├── .github └── workflows │ └── main.yml ├── README.md └── LICENSE /.github/workflows/main.yml: -------------------------------------------------------------------------------- 1 | name: Push File 2 | 3 | on: push 4 | 5 | jobs: 6 | copy-file: 7 | runs-on: ubuntu-latest 8 | steps: 9 | - name: Checkout 10 | uses: actions/checkout@v2 11 | 12 | - name: Sync file to blog 13 | uses: dmnemec/copy_file_to_another_repo_action@main 14 | env: 15 | API_TOKEN_GITHUB: ${{ secrets.API_TOKEN_GITHUB }} 16 | with: 17 | source_file: 'README.md' 18 | destination_repo: 'LanglandsLearningGroup/LanglandsLearningGroup.github.io' 19 | destination_branch: 'master' 20 | destination_folder: '_posts' 21 | user_email: '941201yuan@gmail.com' 22 | user_name: 'YijunYuan' 23 | commit_message: 'Sync file to blog' 24 | rename: '2022-01-04-video-lecture.md' -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | --- 2 | layout: article 3 | title: Videos & Lectures 4 | mathjax: true 5 | permalink: video_lecture.html 6 | --- 7 | 8 | ## Modular forms, Modularity Lifting theorem and Fermat last theorem 9 | 10 | 1. **[Lecture]** [Fermat’s Last Theorem by Liang Xiao](http://bicmr.pku.edu.cn/~lxiao/2020fall/2020fall.htm ) [B站](https://www.bilibili.com/video/BV17y4y127sG) [Note](https://yufanluo.wpcomstaging.com/wp-content/uploads/2021/01/FLT-by-xiao-liang.pdf) 11 | 2. **[Lecture]** [Modularity Lifting by Patrick Allen](https://patrick-allen.github.io/teaching/f20/f20-modularity-lifting.html) 12 | [B站](https://www.bilibili.com/video/BV1mv411k76k) [Notes on lecture by Wang](https://yufanluo.wpcomstaging.com/wp-content/uploads/2021/01/Modularity-Lifting-by-Patrick-Allen.pdf) 13 | 3. **[Lecture]** [Modularity lifting theorems by Toby Gee](https://www.math.arizona.edu/~swc/aws/2013/index.html) 14 | 4. **[Lecture]** [Fermat’s Last Theorem Conference (Summer 1995)](https://www.bilibili.com/video/BV1rt411R7uM) 15 | The video is not clear enough, you can compare with [book](https://yufanluo.wpcomstaging.com/wp-content/uploads/2021/01/标准版.pdf) 16 | 5. **[Lecture]** [Arizona Winter Semester 2021 and 2022](https://www.math.arizona.edu/~swc/index.html) [B站](https://www.bilibili.com/video/BV1ku411v7zs?p=1) 17 | 6. **[Lecture]** [An introduction to modular forms by Yitang Zhang (in Chinese)](https://www.bilibili.com/video/BV1B4411y7N1?from=search&seid=2629272658836513858) 18 | 7. **[Talk]** [A 2020 View of Fermat's Last Theorem by Kenneth A. Ribet](https://www.youtube.com/watch?v=mq9BS6S2E2k&ab_channel=JointMathematicsMeetings) 19 | 20 | 21 | ## Galois representations, $p$-adic Hodge theory and $p$-adic Langlands Program 22 | 23 | 1. **[Lecture]** [A quick overview to p-adic Hodge theory by Liang Xiao](https://www.bilibili.com/video/BV17y4y127sG?p=14) 24 | 2. **[Lecture]** Introduction to p-adic Hodge theory by Denis Benois 25 | [1](https://www.youtube.com/watch?v=zk8_hbE-w3o&feature=youtu.be&ab_channel=InternationalCentreforTheoreticalSciences) 26 | [2](https://www.youtube.com/watch?v=hqjDJshJmkw&feature=youtu.be&ab_channel=InternationalCentreforTheoreticalSciences) 27 | [3](https://www.youtube.com/watch?v=3n_sNGKgqgg&feature=youtu.be&ab_channel=InternationalCentreforTheoreticalSciences) 28 | [4](https://www.youtube.com/watch?v=YDBUfgsld1k&feature=youtu.be&ab_channel=InternationalCentreforTheoreticalSciences) 29 | 3. **[Lecture]** An overview of the theory