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These notes for a master class at Aarhus University (March 22--24, 2023) provide an introduction to the theory of completion for triangulated categories.

Category Theory · Mathematics 2023-09-06 Henning Krause

These lecture notes were prepared for a special topics course in the Department of Statistics at the University of Washington, Seattle. They comprise the first eight chapters of a book currently in progress.

Statistics Theory · Mathematics 2024-07-16 Fang Han

These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…

Algebraic Topology · Mathematics 2023-05-09 Olivia Borghi , Marcy Robertson

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…

Representation Theory · Mathematics 2016-09-06 Steve Gelbart

These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$-Positivity Preserver, and their Generators''. The lecture was given at the University of Konstanz in the winter semester 2025/26.

Functional Analysis · Mathematics 2026-02-12 Philipp J. di Dio

This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…

Statistical Mechanics · Physics 2023-12-18 Giampaolo Folena , Alessandro Manacorda , Francesco Zamponi

These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…

Machine Learning · Computer Science 2024-11-07 Nadav Cohen , Noam Razin

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

Mathematical Physics · Physics 2023-07-07 Gaëtan Borot

These are lecture notes of the course in infinity categories given in the fall 2016 at Weizmann Institute.

Category Theory · Mathematics 2018-11-06 Vladimir Hinich

This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.

Analysis of PDEs · Mathematics 2023-12-29 Dongfen Bian , Emmanuel Grenier

The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…

Representation Theory · Mathematics 2010-04-20 Pavel Etingof , Xiaoguang Ma

These notes are based on the lecture courses given at the Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul Sabatier (Toulouse, 08-12.01.1996).

Algebraic Geometry · Mathematics 2007-05-23 Mikhail Zaidenberg

This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.

Algebraic Geometry · Mathematics 2011-12-19 Michael Temkin

These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…

Probability · Mathematics 2017-10-31 Gaëtan Borot

Notes from a course on linear dynamics given by the author at the University of Da Nang in January 2024.

Dynamical Systems · Mathematics 2025-03-03 C. A. Morales

This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…

Algebraic Geometry · Mathematics 2026-05-06 Peter Scholze

These are extended notes for my lectures at the workshop ``Reconstructing the Gravitational Hologram'' held at Galileo-Galilei Institute, Florence, in June 2022.

High Energy Physics - Theory · Physics 2025-03-10 Stefan Hollands

These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon…

High Energy Physics - Phenomenology · Physics 2022-09-07 Cédric Mezrag

A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…

Information Theory · Computer Science 2021-05-12 Peter Gacs

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