Related papers: The wild McKay correspondence and $p$-adic measure…

We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure theoretic notion of…

This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime…

For each of the $15$ known sporadic Ap\'ery-like sequences, we prove congruences modulo $p^2$ that are natural extensions of the Lucas congruences modulo $p$. This extends a result of Gessel for the numbers used by Ap\'ery in his proof of…

We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A^g over a p-adic field, endowed with polynomial actions on each coordinate of A^g. We use analytic methods similar to the ones employed by…

Three massless limits of the Dirac-Kahler theory are considered. It is shown that the Dirac-Kahler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless…

For an odd prime $p$ and a positive integer $n$, let ${_n}G_n[\cdots]_p$ denote McCarthy's $p$-adic hypergeometric function. In this article, we prove $p$-adic analogue of certain classical hypergeometric identities and using these…

We calculate extensions between certain irreducible admissible representations of p-adic groups.

The aim of this paper is to generalize the results on expansive mappings of Yesilkaya and Aydin from \cite{Yesilkaya}. We give some fixed point results for q-expansive mappings in metric spaces and prove some fixed point theorems for this…

This is an informal expository article on geometric Satake correspondence for affine Kac-Moody Lie algebras of type $A$ given in arXiv:1810.04293. We emphasize formal analogies between this result and the author's earlier results on…

We prove that all bounded subsets of $\mathbb{Q}_p^n$ containing a line segment of unit length in every direction have Hausdorff and Minkowski dimension $n$. This is the analogue of the classical Kakeya conjecture with $\mathbb{R}$ replaced…

We start with background that goes into an Iwahori-theoretic reformulation of the mod $p$ Local Langlands Correspondence (\S 2). We then explain some classical $p$-adic functional analytic results (\S 3) that go into defining the $p$-adic…

Recently it was proved that usual (real) Potts model on a Cayley tree has up to $2^q-1$ translation-invariant Gibbs measures. This paper is devoted to description of translation- invariant $p$-adic Gibbs measures (TIpGMs) of the $p$-adic…

We show that, over a nonarchimedean local field, the rigid refined local Langlands correspondence and associated endoscopic character identities for connected reductive $G$ follow if one only has them for all such $G$ with connected center.…

We construct measures on the space $\mathcal D'(Q_p^n)$, $n\le 4$, of Bruhat-Schwartz distributions over the field of $p$-adic numbers, corresponding to finite volume polynomial interactions in a $p$-adic analog of the Euclidean quantum…

For a local field with finite residue field of characteristique p, we give some refinements of Serre's mass formula in degree p which allow us to compute for example the contribution of cyclic extensions, or of those whose galoisian closure…

We present a construction of a measure-zero Kakeya-type set in a finite-dimensional space $K^d$ over a local field with finite residue field. The construction is an adaptation of the ideas appearing in [12] and [13]. The existence of…

In this paper, we take interest in finding applications for a hook-length formula recently proved in (Morales Pak Panova 2016). This formula can be applied to give a non trivial relation between alternating permutations and weighted Dyck…

We derive exact, modified geodesic equations for a system of non-spinning, self-gravitating interacting bodies in a class of alternative theories of gravity to general relativity. We use a prescription proposed by Eardley for incorporating…

This paper is devoted to the construction of generalized multi-scale Young measures, which are the extension of Pedregal's multi-scale Young measures [Trans. Amer. Math. Soc. 358 (2006), pp. 591-602] to the setting of generalized Young…

By the works of Yu, Kim and Hakim-Murnaghan, we have a parameterization and construction of all supercuspidal representations of a reductive $p$-adic group in terms of supercuspidal data, when $p$ is sufficiently large. In this paper, we…