We prove that the wrapped Fukaya category of a punctured sphere (S with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburgâ€¦ (More)

Katzarkov has proposed a generalization of Kontsevichâ€™s mirror symmetry conjecture, covering some varieties of general type. Seidel [Se1] has proved a version of this conjecture in the simplest caseâ€¦ (More)

In this paper, we construct infinitely many examples of toric Fano varieties with Picard number three, which do not admit full exceptional collections of line bundles. In particular, this disprovesâ€¦ (More)

A new short clear proof of the asymptotics for the number cn of real roots of the Bernoulli polynomials Bn(x), as well as for the maximal root yn: yn = n 2Ï€e + ln(n) 4Ï€e +O(1) and cn = 2n Ï€e + ln(n)â€¦ (More)

This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to studyâ€¦ (More)

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors toâ€¦ (More)

In this paper we propose a generalization of the Kontsevichâ€“Soibelman conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for smooth and compact DG category. Our conjectureâ€¦ (More)