Related papers: Weak local-global compatibility and ordinary repre…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this conjecture and present supporting evidence. In particular we…
We compare various notions of weak subsolutions to degenerate complex Monge-Amp\`ere equations, showing that they all coincide. This allows us to give an alternative proof of mixed Monge-Amp\`ere inequalities due to Kolodziej and Dinew.
We shall establish the interior H\"older continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are \begin{equation} u_t= \nabla \cdot \bigg( |\nabla u|^{p-2} \nabla u \bigg), \quad \text{…
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…
We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…
This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient…
We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…
We prove a general result on the depth of Du Bois complexes of a singular variety. We apply it to prove a conjecture of Mustata-Popa and to study the local cohomological defect, extending results of Ogus and Dao-Takagi over the complex…
In a recent manuscript, D.Vogan conjectures that four canonical globalizations of Harish-Chandra modules commute with certain n-cohomology groups. In this article we prove that Vogan's conjecture holds for one of the globalizations if and…
We prove new results in generalized Harish-Chandra theory providing a description of the so-called Brauer--Lusztig blocks in terms of the information encoded in the $\ell$-adic cohomology of Deligne--Lusztig varieties. Then, we propose new…
We introduce a family of modal expansions of {\L}ukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics…
Zagier introduced special bases for weakly holomorphic modular forms to give the new proof of Borcherds' theorem on the infinite product expansions of integer weight modular forms on $\SL_2(\ZZ)$ with a Heegner divisor. These good bases…
Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…
Assuming the Morrison-Kawamata cone conjecture for the generic fiber of a Calabi-Yau fibration and the abundance conjecture, we show (1) the finiteness of minimal models, (2) the existence of a weak rational polyhedral fundamental domain…
Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab\pm 1, but an…
We study the notion of Wach modules in relative setting, generalizing the arithmetic case. Over an unramified base, for a $p$-adic representation admitting such structure, we examine the relationship between its relative Wach module and…
We first propose a generalization of the image conjecture [Z3] for the commuting differential operators related with classical orthogonal polynomials. We then show that the non-trivial case of this generalized image conjecture is equivalent…
The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and…
This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars.…