We describe the derived functor DRep V (A) of the affine representation scheme Rep V (A)
parametrizing the representations of an associative k-algebra A on a finite-dimensional …

We establish a system of formal noncommutative calculus for differential forms and
polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories …

We study the derived representation scheme DRepn (A) parametrizing the n-dimensional
representations of an associative algebra A over a field of characteristic zero. We show that …

We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both
commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem …

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This paper is a sequel to [Adv. Math. 245 (2013), 625–689], where we study the derived
affine scheme DRep n (A) parametrizing the n-dimensional representations of an …

We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw,
are 2-Calabi–Yau algebras, in the case of quivers containing unoriented cycles. If the quiver …

Let A be a Koszul (or more generally, N-Koszul) Calabi–Yau algebra. Inspired by the works
of Kontsevich, Ginzburg and Van den Bergh, we show that there is a derived …

In this paper, we introduce and study representation homology of topological spaces, which
is a natural homological extension of representation varieties of fundamental groups. We …

In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic
structure in the sense of Crawley-Boevey-Etingof-Ginzburg [15], on the cobar construction of …