Related papers: Deformed Harish-Chandra homomorphism for the cycli…
We define Hochschild and cyclic homologies for bornological coarse spaces: for a fixed field $k$ and group $G$, these are lax symmetric monoidal functors $\mathcal{X}HH_{k}^G$ and $\mathcal{X}HC_{k}^G$ from the category of equivariant…
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…
A simple new proof of the Harish-Chandra condition, preceded by an expository part on Hermitian symmetric spaces, holomorphic induction, and on some analytic tools.
In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…
From the structure of the category of representations of an affine cycle-free quiver, we determine an explicit linear form on the space of regular cuspidal functions over a finite field: its kernel is exactly the space of cuspidal…
We obtain a mixed complex, simpler that the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values…
We construct a Hochschild-Kostant-Rosenberg-type quasi-isomorphism for the negative cyclic homology of the category of global matrix factorizations on a smooth separated scheme of finite type over a field. The map is explicit enough to…
In this paper, we study relative deformations of maps into a family of K\"ahler manifolds whose images are divisors. We show that if the map satisfies a condition called semiregularity, then it allows relative deformations if and only if…
In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…
We obtain an infinite-dimensional cone of singular twisted Hilbert spaces $Z(\varphi)$ which are isomorphic to their duals but not to their conjugate duals. We do that by showing that the subset of all bi-Lipschitz maps from $[0, \infty)$…
In this paper a new form of the Hossz\'u-Gluskin theorem is presented in terms of polyadic powers and using the language of diagrams. It is shown that the Hossz\'u-Gluskin chain formula is not unique and can be generalized ("deformed")…
The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( \lambda_{1}+r\lambda_{2} ,r\lambda_{1}\lambda_{2}):…
Motivated by Harish-Chandra theory, we construct, starting from a simple CDD\--pole $S$\--matrix, a hierarchy of new $S$\--matrices involving ever ``higher'' (in the sense of Barnes) gamma functions.These new $S$\--matrices correspond to…
We present a comparison between the anticyclotomic Euler system of diagonal cycles associated with the convolution of two modular forms and the cyclotomic Beilinson--Flach Euler system. This extends the seminal work of Bertolini, Darmon,…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…
This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…
In [10] it was shown that there is a mapping class group-equivariant deformation retraction of the Teichm\"uller space of a closed surface onto a CW complex with dimension equal to the virtual cohomological dimension of the mapping class…
The classical Hadamard three circle theorem is generalized to complete K\"ahler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle…
In this paper we study Holder continuous linear cocycles over transitive Anosov diffeomorphisms. Under various conditions of relative pinching we establish properties including existence and continuity of measurable invariant sub-bundles…