67 citations · 818 across the 113 of their papers we have counts for
119 papers
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…
Effective infinitesimals in R
Karel Hrbacek, Mikhail G. Katz
We survey the effective foundations for analysis with infinitesimals developed by Hrbacek and Katz in 2021, and detail some applications. Theories SPOT and SCOT are conservative ov…
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…
Constructing nonstandard hulls and Loeb measures in internal set theories
Karel Hrbacek, Mikhail G. Katz
Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the i…
Is pluralism in the history of mathematics possible?
Jacques Bair, Alexandre Borovik, Vladimir Kanovei +6
Leibniz scholarship is currently an area of lively debate. We respond to some recent criticisms by Archibald et al.
Historical infinitesimalists and modern historiography of infinitesimals
Jacques Bair, Alexandre Borovik, Vladimir Kanovei +5
In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores,…