Related papers: The Langlands functoriality conjecture in the bise…

The analogy between Yetter's deformation theory form (lax) monoidal functors and Gerstenahaber's deformation theory for associative algebras is solidified by shown that under reasonable conditions the category of functors with an action of…

Let $K$ be a commutative ring with unit and $S$ an inverse semigroup. We show that the semigroup algebra $KS$ can be described as a convolution algebra of functions on the universal \'etale groupoid associated to $S$ by Paterson. This…

In [19] we studied a Fadell-Neuwirth type fibration theorem for orbifolds, and gave a short exact sequence of fundamental groups of configuration Lie groupoids of Lie groupoids corresponding to the genus zero 2-dimensional orbifolds with…

We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands…

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…

We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary abelian categories. The results are strongest for module categories of rngs with enough idempotents. We also reformulate the notion of Frobenius…

Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations…

If one wishes to define a complete Leibniz algebra in such a way as to extend the notion of a complete Lie algebra, two distinct definitions can be found in the current literature. Since biderivations on complete Lie algebras have already…

Let $R$ be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an $R$-algebra with involution, which are rationally ismorphic and have isomorphic semisimple coradicals,…

In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic…

In his proof of the fundamental lemma of the Langlands program, Ng\^o initiated the study of the decomposition theorem for abelian fibrations. When an abelian fibration admits a duality structure, the decomposition theorem and the perverse…

Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS…

For any finitely dimensional associative algebra with global dimension $\leq 2$, we show that there is an embedding from the twisted Ringel-Hall algebra to the Brigeland's Ringel-Hall algebra. In particular, this result is true for tilted…

In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.

Irreducible representations are the building blocks of general, semisimple Galois representations \rho, and cuspidal representations are the building blocks of automorphic forms \pi of the general linear group. It is expected that when an…

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types of algebras with the aim of providing an inductive step towards the proof of this conjecture. Firstly we show that if an algebra…

We construct a duality functor on the category of continuous representations of linearly compact Lie superalgebras, using representation theory of Lie conformal superalgebras. We compute the dual representations of the generalized Verma…