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 …

In this paper, we investigate a Cartan calculus on the homology of free loop spaces which is
introduced by Kuribayashi, Wakatsuki, Yamaguchi and the author [Cartan calculi on the free …

Let GG be an affine algebraic group defined over a field kk of characteristic 0. We study the
derived moduli space of GG‐local systems on a pointed connected CW complex XX …

In this paper, we define and study derived character maps of finite-dimensional
representations of homotopy simplicial groups, which are homotopy algebras over the …

The main goal of this thesis is to provide a systematic study of several integrable systems
defined on complex Poisson manifolds associated to extended cyclic quivers. These spaces …

Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type.
We prove that the string topology bracket on the-equivariant homology of the free loop space …

We define and study (derived) character maps of finite-dimensional representations of∞–
groups. As models for∞–groups we take homotopy simplicial groups, ie the homotopy …

By a fundamental theorem of Quillen, there is a natural duality-an instance of general Koszul
duality-between differential graded (DG) Lie algebras and DG cocommutative coalgebras …

In this paper, we study the cotangent complex of the derived G-representation scheme
DRepG (X) of a pointed connected topological space X. We construct an (algebraic version …

This thesis has four parts. In the first part, we introduce and study representation homology
of topological spaces, which is a higher homological extension of representation varieties of …