# 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.

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

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.

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.