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- Twelves short videos about members of the Department of Mathematics and Statistics at the University of Victoria
- Jozsef Solymosi is Giving the 2017 Erdős Lectures in Discrete Mathematics and Theoretical Computer Science
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- The Race to Quantum Technologies and Quantum Computers (Useful Links)
- Around the Garsia-Stanley’s Partitioning Conjecture
- My Answer to TYI- 28
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Category Archives: Convex polytopes
Here is a link to Igor Pak’s book on Discrete and Polyhedral Geometry (free download) . And here is just the table of contents. It is a wonderful book, full of gems, contains original look on many important directions, things that … Continue reading
This post is devoted to the polymath-proposal about the polynomial Hirsch conjecture. My intention is to start here a discussion thread on the problem and related problems. (Perhaps identifying further interesting related problems and research directions.) Earlier posts are: The polynomial Hirsch … Continue reading
I can see three main avenues toward making progress on the Polynomial Hirsch conjecture. One direction is trying to improve the upper bounds, for example, by looking at the current proof and trying to see if it is wasteful and if so where … Continue reading
The Abstract Polynomial Hirsch Conjecture A convex polytope is the convex hull of a finite set of points in a real vector space. A polytope can be described as the intersection of a finite number of closed halfspaces. Polytopes have … Continue reading
This post is continued here. Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices facets has diameter at most n-d. We devoted several … Continue reading
Richard Stanley This post is authored by Eran Nevo. (It is the second in a series of five posts.) The g-conjecture: the commutative algebra connection Let be a triangulation of a -dimensional sphere. Stanley’s idea was to associate with a ring … Continue reading
This post complements Eran Nevo’s first post on the -conjecture 1) Euler’s theorem Euler Euler’s famous formula for the numbers of vertices, edges and faces of a polytope in space is the starting point of many mathematical stories. (Descartes came close … Continue reading
This post is authored by Eran Nevo. (It is the first in a series of five posts.) Peter McMullen The g-conjecture What are the possible face numbers of triangulations of spheres? There is only one zero-dimensional sphere and it consists … Continue reading
The associahedron in 3 dimension, and James Stasheff. This picture is taken from Bill Casselman’s article on the associahedron. The article is entitled “Strange Associations” and starts with “There are many other polytopes that can be described in purely combinatorial terms. Among the … Continue reading
Peter Mani (a photograph by Emo Welzl) Simple polytopes, puzzles Micha A. Perles conjectured in the ’70s that the graph of a simple -polytope determines the entire combinatorial structure of the polytope. This conjecture was proved in 1987 by Blind … Continue reading