discrete geometry

Tuesday, February 24, 2015 - 10:15am - 11:05am
Kazuo Murota (University of Tokyo)
A discrete analogue of the theory of DC programming is constructed
on the basis of discrete convex analysis.
Since there are two classes of discrete convex functions (M-convex
functions and L-convex functions),
there are four types of discrete DC functions
(an M-convex function minus an M-convex function, an M-convex function minus an L-convex function, and so on) and four types of DC programs.
The discrete Toland-Singer duality establishes the relation among the four types of discrete DC programs.
Tuesday, November 11, 2014 - 11:00am - 11:25am
Peter Paule (Johannes Kepler Universität Linz)
In a joint project with George Andrews, aspects of
MacMahon's partition analysis have led us to consider
broken partition diamonds, an infinite family of
combinatorial objects whose generating functions give
rise to a variety of number theoretic congruences.
Recently, in the context of modular forms, Silviu
Radu has set up an algorithmic machinery to prove such
congruences automatically. The talk reports on
recent developments, some being joint work with Radu,
which are related to discrete geometry and computer
Wednesday, May 30, 2012 - 4:30pm - 5:00pm
Maria Alfonseca-Cubero (North Dakota State University)
There are many open problems related to the reconstruction of an origin-symmetric convex body K in Rn from its lower dimensional information (areas of sections or projections, perimeters of sections or projections, length of cords, etc.)

In this talk we will survey known results on the determination of a convex body from its central sections, parallel sections, or maximal sections. Some of these problems have been long-time open, and a few very recent results will be presented.
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