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Algebra Seminar: Polynomials, generating functions, and lattice point counting
2007-04-02
1:10pm; Neill Hall, Room 106W
Bala Krishnamoorthy
Abstract: The number of integral points (i.e., points with integer entries) in a convex polytope P in R^d gives its DISCRETE VOLUME. This quantity is the number of elements in the set P n Z^d ('n' represents intersection). We get a better approximation to the usual continuous volume of P if we shrink the lattice Z^d by an integer factor k and count the number of elements in the set P n (1/k)Z^d. This quantity is a polynomial in k and is called the Ehrhart polynomial of P. Discrete volumes of polytopes appear in several areas such as number theory, discrete optimization, algebraic geometry and others. In this talk, I will present a few simple examples of polytopes, and derive expressions for their discrete volumes by analyzing their generating functions.
Weekly Scheduled Seminars
For more information please contact the individuals listed below.Monday
1:10pmAlgebra Seminar - Google Group
Neill Hall 106W
Contact: Judi McDonald
Tuesday
4:30-5:30pmMathematics Education Seminar
One World Cafe - Moscow, ID
Contact: Libby Knott
Wednesday
3:00-4:00pmApplied Math Seminar
Neill Hall 3W
Contact: Alan Genz
4:00-5:00pm
Reliability and Risk Seminar
Neill Hall 106W
Contact: Haijun Li
Thursday
Friday
4:15-5:15pmSpatial Reasoning: An Interdisciplinary Seminar
Cleveland Annex 309
Contact Co-organizers: Kim Vincent and Kathleen Ryan, Interior Design.
Various disciplines dealing with spatial relationships and reasoning will be examined. We will discuss what spatial reasoning is and how to improve students' spatial reasoning. The book, Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum will be used. A read-only version may be found at www.nap.edu/catalog.php?record_id=11019