Related papers: Period mappings and differential equations. From $…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
Some question about representations of $p$-adic groups are discussed.
The geometry of antisymmetric fields with nontrivial transitions over a base manifold is described in terms of exact sequences of cohomology groups. This formulation leads naturally to the appearance of nontrivial topological charges…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…
With the help of Wick rotation over $p$-adic numbers $\mathbb{Q}_p$, the $p$-adic version of Euclidean $\textrm{dS}_2$ space(noted as $p\textrm{dS}_2$) is obtained based on $p\textrm{AdS}_2$($p$-adic version of Euclidean $\textrm{AdS}_2$…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
In this paper we give an algorithm to calculate the coefficients of the p-adic expansion of a rational numbers, and we give a method to decide whether this expansion is periodic or ultimately periodic.
This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
This is my habilitation thesis. As the tradition wants, I tried to give an introduction of my field of research. I post it on the ArXiv with the hope it can be useful to young researchers looking for a short and friendly text on…
In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. We determine the image of these…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
Let $L/K$ be an extension of number fields that is ramified above $p$. We give a new obstruction to the descent to $K$ of smooth projective varieties defined over $L$. The obstruction is a matrix of $p$-adic numbers that we call ``ramified…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…
We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fourier transform, Poisson formula); representations of…
The differential geometric aspects of Geometric Phases are reviewed.
Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…