Related papers: Unstable $K$-cohomology algebra is filtered lambda…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
The Jiang--Su algebra Z has come to prominence in the classification program for nuclear C*-algebras of late, due primarily to the fact that Elliott's classification conjecture predicts that all simple, separable, and nuclear C*-algebras…
We extend an argument of Stoppa to make some prgress towards a proof that K\"ahler-Einstein manifolds are "b-stable". We point out some algebro-geometric questions, involving finite generation, that arise.
In this paper, we prove that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper.
Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide. We use this…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…
The filamentation instability occurring when a non relativistic electron beam passes through a quantum magnetized plasma is investigated by means of a cold quantum magnetohydrodynamic model. It is proved that the instability can be…
The traditional conjecture that RR-flux is quantized in stable K-cohomology fails to account for the presence of NS-brane sources: These impose nonlinear relations -- reductions of the famous quadratic relation on M-brane flux -- that can…
We algebraically prove K-stability of polarized Calabi-Yau varieties and canonically polarized varieties with mild singularities. In particular, the} "stable varieties" introduced by Kollar-Shepherd-Barron and Alexeev, which form compact…
Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent…
We study the K-homology of the rotation algebras $A_{\theta}$ using the six term cyclic sequence for the K-homology of a crossed product by ${\bf Z}$. In the case where $\theta$ is irrational we use Pimsner and Voiculescu's work on…
In this note, we study some properties of the filtration of the Steenrod algebra defined from the excess of admissible monomials. We give several conditions on a cocommutative graded Hopf algebra A^* which enable us to develop the theory of…
In this paper we consider a family of generalized Korteweg-de Vries equations and study the linear modulational instability of small amplitude traveling waves solutions. Under explicit non-degeneracy conditions on the dispersion relation,…
We prove the K\"unneth formula for the irregular Hodge filtrations on the exponentially twisted de Rham and the Higgs cohomologies of smooth quasi-projective complex varieties. The method involves a careful comparison of the underlying…
We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in…
We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable $\infty$-category of non-$\mathbb A^1$-invariant motivic spectra, which turns out to be…
We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…
Let $\mathbb{K}$ be an algebraically closed field of characteristic 0. A finite dimensional Lie algebra $\mathfrak{g}$ over $\mathbb{K}$ is said to be stable if there exists a linear form $g\in\mathfrak{g}^{*}$ and a Zariski open subset in…