2 papers
math.CO2024
Extremal spherical polytopes and Borsuk's conjecture
Mikhail Katz, Facundo Mémoli, Qingsong Wang
We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and p…
math.DG2024
Extending Gromov's optimal systolic inequality
Thomas G. Goodwillie, James J. Hebda, Mikhail G. Katz
The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal…