Related papers: An introduction to Mathieu subspaces
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
These notes basically contain a material of two mini--courses which were read in G\"{o}teborg in April 2015 during the author visit of Chalmers & G\"{o}teborg universities and in Beijing in November 2015 during "Chinese--Russian Workshop on…
These are notes accompanying lectures at 7th ILJU School of Mathematics "Banach Spaces and Related Topics" in Gyeongju, Koera. The lectures are devoted to exposition of the theory of quantum families of maps with emphasis on the study of…
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers, affine Springer fibers and Hitchin…
These notes are from a series of lectures given at the Universidad de Los Andes in Bogot\'a, Colombia on some topics of current interest in quantum information. While they aim to be self-contained, they are necessarily incomplete and…
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is…
These lectures give an introduction to the interrelated topics of Calabi-Yau compactification of the type II string, black hole attractors, the all-orders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture.…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon, 2012
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer…
These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.
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 lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.