Related papers: Differential operators on locally analytic Shimura…

A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…

We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential…

This text is a revised version of the authors Habilitationsschrift which was submitted to the University of Augsburg, 1993. Fuchs type differential operators are used to model the analysis on manifolds with cone--like singularities, or more…

We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex operator algebras and conformal nets to the case of vertex operator superalgebras and graded-local conformal nets by introducing the notion of strongly…

We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $\gamma$-, $L$- and $\epsilon$-factors for pairs of genuine…

Let $n\geq 2$ be an integer, $p$ be a prime number and $K$ be a finite extension of $\mathbb{Q}_p$. Motivated by Schraen's thesis and Gehrmann's definition of automorphic simple $\mathscr{L}$-invariants, we study the first non-vanishing…

Let $\mathbf{G}$ be a reductive group and $\mathbf{X}$ a spherical $\mathbf{G}$-variety over a local non-archimedean field $\mathbb{F}$. We denote by $S(\mathbf{X}(\mathbb{F}))$ the Schwartz-functions on $\mathbf{X}(\mathbb{F})$. In this…

We give the sufficient conditions for the vector-valued Kurokawa-Mizumoto congruence related to the Klingen-Eisenstein series to hold. And we give a reinterpretation for differential operators on automorphic forms by the representation…

In the geometric Langlands program over function fields, Braverman-Gaitsgory and Laumon constructed geometric Eisenstein functors which geometrize the classical construction of Eisenstein series. Fargues and Scholze very recently…

In this text we consider discrete Laplace operators defined on lattices based on finitely-ramified self-similar sets, and their continuous analogous defined on the self-similar sets themselves. We are interested in the spectral properties…

We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…

Let $H$ be a Schr\"odinger type operator with long-range perturbation. We study the wave front set of the distribution kernel of $(H-\lambda\mp i0)^{-1}$, where $\lambda$ is in the absolutely continous spectrumof $H$.The result is a…

We study the two primary families of spaces of finite element differential forms with respect to a simplicial mesh in any number of space dimensions. These spaces are generalizations of the classical finite element spaces for vector fields,…

We study several categories of analytic stacks relative to the category of bornological modules over a Banach ring. When the underlying Banach ring is a non-Archimedean valued field, this category contains derived rigid analytic spaces as a…

We give a simple construction of the Bernstein-Gelfand-Gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear…

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…

We study the integral models of meta-unitary Shimura varieties through the lens of Scholze's fiber product conjecture. Reformulating Bultel's original construction in terms of moduli stacks of Shtukas and Igusa stacks, we prove the validity…

A Beilinson completion algebra (BCA) A is a complete semilocal algebra over a perfect field k, whose residue fields are high dimensional local fields. In addition A is a semi-topological algebra. The completion of the structure sheaf of an…

This paper establishes semiorthogonal decompositions for derived Grassmannians of perfect complexes with Tor-amplitude in $[0,1]$. This result verifies the author's Quot formula conjecture [J21a] and generalizes and strengthens Toda's…

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal…