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【哥伦比亚大学】Geometric categorification in representation theory
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https://www.youtube.com/playlist?list=PLj6jTBBj-5B80o67TXsK6K99Y5H2muMsd Roman Bezrukavnikov The Kazhdan-Lusztig conjectures (stated in the late 70’s, proved in 1980) are a celebrated example of a numerical representation-theoretic question resolved by linking it to a deep algebro-geometric phenomenon. The solution is based on comparing two ways to categorify a given vector space (in this case, the space of functions on the Weyl group): a geometric and an algebraic one. Comparisons of this sort turn out to be a common thread in a number of later results motivated by geometric Langlands duality, mirror duality etc, providing new ways to apply algebraic geometry to representation theory and vice versa. Such results and their consequences will be discussed in the lectures.
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Geometric measure theory and calculus of variations: theory and applications
Galois Theory 伽罗瓦理论
Introduction to Category Theory 范畴论简介
Module theory 模论
Gromov-Witten/Donaldson Thomas theory and Birational/Symplectic invariants
Geometric Representation Theory 几何表示论
【IAS】Representation Theory & Categorification 表示论与范畴化
【乌普萨拉大学】Representation theory of finite groups 有限群的线性表示
【ETHZ】Symmetric Spaces 对称空间
【HSE】Introduction to Functional Analysis 2 Operator Theory 泛函分析2:算子理论
【Arizona 2021】A friendly introduction to the theory of modular forms
【厦门大学数论短课】From Galois theory to Galois representations
Lectures on geometric Langlands 几何朗兰兹
∞-categories and Higher Algebra
【Fields Institute】Symplectic Geometry 辛几何
Lie Groups and Lie Algebras 李群和李代数
Étale Cohomology and the Weil conjectures
Geometric Analysis, Metric Geometry and Topology
Birch Swinnerton-Dyer conjecture BSD猜想
【IMSc India】Representation Theory 表示论
Commutative algebra 交换代数
【罗马二大】An introduction to optimal transport
【UCLA】Spectral Sequences 谱序列
Geometric realization of p-adic local Langlands
【UC Berkeley】Differential Manifold 微分流形
Moduli spaces of parabolic connections, parabolic bundles and Geometric Langland
【ETHZ】Spectral Theory of Hyperbolic Surfaces 双曲曲面的谱理论
【乌普萨拉大学】Lie Algebra 李代数
Seminar on Geometric and Modular Representation Theory
【SLS】What is geometric group theory? by Ian Agol
Joint Columbia-CUNY-NYU Number Theory Seminar
Seminar on A1-topology, motives and K-theory
Abelian Varieties 阿贝尔簇
Topics in Combinatorics: The Theory of Alternating Sign Matrices
Linear Algebra 线性代数
【模形式研讨会】p-adic modular form and galois representation
Potential theory on Berkovich spaces by Matt Baker
p-adic Galois representations
Nonlinear algebra 非线性代数
Group Theory 群论