Related papers: The Master Thesis of Mosh\'e Flato

Koya's and author's approach to the higher local reciprocity map as a generalization of the classical class formations approach to the level of complexes of Galois modules.

Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…

This article gives a self-contained proof of Mostow Rigidity, at least modulo undergrad real analysis. The proof should be accessible to grad students interested in geometry and topology. It has no new research, but I think that this is an…

In his foundational paper [ICM 1983, Warzaw], Ma\~n\'e suggested that some aspects of the Oseledets splitting could be improved if one worked under C1-generic conditions. He announced some powerful theorems, and suggested some lines to…

In his foundational study of $p$-adic Hodge theory, Faltings introduced the method of almost \'etale extensions to establish fundamental comparison results of various $p$-adic cohomology theories. Scholze introduced the tilting operations…

Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the…

I discuss a memorandum entitled " A True state of the Case and Controversy between Sir Isaak Newton and Dr. Robert Hooke as the Priority of that Noble Hypothesis of motion of ye Planets about ye Sun as their Centers", where Hooke summarizes…

This paper, in French, is a celebration of Max Dehn, and an essay of describing some of his results published in the beginning of the 1910's, and their offspring. It has been written up for a winter school in Les Diablerets, March 7-12,…

Since its inception the Metropolis-Hastings kernel has been applied in sophisticated ways to address ever more challenging and diverse sampling problems. Its success stems from the flexibility brought by the fact that its verification and…

This article gives a summary of the author's Ph.D. dissertation (arXiv:1609.06297). In addition to an overview of notions and results, it also provides sketches of various proofs and simplified presentations of certain abstract results of…

Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…

Revised: just some typos, reorganized a bit the article. It will be published in the VIASM Annual meeting, Hanoi. We give a detailed account of Deligne's letter to Drinfeld dated June 18, 2011, in which he shows that there are finitely many…

The philosopher Plato is remembered even today by scientists, and his writings are still inspiring the scientific research. In the present short note (intended essentially for public outreach) two examples are briefly illustrated: 1) the…

We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

Notes of my lectures at the CIME (Levico Terme, june 2015). The lectures gave an overview of the L\"uroth problem, its history, the counter-examples found in the 70's, and the recent developments on stable rationality following the new…

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations,…

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new…

Isaac Newton, in popular imagination the Ur-scientist, was an outstanding humanist scholar. His researches on, among others, ancient philosophy, are thorough and appear to be connected to and fit within his larger philosophical and…

Article purpose is the analysis of a question of possibility of technologization of philosophical knowledge. We understand the organization of cognitive activity which is guided by the set of methods guaranteed bringing to successful (i.e.…

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of…