Talk at SIAM Conference on Optimisation

The talk is based on the joint paper with Tian Sang and David Yost.

Title: On Facial Structure of Convex Sets

Abstract: Whilst faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, the latter property is not true for general compact convex sets. We address the question of which dimensional patterns are possible for the faces of general closed convex sets. We show that for any finite sequence of positive integers there exist compact convex sets which only have extreme points and faces with dimensions from this prescribed sequence.

We also discuss another approach to dimensionality, considering the dimension of the union of all faces of the same dimension. We show that the questions arising from this approach are highly nontrivial and give examples of convex sets for which the sets of extreme points have fractal
dimension.

Date and time: 24 May 2017, 11:00am.

Location: Sheraton Vancouver Wall Centre, Vancouver, Canada

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