In 2013, Abouzaid, Auroux, Efimov, Katzarkov and Orlov showed that the wrapped Fukaya
categories of punctured spheres and finite unbranched covers of punctured spheres are …

We give sufficient conditions for a Frobenius category to be equivalent to the category of
Gorenstein projective modules over an Iwanaga–Gorenstein ring. We then apply this result …

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 …

We construct noncommutative Donaldson–Thomas invariants associated with abelian
orbifold singularities by analyzing the instanton contributions to a six-dimensional …

We formulate a conjecture which describes the Fukaya category of an exact Lefschetz
fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a …

Given a consistent bipartite graph Γ Γ in T^ 2 T 2 with a complex-valued edge weighting EE
we show the following two constructions are the same. The first is to form the Kasteleyn …

We compute the wrapped Fukaya category $\mathcal {W}(T^* S^ 1, D) $ of a cylinder relative
to a divisor $ D=\{p_1,\ldots, p_n\} $ of $ n $ points, proving a mirror equivalence with the …

Bondal's conjecture states that the Frobenius push-forward of the structure sheaf 𝒪X
generates the derived category Db (X) for smooth projective toric varieties X. Bernardi and …

A version of the Bondal-Orlov conjecture, proved by Bridgeland, states that if $ X $ and $ Y $
are smooth complex projective threefolds linked by a flop, then they are derived equivalent …

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten
invariants on geometric invariant theory (git) quotients related by a change in polarization …