Related papers: On modular semifinite index theory
The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in…
We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We…
We extend twisted inner fluctuations to twisted spectral triples that do not meet the twisted first-order condition, following what has been done in [6] for the non-twisted case. We find a similar non-linear term in the fluctuation, and…
This survey provides a comprehensive overview of the recent advancements in the theory of ``uniformly $S$''-algebraic structures in commutative ring theory. Originating from the classical concepts of Noetherian, coherent, von Neumann…
We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…
We want to compute generic $\mathrm{Ext}$-spaces of twisted polynomial functors in relation to the $\mathrm{Ext}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in…
We construct a quasi-inverse of the cochain map on the negative cyclic complexes of the second kind induced from the quasi-Yoneda embedding on a curved dg algebra. This gives an explicit formula for the Chern character of a perfect module.
A pair of rooted tangents -- defining a quantum triangle -- with an associated quantum wave of spin 1/2 is proposed as the primitive to represent and compute symmetry. Measures of the spin characterize how "isosceles" or how "degenerate"…
An analogue of a spectral triple over SUq(2) is constructed for which the usual assumption of bounded commutators with the Dirac operator fails. An analytic expression analogous to that for the Hochschild class of the Chern character for…
The quasi-SU(3) symmetry, as found in shell model calculations, refers to the dominance of the single particle plus quadrupole-quadrupole terms in the Hamiltonian used to describe well deformed nuclei, and to the subspace relevant in its…
We recapture Douglas' framework for twisted parametrized stable homotopy theory in the language of $\infty$- categories. A twisted spectrum is essentially a section of a bundle of presentable stable $\infty$-categories whose fiber is the…
For an integral cohomology class H of degree n+2 on a space X, we define twisted Morava K-theory K(n)(X; H) at the prime 2, as well as an integral analogue. We explore properties of this twisted cohomology theory, study a twisted…
We investigate the unflavoured Schur indices of class $\mathcal S$ theories of modest rank, and in the case of $\mathcal{N}=4$ super Yang-Mills theory with special unitary gauge group of somewhat more general rank, with an eye towards their…
We analyse the noncommutative space underlying the quantum group SUq(2) from the spectral point of view which is the basis of noncommutative geometry, and show how the general theory developped in our joint work with H. Moscovici applies to…
We count the Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel…
We explore the geometric interpretation of the twisted index of 3d ${\mathcal N} =4$ gauge theories on $S^1\times \Sigma$ where $\Sigma$ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have…
We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I.…
The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times \Sigma$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the…
We introduce modular inequalities for complements of plane curves, based on a Combinatorial Aomoto complex construction associated with the weak combinatorial type of a curve. We use this as a tool to investigate twisted Alexander…
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is…