3 citations · 5 across the 2 of their papers we have counts for
8 papers
Affine structures and non-archimedean analytic spaces
Maxim Kontsevich, Yan Soibelman
In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our…
Topological Borsuk problem
Yan Soibelman
Classical Borsuk problem asks about the minimal number of closed subsets of smaller diameter necessary to partition every compact in the Euclidean space. Topological version of the…
Non-commutative compactifications and elliptic curves
Yan Soibelman, Vadim Vologodsky
We study non-commutative degenerations of elliptic curves over local fields. The corresponding objects are close relatives of non-commutative tori of Connes and Rieffel.
Mirror symmetry and deformation quantization
Paul Bressler, Yan Soibelman
The paper is devoted to the comparison of the Fukaya category (it is responcible for the A-side of mirror symmetry) with the category of holonomic modules over the quantized algebr…
Quantum tori, mirror symmetry and deformation theory
Yan Soibelman
We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with…
Homological mirror symmetry and torus fibrations
Maxim Kontsevich, Yan Soibelman
In this paper we discuss two major conjectures in Mirror Symmetry: Strominger-Yau-Zaslow conjecture about torus fibrations, and the homological mirror conjecture (about an equivale…