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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…
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…
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…