3 papers
math.GT2026
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…
cs.AI2026
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…
math.CO2024
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…