Related papers: Betti Spectral Gluing

We consider compact locally symmetric spaces $\Gamma\backslash G/H$ where $G/H$ is a non-compact semisimple symmetric space and $\Gamma$ is a discrete subgroup of $G$. We discuss some features of the joint spectrum of the (commutative)…

We consider several aspects of holomorphic brane configurations. We recently showed that an important part of the defining data of such a configuration is the gluing morphism, which specifies how the constituents of a configuration are…

We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertoric variety match a category of A-branes on a Dolbeault…

Let $W$ be the Weyl group of a split semisimple group $G$. Its Hecke category $\mathsf{H}_W$ can be built from pure perverse sheaves on the double flag variety of $G$. By developing a formalism of generalized realization functors, we…

We define a filtration by DG-subcategories on the DG-category Shv(Bun_G) of sheaves on the moduli of G-torsors on a curve, which is stable under the action of Hecke functors. We formulate a conjecture relating this filtration with another…

The global geometric Langlands correspondence relates Hecke eigensheaves on the moduli stack of G-bundles on a smooth projective algebraic curve X and holomorphic G'-bundles with connection on X, where G' is the Langlands dual group of G.…

We construct analogues of the Hecke operators for the moduli space of G-bundles on a curve X over a local field F with parabolic structures at finitely many points. We conjecture that they define commuting compact normal operators on the…

We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral…

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…

For the group GL(n), we construct an action of the equivariant derived category of coherent sheaves on the Grothendieck-Springer resolution on a certain subcategory of a finite monodromic Hecke category. We use this to construct a partial…

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

In math.RT/0205144 we observed that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character can be…

We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack \tilde\Bun_G of…

We examine two types of half-BPS surface defects $-$ regular monodromy surface defect and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal{N}=2$ supersymmetry and…

The aim of this paper is two--fold. We first strongly improve our previous main result Theorem 3.1 in Arxiv 1702.00918v3 12Feb2018 ("Brill-Noether loci of rank two vector bundles on a general $\nu$-gonal curve"), concerning classification…

For a motivic spectrum $E\in \mathcal{SH}(k)$, let $\Gamma(E)$ denote the global sections spectrum, where $E$ is viewed as a sheaf of spectra on $\mathrm{Sm}_k$. Voevodsky's slice filtration determines a spectral sequence converging to the…

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional $gl_2$-modules. As a byproduct we show that there…

We introduce the family of stable Klingen congruence subgroups of GSp(4). We use these subgroups to study both local paramodular vectors and Siegel modular forms of degree $2$ with paramodular level. In the first part, when $F$ is a…

We consider the Schr\"odinger operator with constant magnetic field defined on the half-plane with a Dirichlet boundary condition, $H_0$, and a decaying electric perturbation $V$. We analyze the spectral density near the Landau levels,…

Let $G$ be a connected reductive complex algebraic group, and $E$ a complex elliptic curve. Let $G_E$ denote the connected component of the trivial bundle in the stack of semistable $G$-bundles on $E$. We introduce a complex analytic…