Mikhail Kapranov is a professor of mathematics at Kavli IPMU in Tokyo.
A list of publications html
lecture at msri 2000 Noncommutative neighborhoods and noncommutative Fourier transform: link
Introducing Serre functors:
On Rozansky-Witten invariants:
Discussion of superalgebra as induced from free groupal symmetric monoidal categories (abelian 2-groups) and hence ultimately from the sphere spectrum (cf. super 2-algebra and spectral superscheme):
Mikhail Kapranov, Categorification of supersymmetry and stable homotopy groups of spheres, talk at Algebra, Combinatorics and Representation Theory: in memory of Andrei Zelevinsky (1953-2013) (April 2013) [pdf, video:YT]
Abstract:. The “minimal sign skeleton” necessary to formulate the Koszul sign rule is a certain Picard category, a symmetric monoidal category with all objects and morphisms invertible. It can be seen as the free Picard category generated by one object and corresponds, by Grothendieck‘s dictionary, to the truncation of the spherical spectrum $S$ in degrees 0 and 1, so that $\{\pm 1\}$ appears as the first stable homotopy group of spheres $\pi_{n+1}(S^n)$. This suggest a “higher” or categorified versions of super-mathematics which utilize deeper structure of $S$. The first concept on this path is that of a supersymmetric monoidal category which is categorified version of the concept of a supercommutative algebra.
Mikhail Kapranov, Supergeometry in mathematics and physics, in Gabriel Catren, Mathieu Anel, (eds.) New Spaces for Mathematics and Physics (arXiv:1512.07042)
Mikhail Kapranov, Super-geometry, talk at New Spaces for Mathematics & Physics, IHP Paris, Oct-Sept 2015 (video recording)
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