Related papers: A Negative Answer to a Question by Rieffel

In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…

Let $\hat{\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\hat{\mathfrak{h}}$ be the dual Lie bialgebra. By dualizing the quantum double construction - via formal…

We discuss some consequences of the invertibility of Rickard complexes in a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations…

We prove an equivariant implicit function theorem for variational problems that are invariant under a varying symmetry group (corresponding to a bundle of Lie groups). Motivated by applications to families of geometric variational problems…

We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…

Suppose $K$ is unramified over $\mathbb Q _p$ and $\Gamma _K=\operatorname{Gal}(\bar K/K)$. Let $H$ be a torsion $\Gamma _K$-equivariant subquotient of crystalline $\mathbb Q _p[\Gamma _K]$-module with HT weights from $[0,p-2]$. We give a…

We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a…

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation…

We study deformations of Fourier-Mukai transforms in general complex analytic settings. We start with two complex manifolds X and Y together with a coherent Fourier-Mukai kernel P on their product. Suppose that P implements an equivalence…

We present a decomposition of rational twisted $G$-equivariant K-theory, $G$ a finite group, into cyclic group equivariant K-theory groups of fixed point spaces. This generalises the untwisted decomposition by Atiyah and Segal as well as…

We prove the Farrell-Jones Isomorphism Conjecture about the algebraic K-theory of a group ring RG in the case where the group G is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The…

Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…

Let G be a real reductive Lie group and H a closed reductive subgroup of G. We investigate the deformation of "standard" compact quotients of G/H, i.e., of quotients of G/H by discrete subgroups Gamma of G that are uniform lattices in a…

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

The recent negative answer to Hilbert's tenth problem over rings of integers relies on a theorem that for every extension of number fields $L/K$, if there is an abelian variety $A$ over $K$ such that $0 < \operatorname{rank} A(K) =…

We discuss Heisenberg uncertainty inequality for groups of the form $K \ltimes \mathbb{R}^n$, $K$ is a separable unimodular locally compact group of type I. This inequality is also proved for Gabor transform for several classes of groups of…

Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears "frozen." Two strategies towards the…

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…

We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…

Let $X$ be an asymptotically hyperbolic manifold and $M$ its conformal infinity. This paper is devoted to deduce several existence results of the fractional Yamabe problem on $M$ under various geometric assumptions on $X$ and $M$: Firstly,…