (e.g., the space of phylogenetic trees). Some of the material will reflect recent research trends from the Fall 2003 program at MSRI in this field.

Familiarity with linear algebra and discrete mathematics will be assumed for some of the topics considered.

SCHEDULE

The workshop will begin at 9 am on Monday, June 6 and end by 5pm on Thursday, June 9. There will be a mixture of lectures and group work. Some of the group work time will be explorations of topics from lectures and/or thinking about actual research problems, and other times will be devoted to thinking about how to incorporate some of this material into courses taught at the undergraduate level.

REFERENCES

Posted here is a list of Preparatory Problems to think about before you arrive for the workshop. You'll be working in groups to think about problems like these during the workshop. I'll also post other reference materials here later.

TRAVEL

Participants will be expected to arrive by the night of Sunday, June 5 and depart on the morning of Friday, June 10. As a participant, you will be receiving an e-mail with information about your lodging arrangements. The most convenient airports are San Francisco (SFO) and Oakland (OAK). At SFO, you can take the subway (BART) to Berkeley. From OAK, you can take a shuttle from the airport to the BART station, and then take a subway to Berkeley.

REGISTRATION and NOTIFICATION

To register, please use the form on the MAA PREP website. Applicants will be notified of their status by mid-April.

MATERIALS FROM THE 2005 WORKSHOP

After the workshop ends, you may visit this page for materials from the 2005 workshop.