An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector
space. These highly symmetric convex bodies lie at the crossroads of several fields …

Thickenings of a metric space capture local geometric properties of the space. Here, we
exhibit applications of lower bounding the topology of thickenings of the circle and more …

The Convex Hull of a Variety Page 1 Trends in Mathematics, 331–344 The Convex Hull of a
Variety Kristian Ranestad and Bernd Sturmfels Abstract. We present a characterization, in …

We show that for each k and n, the cyclic shift map on the Grassmannian Gr k, n (C) has
exactly nk fixed points. There is a unique totally nonnegative fixed point, given by taking n …

This writeup describes ongoing work on designing and testing a certain family of
correspondences between compact metric spaces that we call\emph {embedding-projection …

We consider the convex hull ℬk of the symmetric moment curve Uk (t)=(cos t, sin t, cos 3t, sin
3t,…, cos (2k− 1) t, sin (2k− 1) t) in ℝ2k, where t ranges over the unit circle. The curve Uk (t) …

The geometric realization of a simplicial complex equipped with the 1-Wasserstein metric of
optimal transport is called a simplicial metric thickening. We describe relationships between …

This paper is a survey of recent advances as well as open problems in the study of face
numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed …

We analyze the facial structures of the convex set consisting of all two qubit separable
states. One of faces is a four dimensional convex body generated by the trigonometric …

We survey the theory of face numbers of simplicial complexes through the lens of upper
bound type results and neighborliness. We focus on the classes of polytopes, simplicial …