We study rational curves on smooth complex Calabi--Yau threefolds via noncommutative
algebra. By the general theory of derived noncommutative deformations due to Efimov …

Nous montrons que la cohomologie de Hochschild singulière (cohomologie de Tate–
Hochschild) d'une algèbre A est isomorphe, en tant qu'algèbre graduée, à la cohomologie …

We describe two major string topology operations, the Chas–Sullivan product and the
Goresky–Hingston coproduct, from geometric and algebraic perspectives. The geometric …

The singularity category of a ring detects the homological singularity of the given ring, and
appears in many different contexts. We describe two different dg enhancements of the …

We introduce a symmetric operad $\square p $(" box-op") which describes a certain calculus
of rectangular labeled``boxes''. Algebras over $\square p $, which we call box operads, have …

The singularity category of a ring makes only the modules of finite projective dimension
vanish among the modules, so that the singularity category is expected to characterize a …

For any finite dimensional algebra Λ given by a quiver with relations, we prove that its dg
singularity category is quasi-equivalent to the perfect dg derived category of a dg Leavitt …

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild
cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his …

We prove that two quasi‐isomorphic simply connected differential graded associative
Frobenius algebras have isomorphic Goresky–Hingston algebras on their reduced …

For a commutative Gorenstein Noetherian ring $ R $, we construct an affine scheme $ X $
solely from singularity category $ D_ {sg}(R) $ of $ R $ such that there is a finite surjective …