Related papers: Notes on Central Extensions
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for…
These are the lecture notes for the introductory course on Whitehead, Reidemeister and Ray-Singer torsions, given by the author at the University of Zurich in Spring semester 2014.
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…
Notes from a course on linear dynamics given by the author at the University of Da Nang in January 2024.
From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
This monograph is derived from a series of six lectures I gave at the Centre de Recherches Mathematiques in Montreal, in March and June 2000, while titulary of the Aisenstadt Chair.
These are the expanded notes of a mini-course of four lectures by the same title given in the workshop "p-adic aspects of modular forms" held at IISER Pune, in June, 2014. We give a brief introduction of p-adic L-functions attached to…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
The article on the upper central series of infinite groups by M. de Falco, F. de Giovanni, C. Musella and Y.P. Sysak, proceedings of the american mathematical society, Volume 139, Number 2, February 2011, 385--389 consists of a quite long…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
These are the notes from a survey talk given at Arbeitstagung 2001 covering the author's work with Lev Borisov and Sorin Popescu on toric varieties, modular forms, and equations of modular curves.
The paper is devoted to calculating the higher Schur-multiplicator of certain classes of groups with respect to the variety of nilpotent groups. Our results somehow generalize the works of M.R.R. Moghaddam (1979), and N.D. Gupta and M.R.R.…