Zobrazeno 1 - 5
of 5
pro vyhledávání: '"Sadovek, Nikola"'
Autor:
McGinnis, Daniel, Sadovek, Nikola
We establish a necessary and sufficient condition for a family of convex sets in $\mathbb{R}^d$ to admit a $k$-transversal, for any $0 \le k \le d-1$. This result is a common generalization of Helly's theorem ($k=0$) and the Goodman-Pollack-Wenger th
Externí odkaz:
http://arxiv.org/abs/2411.07241
This article has two goals. First, we hope to give an accessible introduction to persistent equivariant cohomology. Given a topological group $G$ acting on a filtered space, persistent Borel equivariant cohomology measures not only the shape of the f
Externí odkaz:
http://arxiv.org/abs/2408.17331
Autor:
Sadovek, Nikola, Soberón, Pablo
The Tverberg--Vre\'cica conjecture is a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpoint theorem and the ham sandwich theorem. In this manuscript, we establis
Externí odkaz:
http://arxiv.org/abs/2408.14337
A decade ago two groups of authors, Karasev, Hubard and Aronov, and Blagojevi\'c and Ziegler, have shown that the regular convex partitions of a Euclidean space into $n$ parts yield a solution to the generalised Nandakumar and Ramana-Rao conjecture w
Externí odkaz:
http://arxiv.org/abs/2305.10711
Autor:
Adams, Henry, Bush, Johnathan, Clause, Nate, Frick, Florian, Gómez, Mario, Harrison, Michael, Jeffs, R. Amzi, Lagoda, Evgeniya, Lim, Sunhyuk, Mémoli, Facundo, Moy, Michael, Sadovek, Nikola, Superdock, Matt, Vargas, Daniel, Wang, Qingsong, Zhou, Ling
We explore emerging relationships between the Gromov-Hausdorff distance, Borsuk-Ulam theorems, and Vietoris-Rips simplicial complexes. The Gromov-Hausdorff distance between two metric spaces $X$ and $Y$ can be lower bounded by the distortion of (poss
Externí odkaz:
http://arxiv.org/abs/2301.00246