Campuses:

Computational geometry

Thursday, January 28, 2016 - 9:00am - 9:50am
Jean Lasserre (Centre National de la Recherche Scientifique (CNRS))
We consider the family of nonnegative homogeneous polynomials of even degree p whose sublevel set G = {x : g(x) ≤ 1} (a unit ball) has same fixed volume and want to find in this family the one that minimizes either the parsimony-inducing ell_1-norm or the ell_2-norm of its vector of coefficients. We first show that in both cases this is a convex optimization problem with a unique optimal solution. In the former case, the unique solution is the polynomial associated with the L_p-ball, thus recovering a parsimony property of its representation via ell_1-minimization.
Tuesday, November 11, 2014 - 9:00am - 9:50am
János Pach (École Polytechnique Fédérale de Lausanne (EPFL))
In this survey talk, I collect a lot of results from discrete and computational geometry, explaining the special role that touchings (tangencies) play in te subject. These questions contributed to the early development of the theory of Davenport-Schinzel sequences, algorithmic motion planning, geometric graph theory, and incidence geometry. We will also report on the recent solution of the Richter-Thomassen conjecture on intersecting closed (convex) curves.
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