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These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

Representation Theory · Mathematics 2026-05-26 Pavel Etingof

Lecture notes on selected topics in the theory of gravitation.

General Relativity and Quantum Cosmology · Physics 2017-03-16 Pietro Menotti

Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).

Statistical Mechanics · Physics 2008-06-20 Remi Monasson

This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…

Number Theory · Mathematics 2017-01-25 Xavier Caruso

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…

Algebraic Geometry · Mathematics 2010-09-27 Michael Atiyah

A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…

Number Theory · Mathematics 2015-07-28 Steve Wright

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.

Differential Geometry · Mathematics 2009-01-26 D. B. McReynolds

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

Differential Geometry · Mathematics 2012-11-20 Jonathan Holland , Bogdan Ion

These notes are based on my four lectures given at the Newton Institute in April 2004 during the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpose is to introduce the reader to the analytic number theory…

Number Theory · Mathematics 2007-05-23 D. A. Goldston

Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…

Algebraic Geometry · Mathematics 2021-10-12 Mark Goresky

These lecture notes accompanied the course Time-Frequency Analysis given at the Faculty of Mathematics of the University of Vienna in the summer term 2021. The material is suitable for an advanced undergraduate course in mathematics or a…

Functional Analysis · Mathematics 2022-04-05 Markus Faulhuber

These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…

Commutative Algebra · Mathematics 2007-05-23 J. Migliore , U. Nagel

We give here the contents pages for the Proceedings of the Lattice 2001 conference (19th International Symposium on Lattice Field Theory) that took place in August 2001 in Berlin, Germany. The contents are in HTML form with clickable links…

High Energy Physics - Lattice · Physics 2009-09-10 M. Mueller-Preussker , W. Bietenholz , K. Jansen , F. Jegerlehner , I. Montvay , G. Schierholz , R. Sommer , U. Wolff

These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of…

Group Theory · Mathematics 2015-02-10 Dipendra Prasad

Lecture notes from a minicourse given at the ICTP in May 2002.

Combinatorics · Mathematics 2007-05-23 Richard Kenyon

These expository lectures focus on the distribution of zeros of the Riemann zeta function. The topics include the prime number theorem, the Riemann hypothesis, mean value theorems, and random matrix models.

Number Theory · Mathematics 2007-05-23 S. M. Gonek

These notes are the written version of my lectures at the Banach Center mini-school "Schubert Varieties" in Warsaw, May 18-22, 2003. Their aim is to give a self-contained exposition of some geometric aspects of Schubert calculus.

Algebraic Geometry · Mathematics 2007-05-23 Michel Brion

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.

dg-ga · Mathematics 2008-02-03 M. Marcolli

These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.

High Energy Physics - Phenomenology · Physics 2013-08-06 Renata Zukanovich Funchal , Benoit Schmauch , Gaëlle Giesen

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

Differential Geometry · Mathematics 2015-03-19 Vladimir G. Ivancevic , Tijana T. Ivancevic