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Let $\sigma$ be a stability condition on the bounded derived category $D^b({\mathop{\rm Coh}\nolimits} W)$ of a Calabi-Yau threefold $W$ and $\mathcal{M}$ a moduli stack parametrizing $\sigma$-semistable objects of fixed topological type.…

Algebraic Geometry · Mathematics 2023-09-07 Michail Savvas

We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locally and we provide some evidence for this conjecture.…

Algebraic Geometry · Mathematics 2017-12-12 Jarod Alper

We obtain a perturbative proof of localization for quasiperiodic operators on $\ell^2(\Z^d)$ with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which…

Spectral Theory · Mathematics 2025-09-03 Ilya Kachkovskiy , Leonid Parnovski , Roman Shterenberg

Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\mathcal{H}$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let…

Operator Algebras · Mathematics 2022-05-31 Airat M. Bikchentaev

We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of \'etale, smooth, or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove…

Algebraic Geometry · Mathematics 2022-05-19 Jarod Alper , Daniel Halpern-Leistner , Jack Hall , David Rydh

We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…

Quantum Algebra · Mathematics 2009-11-07 Oleg Chalykh , Pavel Etingof , Alexei Oblomkov

Recent results of L. Zsido, based on his previous work with C. P. Niculescu and A. Stroh, on actions of topological semigroups on von Neumann algebras, give a Jacobs-de Leeuw-Glicksberg splitting theorem at the von Neumann algebra (rather…

Operator Algebras · Mathematics 2014-06-03 Volker Runde , Ami Viselter

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D^V of differential operators, and give conditions under which D^V acts irreducibly. We show how this problem,…

Algebraic Geometry · Mathematics 2007-05-23 Rikard Bögvad , Rolf Källström

Suppose $\mathcal{S}$ is a smooth, proper, and tame Deligne-Mumford stack. To\"en's Grothendieck-Riemann-Roch theorem requires correction terms, involving components of the inertia stack, to the standard formula for schemes. We give a brief…

Algebraic Geometry · Mathematics 2023-03-22 Bronson Lim , Franco Rota

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack which is generically a scheme and has quasi-projective coarse moduli. If $\mathcal{X}$ has elementary Abelian 2-group stabilizers and the coarse moduli of the inertia stack is smooth, we…

Algebraic Geometry · Mathematics 2021-03-12 Bronson Lim

We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are $*$-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main…

Representation Theory · Mathematics 2007-05-23 Vasyl Ostrovskyi

We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…

Functional Analysis · Mathematics 2025-06-04 Arvin Lamando , Henry McNulty

Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…

Operator Algebras · Mathematics 2009-10-25 N. Filonov , Y. Safarov

We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…

Algebraic Geometry · Mathematics 2023-05-24 Matthias Stiefenhofer

We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…

Operator Algebras · Mathematics 2021-07-01 Nik Weaver

We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta +iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this non-selfadjoint operator is provided for bounded and unbounded domains with common…

Spectral Theory · Mathematics 2020-01-03 D. S. Grebenkov , B. Helffer

We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein-Gordon type Hamiltonian operators. We first study operators of the form $JG$, where $J$, $G$ are selfadjoint…

Mathematical Physics · Physics 2019-08-09 Ivica Nakić , Krešimir Veselić

We investigate a general structure theory for a vertex operator algebra. We discuss the center and blocks, the Jacobson radical and solvable radical and local vertex operator algebras. The main consequence of our structure theory is that if…

Quantum Algebra · Mathematics 2007-05-23 Chongying Dong , Geoffrey Mason

We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of…

Algebraic Geometry · Mathematics 2025-09-01 Noah Olander , Martin Olsson

In this paper we study Schlichting's K-theory groups of the Buchweitz-Orlov singularity category $\mathcal{D}^{sg}(X)$ of a quasi-projective algebraic scheme $X/k$ with applications to Algebraic K-theory. We prove that for isolated quotient…

Algebraic Geometry · Mathematics 2021-09-15 Nebojsa Pavic , Evgeny Shinder