The invariator principle in convex geometry

Convex Geometry of the Generalized

Generalized matrix-fractional (GMF) functions are a class of matrix support func4 tions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix 5 optimization problems associated with inverse problems, regularization and learning. In this paper 6 we dramatically simplify the support function representation for GMF functions as well as the rep7 resentation o...

Harmonic Analysis in Convex Geometry

(in alphabetic order by speaker surname) Speaker: Judit Abardia (Frankfurt University) Title: Projection bodies in complex vector spaces Abstract: The projection body of a convex body in the Euclidean space was characterized by Monika Ludwig as the unique Minkowski valuation which is continuous, translation invariant and contravariant under the (real) special linear group. In a joint work with ...

Convex Geometry of Orbits

We study metric properties of convex bodies B and their polars B, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Salesman Polytope in polyhedral combinatorics (G = Sn, the symmetric group), the set of nonnegative polynomials in real algebraic geometry (G = SO(n), the special orthogonal group), and the convex hull of the Grassmannian ...

Convex and Discrete Geometry

Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are represented by non-overlapping closed disks in the Euclidean plane and where two vertices are connected if their corresponding disks touch. The problem of determining the maximum number of edges of a ...

Math 341: Convex Geometry