Related papers: Proof of the Aubert-Baum-Plymen-Solleveld conjectu…

This paper surveys what is known about (conjectural) $p$-adic and $p$-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary group…

Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special…

We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-$0$ coefficients. We determine the cuspidal pairs in all…

We examine positive and negative results for the Gromov-Lawson-Rosenberg Conjecture within the class of crystallographic groups. We give necessary conditions within the class of split extensions of free abelian by cyclic groups to satisfy…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

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 $A$ be an abelian variety defined over a number field $F$ with supersingular reduction at all primes of $F$ above $p$. We establish an equivalence between the weak Leopoldt conjecture and the expected value of the corank of the…

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…

We derive exact formulas for the proportions of derangements and of derangements of $p$-power order in the affine classical groups $AU_m(q)$, $ASp_{2m}(q)$, $AO_{2m+1}(q)$ and $AO^{\pm}_{2m}(q)$, where $p$ denotes the characteristic of the…

In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group…

Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…

C. Jantzen has defined a correspondence which attaches to an irreducible representation of a classical $p$-adic group, a finite set of irreducible representations of classical $p$-adic groups supported in a single or in two cuspidal lines…

Let $F$ be a non Archimedean local field, and $G$ be the $F$-points of a connected quasi-split reductive group defined over $F$. In this note we propose a converse theorem statement for generic Langlands parameters of $G$ when the Langlands…

The geometric conjecture developed by the authors in [1,2,3,4] applies to the smooth dual Irr(G) of any reductive p-adic group G. It predicts a definite geometric structure - the structure of an extended quotient - for each component in the…

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…

Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…

We establish Grothendieck's section conjecture for an open subset of the Reichardt-Lind curve, and introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension.

In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…