Related papers: Special functions, KZ type equations and Represent…
These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete…
This chapter is based on a series of lectures that I gave at the National University of Singapore in April 2013. The notes survey the representation theory of the cyclotomic Hecke algebras of type A with an emphasis on understanding the KLR…
We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations of the type Z = X + TZ, where T is a known random variable,…
These are notes related to a 12-hour course of lectures given at the Centre de Recerca Mathem\`atica near Barcelona in February, 2010. The aim of the course was to explain results on curves and their Jacobians over function fields, with…
The present review is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich). Being bounded by lecture frames, the selection of the material, by…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers z_{n}, and of an arbitrary additional parameter (a respectively q), and provide finite-dimensional representations of the two…
These notes are based on lectures given at the XIX Modave School on Mathematical Physics and present an introduction to Exceptional Field Theory. We cover the standard Kaluza-Klein reductions on tori, with applications to supergravity. We…
The paper adjoins the book B.Plotkin, S.Vovsi "Varieties of representations of groups", Riga, "Zinatne", 1983, and turns to be, in a sense, its continuation. In the book the varieties of representations had been considered. In the matter of…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
These are lecture notes for an introductory course on Nichols algebras. As a main reference, I work with the book by Heckenberger and Schneider, but I want to take a distinct categorical perspective and try to develop the topic for an…
We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.