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Workshop

PREP Workshop: Geometric Combinatorics June 06, 2005 - June 09, 2005
Registration Deadline: May 01, 2005 about 8 years ago
To apply for Funding you must register by: March 29, 2005 about 8 years ago
Organizers Francis Su
Speaker(s) No Speakers Assigned Yet.
Description This workshop is being held in collaboration with the Mathematical Association of America as part of the MAA's Professional Enhancement Program (PREP). See the PREP website for information about registration and participant support. Note that the application deadline is March 29, 2005. 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 from them are primary examples. Other examples include arrangements of points, lines, planes, convex sets, and their intersection 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 have fun visualizing polytopes and other constructions, and exploring neat applications to other fields such as the social sciences (e.g., fair division problems and voting) and biology (e.g., the space of phylogenetic trees). Many interesting problems in geometric combinatorics are easy to explain, but remain unsolved. 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. Participants will receive some reading materials beforehand as well as some fun problems in the field to whet their appetite. More information at http://www.maa.org/prep/2005/

Schedule
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Jun 06, 2005
09:30 AM - 10:30 AM
  Combinatorial Convexity
Francis Su
10:45 AM - 11:00 AM
  Set Intersections and Helly's Theorem.
Francis Su
01:00 PM - 02:00 PM
  Polytopes I: Examples and Construction.
Francis Su
03:00 PM - 04:00 PM
  Polytopes II: Polar Duality.
Francis Su
Jun 07, 2005
09:00 AM - 10:00 AM
  Polytopes III: Combinatorics of Faces.
Francis Su
11:00 AM - 12:00 PM
  Polytopes IV: Counting Faces.
Francis Su
01:00 PM - 02:00 PM
  Simplicial Complexes and Triangulations.
Francis Su
03:00 PM - 04:00 PM
  Combinatorial Fixed Point Theorems I: Sperner's Lemma.
Francis Su
Jun 08, 2005
09:00 AM - 10:00 AM
  Combinatorial Fixed Point Theorems II: Tucker's Lemma.
Francis Su
11:00 AM - 12:00 PM
  Combinatorial Fixed Point Theorems III: Kneser Colorings.
Francis Su
01:00 PM - 02:00 PM
  An Introduction to Phylogenetic Trees.
Francis Su
03:00 PM - 04:00 PM
  What is Topical Geometry?
Francis Su
Jun 09, 2005
09:00 AM - 10:00 AM
  Minkowski's Theorem.
Francis Su
11:00 AM - 12:00 PM
  What are Ehrhart Polynomials?
Francis Su