1 citations · 1 across the 10 of their papers we have counts for
10 papers
Counterexamples to the Ramos conjecture for two hyperplanes
Florian Frick
For every , we construct nondegenerate Gaussian measures on that cannot be simultaneously equipartitioned by two affine hyperplanes. This disprove…
A Topological Figiel-Lindenstrauss-Milman Theorem and its Applications
Florian Frick, Kaave Hosseini, Eric Myzelev +2
We prove a topological generalization of the Figiel--Lindenstrauss--Milman inequality, answering a recent question of Frick, Hosseini, and Vasileuski: every nonempty strongly regul…
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…
Youden's Demon is Sylvester's Problem
Florian Frick, Andrew Newman, Wesley Pegden
If four people with Gaussian-distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of th…
Topological methods in zero-sum Ramsey theory
Florian Frick, Jacob Lehmann Duke, Meenakshi McNamara +5
A cornerstone result of Erd\H os, Ginzburg, and Ziv (EGZ) states that any sequence of elements in contains a zero-sum subsequence of length . While algebra…
Colorful Borsuk--Ulam theorems and applications
Florian Frick, Zoe Wellner
We prove a colorful generalization of the Borsuk--Ulam theorem and derive colorful consequences from it, such as a colorful generalization of the ham sandwich theorem. Even in the…
On the generalized Erdős--Kneser conjecture: proofs and reductions
Jai Aslam, Shuli Chen, Ethan Coldren +2
Alon, Frankl, and Lovász proved a conjecture of Erdős that one needs at least colors to color the -subsets of such that an…