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Mathematical Sciences Research Institute

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Workshop

Geometric Combinatorics May 23, 2004 - May 27, 2004
Registration Deadline: May 27, 2004 over 14 years ago
To apply for Funding you must register by: February 23, 2004 almost 15 years ago
Parent Program: --
Organizers Francis Su
Description
This workshop is aimed at faculty who wish to learn about this exciting field and would like to enrich a variety of undergraduate courses with new examples and applications, or teach a stand-alone course in geometric combinatorics. The 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 April 16, 2004. 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. Some of 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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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May 23, 2004
Sunday
08:00 AM - 05:00 PM
  Lecture 2- Set Intersections & Helly's Theorem
Francis Su
08:00 AM - 05:00 PM
  Lecture 3- Polytopes I: Examples & Construction
Francis Su
08:00 AM - 05:00 PM
  Lecture 4- Polytopes II: Polar Duality
Francis Su
08:00 AM - 05:00 PM
  Lecture 5- Polytopes III: Combinatorics of Faces
Francis Su
08:00 AM - 05:00 PM
  Lecture 6- Polytopes IV: Counting Faces
Francis Su
08:00 AM - 05:00 PM
  Lecture 7- Simplicial Complexes & Triangulations
Francis Su
08:00 AM - 05:00 PM
  Lecture 8- Combinatorial Fixed Point Theorems I: Sperner's Lemma
Francis Su
08:00 AM - 05:00 PM
  Lecture 9- Combinatorial Fixed Point Theorems II: Tucker's Lemma
Francis Su
08:00 AM - 05:00 PM
  Lecture 10- Combinatorial Fixed Point Theorems III: Kneser Colorings
Francis Su
08:00 AM - 05:00 PM
  Lcture 11- Combinatorial Fixed Point Theorems IV: Trees
Francis Su
08:00 AM - 05:00 PM
  Lecture 12- An Introduction to Phylogenetic Trees
Francis Su
08:00 AM - 05:00 PM
  Lecture 13- What is Tropical Geometry
Francis Su
08:00 AM - 05:00 PM
  Lecture 14- Minkowski's Theorem
Francis Su
08:00 AM - 05:00 PM
  Lecture 15- What are Ehrhart Polynomials?
Francis Su
09:30 AM - 10:00 AM
  Lecture 1- Combinatorial Convexity
Francis Su (Harvey Mudd College)
May 24, 2004
Monday
09:00 AM - 10:00 AM
  Cross-Program Lecture - WeBWork
Michael Gage (University of Rochester)