Related papers: The Master Thesis of Mosh\'e Flato
This is an expansion on my talk at the Geometry and Topology conference at McMaster University, May 2004. We outline a program to relate the Heegaard Floer homologies of Ozsvath-Szabo, and Seiberg-Witten-Floer homologies as defined by…
In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…
This paper debates the contribution of Econophysics to the economic or financial domains. Since the traditional approach performed by Economics or Finance has revealed to be insufficient in fully characterizing and explaining the…
In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider…
We strengthen some results in \'etale (and real \'etale) motivic stable homotopy theory, by eliminating finiteness hypotheses, additional localizations and/or extending to spectra from HZ-modules.
A general slice theorem for the action of a Fr\'echet Lie group on a Fr\'echet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The…
These are notes for a mini-course given at the summer school and conference "The Six-Functor Formalism and Motivic Homotopy Theory" in Milan 9/2021. They provide an introduction to the formalism of Grothendieck's six operations in algebraic…
We study some specializations and extensions of the quantum version of the MacMahon Master Theorem derived by Garoufalidis, Le and Zeilberger. In particular, we obtain a (t,q)-analogue for the Cartier-Foata noncommutative version and a…
Personal recollections on theoretical particle physics in the years when the Standard Theory was formed. In the background, the remarkable development of Italian theoretical physics in the second part of the last century, with great…
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout…
Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's breakthroughs are quietly prepared. In…
In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
This is a free summary of a much longer article published in german in "Forschung Frankfurt". This article presents facts concerning the works of Max Dehn and the history of Frankfurt University. E. Hellinger, R. Moufang, C. L. Siegel, A.…
Mixture of experts (MoE), introduced over 20 years ago, is the simplest gated modular neural network architecture. There is renewed interest in MoE because the conditional computation allows only parts of the network to be used during each…
Artificial intelligence (AI) has achieved astonishing successes in many domains, especially with the recent breakthroughs in the development of foundational large models. These large models, leveraging their extensive training data, provide…
Mixed Tate motives are central objects in the study of cohomology groups of algebraic varieties and their arithmetic invariants. They also play a crucial role in a wide variety of questions related to multiple zeta values and…
In this note, we explore the connections between the confluent Vandermonde matrix over an arbitrary field and several mathematical topics, including interpolation polynomials, Hasse derivatives, LU factorization, companion matrices and…
The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular…
The goal of this text is to exhibit some of the ideas and methods from geometric model theory, translated to the particular context of differentially closed fields, exhibiting in a more or less self-contained way the tools needed for the…