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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

This is the arXiv index for the electronic proceedings of GD 2022, which is held at the Tokyo Institute of Technology, Tokyo, Japan, on September 13 - 16, 2022. It contains the peer-reviewed and revised accepted papers with an optional…

Computational Geometry · Computer Science 2022-09-12 Patrizio Angelini , Reinhard von Hanxleden

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…

Algebraic Geometry · Mathematics 2014-03-26 Richard Hain

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…

Representation Theory · Mathematics 2014-09-30 M. Wemyss

This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.

Representation Theory · Mathematics 2011-09-08 Volodymyr Mazorchuk

These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…

Machine Learning · Computer Science 2024-03-11 Bart M. N. Smets

This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on…

Symplectic Geometry · Mathematics 2024-03-07 Jonathan David Evans

These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.

Number Theory · Mathematics 2007-05-23 Laurent Berger , Christophe Breuil

This article contains a slightly expanded version of the lectures given by the author at the summer school "Algebraic stacks and related topics" in Mainz, Germany from August 31 to September 4, 2015. The content of these lectures is purely…

Algebraic Geometry · Mathematics 2015-10-28 Jarod Alper

These are notes from talks given at a spring school on topological quantum field theory in Nova Scotia during May of 2023. The aim is to introduce the reader to the role of factorization algebras and related concepts in field theory. In…

Algebraic Topology · Mathematics 2023-07-06 Araminta Amabel

This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection between Chen's work on iterated integrals on the one hand, and…

Algebraic Geometry · Mathematics 2007-05-23 Richard Hain

In this paper, we will present the author's interpretation and embellishment of five lectures on cluster theory given by Kiyoshi Igusa during the Spring semester of 2022 at Brandeis University. They are meant to be used as an introduction…

Representation Theory · Mathematics 2022-10-13 Ray Maresca

This article contains a collection of problems contributed during the course of the conference.

Algebraic Topology · Mathematics 2009-03-31 Carles Broto , Nguyen H V Hung , Nicholas J Kuhn , John H Palmieri , Stewart Priddy , Nobuaki Yagita

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 informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might…

History and Overview · Mathematics 2023-10-05 Alex Kontorovich

These are the lecture notes for a course taught at Tsinghua University in the spring of 2022. In these notes, we develop the basic theory of vertex operator algebras (VOAs) and their conformal blocks using complex-analytic methods. In…

Quantum Algebra · Mathematics 2023-05-09 Bin Gui

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.

Data Structures and Algorithms · Computer Science 2017-12-27 Petros Drineas , Michael W. Mahoney

These notes are based on lectures given in Wuhan (China) in July 2007. Their aim is to provide an introduction to Langlands philosophy.

Representation Theory · Mathematics 2007-09-19 G. Lusztig

Brief lecture notes for a course about random matrices given at the University of Cambridge.

Probability · Mathematics 2013-05-10 Vladislav Kargin , Elena Yudovina

This volume of the Electronic Proceedings in Theoretical Computer Science (EPTCS) contains extended abstracts of talks to be presented at the Seventh International Conference on Computability and Complexity in Analysis (CCA 2010) that will…

Computational Complexity · Computer Science 2010-06-04 Xizhong Zheng , Ning Zhong