Related papers: Fiedler-Ptak scaling in max algebra
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…
The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article…
Compact spatial dimension at the TeV scale remain an intriguing possibility that is currently being tested at the LHC. We give an introductory review of extra-dimensional models and ideas, from a phenomenological perspective, but…
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…
This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the algebraic aspects of barycentric algebras. Then, we focus on…
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the…
Talk given at the 6th Philosophy-and-Physics-Workshop ``Epistemological Aspects of the Role of Mathematics in Physical Science'', FEST, Heidelberg, Feb. 1993
A detailed presentation of the results obtained during my Ph.D. research. The main investigations concern explicit descriptions of classes of finite dimensional pointed Hopf algebras and their quasi-isomorphism types.
These notes form an extended version of a minicourse delivered in Universite de Montreal (June 2002) within the framework of a NATO workshop ``Normal Forms, Bifurcations and Finiteness Problems in Differential Equations''. The focus is on…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.
This is an extended version of a talk given at the conference "Algebra and Topology in Interaction" on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995…
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…
The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…