Related papers: An interview with Tsuyoshi Ando
In this Thesis we develop a novel direction in the theory of nano-objects, i.e., structures of nanometer size in a tunnel contact with macroscopic electron reservoirs (metallic leads). In particular we elucidate the Kondo effect predicted…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic operators, a long-standing conjecture posed by Kato in the…
This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…
We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
Large Language Models (LLMs) have demonstrated excellent capabilities in composing various modules together to create programs that can perform complex reasoning tasks on images. In this paper, we propose TANGO, an approach that extends the…
We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…
The rapid evolution of intelligent electronic devices makes information technology, computer science and electronics strongly related to the teaching of natural sciences. Today almost everybody has a smart phone that can convert light,…
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
We consider the problem of learning a manifold from a teacher's demonstration. Extending existing approaches of learning from randomly sampled data points, we consider contexts where data may be chosen by a teacher. We analyze learning from…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this note we give some remarks and improvements on a recent paper of us [3] about an optimization problem for the $p-$Laplace operator that were motivated by some discussion the authors had with Prof. Cianchi.
In his seminal paper ``Computing Machinery and Intelligence'', Alan Turing introduced the ``imitation game'' as part of exploring the concept of machine intelligence. The Turing Test has since been the subject of much analysis, debate,…
The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".
This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…
My thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854-1929). His early life as as a soldier in the Royal Artillery and the events which led to him embarking on a career in mathematical research and…
The current Special Issue of The Annals of Statistics contains three invited articles. Javier Rojo discusses Erich's scientific achievements and provides complete lists of his scientific writings and his former Ph.D. students. Willem van…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
This paper describes a network of teachers and students who form a living system of education at all levels and achieve high standards. The key process of the network is the process of effective learning by inquiry. Physics is distinguished…