4 papers
A -Topological Framework for Sign-rank Lower Bounds
Florian Frick, Kaave Hosseini, Aliaksei Vasileuski
We develop a topological framework for proving lower bounds on sign-rank via -equivariant topology, and use it to resolve the sign-rank of the Gap Hamming Distance pr…
Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra
Florian Frick, Pranav Rajbhandari
The geodesic complexity of a length space quantifies the required number of case distinctions to continuously choose a shortest path connecting any given start and end point. W…
Covering and labeling generalizations of the Borsuk-Ulam theorem
Florian Frick, Zoe Wellner
We prove multiple generalizations of Fan's combinatorial labeling result for sphere triangulations. This can be seen as a comprehensive extension of the Borsuk--Ulam theorem. In ty…
Roots of real-valued zero mean maps: Compositions of linear functionals and equivariant maps
Francesca Cantor, Julia D'Amico, Florian Frick +1
We develop a novel topological framework that yields results constraining the distribution of zeros of certain zero mean real-valued maps, namely those obtained from composing a fi…