KOI Combinatorics Lectures
Date:
Location:
TBA
Event Series:
Math Conference
KOI Combinatorics Lectures
Date:
Location:
TBA
Event Series:
KOI Combinatorics Lectures
See schedule
Date:
Location:
CB 114
Event Series:
KOI Combinatorics Lectures
See schedule
Date:
Location:
CB 114
Event Series:
KOI Combinatorics Lectures
KOI Combinatorics Lectures
KOI Combinatorics Lectures
KOI Combinatorics Lectures
Speaker: Richard Ehrenborg, University of Kentucky
Title: Sharing pizza in n dimensions
Abstract:
We introduce and prove the n-dimensional Pizza Theorem. Let H be a real n-dimensional hyperplane arrangement. If K is a convex set of finite volume, the pizza quantity of K is the alternating sum of the volumes of the regions obtained by intersecting K with the arrangement H. We prove that if H is a Coxeter arrangement different from A1n such that the group of isometries W generated by the reflections in the hyperplanes of H contains the negative of the identity map, and if K is a translate of a convex set that is stable under W and contains the origin, then the pizza quantity of K is equal to zero. Our main tool is an induction formula for the pizza quantity involving a subarrangement of the restricted arrangement on hyperplanes of H that we call the even restricted arrangement. We get stronger results in the case of balls. We prove that the pizza quantity of a ball containing the origin vanishes for a Coxeter arrangement H with |H|-n an even positive integer.
This is joint work with Sophie Morel and Margaret Readdy.
https://www.ms.uky.edu/~readdy/KOI/
Date:
Location:
CB 114
Event Series:
KOI Combinatorics Lectures
KOI Combinatorics Lectures
Speaker: Richard Ehrenborg, University of Kentucky
Title: Sharing pizza in n dimensions
Abstract:
We introduce and prove the n-dimensional Pizza Theorem. Let H be a real n-dimensional hyperplane arrangement. If K is a convex set of finite volume, the pizza quantity of K is the alternating sum of the volumes of the regions obtained by intersecting K with the arrangement H. We prove that if H is a Coxeter arrangement different from A1n such that the group of isometries W generated by the reflections in the hyperplanes of H contains the negative of the identity map, and if K is a translate of a convex set that is stable under W and contains the origin, then the pizza quantity of K is equal to zero. Our main tool is an induction formula for the pizza quantity involving a subarrangement of the restricted arrangement on hyperplanes of H that we call the even restricted arrangement. We get stronger results in the case of balls. We prove that the pizza quantity of a ball containing the origin vanishes for a Coxeter arrangement H with |H|-n an even positive integer.
This is joint work with Sophie Morel and Margaret Readdy.
https://www.ms.uky.edu/~readdy/KOI/
Date:
Location:
CB 114
Event Series:
KOI Combinatorics Lectures
KOI Combinatorics Lectures
Speaker: Eric Katz, Ohio State University
Title: Models of Matroids
Abstract:
Matroids are known for having many equivalent cryptomorphic definitions, each offering a different perspective. A similar phenomenon holds in the algebraic geometric approach to them. We will discuss different ways of viewing matroids, motivated by group actions, intersection theory, and K-theory, each of which has been generalized from the realizable case to a purely combinatorial approach.
Date:
Location:
CB 114
Event Series:
KOI Combinatorics Lectures
KOI Combinatorics Lectures
Speaker: Eric Katz, Ohio State University
Title: Models of Matroids
Abstract:
Matroids are known for having many equivalent cryptomorphic definitions, each offering a different perspective. A similar phenomenon holds in the algebraic geometric approach to them. We will discuss different ways of viewing matroids, motivated by group actions, intersection theory, and K-theory, each of which has been generalized from the realizable case to a purely combinatorial approach.
Date:
Location:
CB 114
Event Series: