Related papers: A Short Course on Orthogonal Polynomials and Speci…
In this paper we study quasi-orthogonality on the unit circle based on the structural and orthogonal properties of a class of self-invariant polynomials. We discuss a special case in which these polynomials are represented in terms of the…
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…
We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
A new class of 2-orthogonal polynomials satisfying orthogonality conditions with respect to a pair of linear functionals $(u_0,u_1)$ was presented in Douak K & Maroni P [On a new class of 2-orthogonal polynomials, I: the recurrence…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
Notes based on lessons given at {\sc Escuela " Fico Gonz\'alez Acu\~na" de Nudos y 3-variedades}, M\'erida Yucat\'an, M\'exico, 7--10 (2015) and {\sc Encuentro de nudos, trenzas y \'algebras}, Oaxaca--M\'exico, 3--10 October (2018).
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
This is a collection of notes for part of a short course on modal methods in fluid mechanics held at DAMTP, University of Cambridge, in the summer of 2019. These notes introduce the reader to resolvent analysis as it is currently used in…
These notes were prepared in occasion of a mini-course given by the author at the "CIMPA Research School - Hamiltonian and Lagrangian Dynamics" (10-19 March 2015 - Salto, Uruguay). The talks were meant as an introduction to the problem of…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
This document contains the lecture notes for a mini-course on special functions from a complex viewpoint given at the OPSFA Summer School OPSFA-S10 2024, in the period July 29th -- August 2nd, 2024. The summer school was hosted by Section…
The aim of this paper is to study finite orthogonal polynomials on a cone of revolution and its surface. We define two classes of finite orthogonal polynomials on the solid cone and derive their corresponding differential equations and…
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…