4 papers
Morse complexity of homology classes
Fedor Manin, Bena Tshishiku, Shmuel Weinberger
The Morse complexity of a manifold is the minimal number of handles required to build it. We explore the Morse complexity of manifolds, bordisms, and homology classes, proving nont…
First Proof
Mohammed Abouzaid, Andrew J. Blumberg, Martin Hairer +8
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the resear…
Persistent homology of function spaces
Jonathan Block, Fedor Manin, Shmuel Weinberger
We can view the Lipschitz constant as a height function on the space of maps between two manifolds and ask (as Gromov did nearly 30 years ago) what its ``Morse landscape'' looks li…
Coboundary expansion of coset complexes
Tali Kaufman, Izhar Oppenheim, Shmuel Weinberger
Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topolog…