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Category Theory 范畴论
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https://www.youtube.com/playlist?list=PLHYBb0FtzAK9TBFhZ8eZzJRc5gW1NNp2K Reading material: Basic Category Theory, by Tom Leinster - This my favourite introductory category theory book, it is easy to read and covers the basics. Category Theory in Context, by Emily Riehl - This is more detailed than BCT and written from a perspective I would describe as 'hardcore category theorist', but it is accessible and has a plethora of examples of each concept. Categories for the Working Mathematician, by Saunders Mac Lane - This is the classic textbook, first published half a century ago. Here is the blurb that I gave attendees: In 1945 Eilenberg and MacLane published ' The General Theory of Natural Equivalences' in which they laid out the basic notions of category theory; mathematics has been reacting ever since. Category theory was born out of algebraic topology and has become a standard language in much of the vast enterprise of mathematics. One of the benefits of category theory is that it distinguishes those aspects of a theory which are specific to the context from those which are "purely formal". This series of lectures will start with the basic notions of category theory, we will define categories, universal properties, functors, natural transformations, and adjunctions, and see many examples of each. Particular attention will be paid to those examples which are tools in algebraic topology. The material covered here will complement that covered in MATH4204, both for those who have taken it and for those who have yet to. Time permitting, when we have covered enough standard material to understand the statement/slogan "all concepts are Kan extensions" we will strike out into the weeds. Potential topics include enriched category theory, homological algebra, homotopical categories, higher category theory, and Morita theory.
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【乌普萨拉大学】Category O BGG范畴
Categories & Sheaves 范畴&层论读书班
Introduction to Category Theory 范畴论简介
Birch Swinnerton-Dyer conjecture BSD猜想
Étale Cohomology and the Weil conjectures
【IAS】Representation Theory & Categorification 表示论与范畴化
Lie Groups and Lie Algebras 李群和李代数
【HSE】Research Seminar "The Weil Conjectures" 韦伊猜想研讨会
The Bernstein Sato polynomial
perverse sheaves 反常层 (偏屈层)
Hodge Theory of p-adic analytic varieties and arithmetic applications
Monge-Ampere equation and Calabi-Yau manifolds
Soergel bimodules and Kazhdan-Lusztig theory
Quiver moduli and applications
Abelian Varieties 阿贝尔簇
Complex surfaces 复曲面
Seminar on Geometric and Modular Representation Theory
Module theory 模论
【厦门大学数论短课】From Galois theory to Galois representations
Modular forms 模形式
An introduction to Gromov-Witten invariants and quantum cohomology
Theory of numbers 基础数论
【乌普萨拉大学】Representation theory of finite groups 有限群的线性表示
Geometric Representation Theory 几何表示论
p-adic Galois representations
Complex analysis 复分析
Introduction to stacks and moduli
Lectures on the Algebraic Index Theorems
Lie groups 李群
【UC Berkeley】R i c c i F l o w
Distribution theory
Algebraic Number Theory 代数数论
Elliptic Curves 椭圆曲线
Geometry of Gauge Theories
Geometric realization of p-adic local Langlands
【MSRI】Ricci Flow by Bennett Chow
Birational geometry of algebraic varieties 双有理几何
【厦门大学Fano Varieties暑校】The existence of complements for Fano type varieties
Lectures on geometric Langlands 几何朗兰兹
Topics in Combinatorics: The Theory of Alternating Sign Matrices