A real matrix is totally nonnegative if each of its minors is nonnegative, and is totally positive if each minor is greater than zero.
In 1643, Rene Descartes discovered a formula relating curvatures of circles in Apollonian circle packings, constructed by Apollonius of Perga in 200 BC. This formula has recently led to a connection between the construction of Apollonius and orbits of a certain so-called thin subgroup G of GL_4(Z). This connection is key in recent results on the arithmetic of Apollonian packings, which I will
Cancelled - will be rescheduled for January 2014
Abstract
“The local consistency algorithm and problems of bounded width”
In this talk, I shall discuss some recent results concerning various geometric properties including fixed point properties for nonexpansive mappings on weakly (or weak*) compact convex sets and Radon-Nikodym property on
There are strong analogies between the problem of finding fixed points for group actions on a manifold, finding sections of a fibration of topological spaces, and finding solutions of systems of polynomial equations.
In showing that finite idempotent algebras generating a congruence meet-semidistributive variety have bounded width, our first step is to reduce the consideration of arbitrary constraint networks to those where the constraints are at most binary.
This is the first of a series of weekly meetings for a class on Lie algebras, following the book by J.E. Humphreys. For the first meeting, Lie algebras will be introduced with examples and we will possibly tread into solvable algebras.
The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincare disk to M is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on Calabi-Yau manifolds.
It is a long standing conjecture, since antiquity, that there exist infinitely many consecutive prime numbers that are separated by 2, which is of course the closest possible distance.