A point in a nd-polytope is the barycenter of n points in its d-faces

A strong equivariant deformation retraction from the homeomorphism group of the projective plane to the special orthogonal group

A Universality Theorem for Nested Polytopes.

Antiprismlessness, or: Reducing combinatorial equivalence to projective equivalence in realizability problems for polytopes

Barycenters of points in polytope skeleta

Continuous dependence of curvature flow on initial conditions

Grassmannians and pseudosphere arrangements

Packing segments in a convex 3-polytope is NP-hard.

Realizability of polytopes as a low rank matrix completion problem

Realization spaces of arrangements of convex bodies

Realization spaces of arrangements of convex bodies (SoCG)

Regular systems of paths and families of convex sets in convex position

Shadows of a closed curve

The Erdős-Szekeres problem for non-crossing convex sets

The inverse Kakeya problem

The number of holes in the union of translates of a convex set in three dimensions

The number of holes in the union of translates of a convex set in three dimensions (SoCG)

The shadows of a cycle cannot all be paths

Weight balancing on boundaries and skeletons

∀∃R-completeness and area-universality