Related papers: Aftermath
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…
Accelerator science and technology is inherently an integrative discipline that combines aspects of physics, computational science, electrical and mechanical engineering. As few universities offer full academic programs, the education of…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
We study the second law in the context of combinatorial processes, focusing on the mechanisms that give rise to irreversible behavior from an underlying deterministic, invertible, and reversible dynamics.
This paper surveys the literature on theories of discrimination, focusing mainly on new contributions. Recent theories expand on the traditional taste-based and statistical discrimination frameworks by considering specific features of…
A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects.…
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
- Synth\`ese des travaux pr\'esent\'es en vue d'une Habilitation \`a Diriger des Recherches - Synthesis of works presented towards the Habilitation degree This is a summary (in French) of my work in number theory, group theory and…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
This two-part review examines how automation has contributed to different aspects of discovery in the chemical sciences. In this first part, we describe a classification for discoveries of physical matter (molecules, materials, devices),…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…
The objective of this article is to stimulate discussions in mathematical society about the role of mathematical departments in the life of the community. University community is the center of knowledge and promotes the intellectual…
Advances in science and engineering often reveal the limitations of classical approaches initially used to understand, predict, and control phenomena. With progress, conceptual categories must often be re-evaluated to better track recently…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…