of p-adic Galois representations by Jared Weinstein $(\varphi,\Gamma)$-modules and p-adic Hodge theory by Gabriel Dospinescu 30 | [1](https://www.youtube.com/watch?v=1KBKSYTWxBA&t=16s) 31 | [2](https://www.youtube.com/watch?v=o1oIOqPWd8k&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) 32 | [3](https://www.youtube.com/watch?v=GU4huGMbxbw&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) 33 | [4](https://www.youtube.com/watch?v=gkPKbrPt9xU&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) 34 | 4. **[Lecture]** p-adic Hodge theory and deformations of Galois representations by Eugen Hellmann 35 | [1](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_d8zm99gi/1_t7jpqb5e) 36 | [2](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_d8zm99gi/1_0750vb3a) 37 | [3](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_z85tr239/1_bq0e6fqy) 38 | [4](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_z85tr239/1_qv4betgv) 39 | [5](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_z85tr239/1_dewzkyby) 40 | 5. **[Lecture]** [An elementary but modern introduction to p-adic Hodge theory by Sean Howe](https://www.math.utah.edu/~howe/6370/) 41 | [B站](https://www.bilibili.com/video/BV1Bv411a7Gw?t=2759) 42 | 6. **[Lecture]** [$\ell$-adic representations by Adrian Iovita](https://www.bilibili.com/video/BV1cr4y1w71S) 43 | 7. **[Lecture]** [$p$-adic Galois representations](https://www.bilibili.com/video/BV1WD4y1R7Kh) 44 | 8. **[Lecture]** [p-adic functions, p-adic representations and ($\varphi, \Gamma)$-modules Given by Yangyi Ou as ASARC intensive lectures at KAIST, 2009](https://www.bilibili.com/video/BV1VW411w7HG?t=13) 45 | 9. **[Lecture]** [Padova School on Serre conjectures and the p-adic Langlands program](https://events.math.unipd.it/indamlanglandsschool/) [B站](https://www.bilibili.com/video/BV1CA411L7zt?p=1&vd_source=b105b6f89f1b8aa3ba97b66e064ddc68) Just have a look first at [stuff on London NT study group](https://nms.kcl.ac.uk/james.newton/lntsg/lntsg2020.html) It starts with Serre's modularity conjecture, and you can see how it evolved step by step. 46 | 10. **[Talk]** [Lifting Galois representations by Toby Gee](https://www.youtube.com/watch?v=CqiFc_lGRWA) 47 | 11. **[Talk]** [Moduli of Galois Representations by David Savitt](https://www.youtube.com/watch?v=DKYkesElbeo) 48 | 12. **[Talk]** [Serre weight conjectures in higher dimension by Brandon Levin](https://www.youtube.com/watch?v=du_ArZaa74w) 49 | 13. **[Talk]** [Deformations of Galois representations and applications by Emerton](https://www.bilibili.com/video/BV19D4y1R7jP?p=1&share_medium=iphone&share_plat=ios&share_session_id=D1D361AA-61C7-418B-805D-293B6E28B011&share_source=COPY&share_tag=s_i×tamp=1641256323&unique_k=F9RB5Uy) [Note](http://www.math.uchicago.edu/~emerton/pdffiles/galois-talk.pdf) 50 | 14. **[Talk]** [Locally symmetric spaces and torsion classes by Ana Caraiani](https://www.youtube.com/watch?v=H3IQKClavtY&t=105s&ab_channel=InstituteforAdvancedStudy) 51 | 15. **[Talk]** [Reciprocity laws for torsion classes by Ana Caraiani](https://www.youtube.com/watch?v=oW85L0OBY2E&ab_channel=InstituteforAdvancedStudy) 52 | 16. **[Talk]** Locally symmetric spaces, and Galois representations by Peter Scholze [1](https://www.youtube.com/watch?v=cFdm0B9KLcQ&ab_channel=HarvardMath) [2](https://www.youtube.com/watch?v=MasLdfDcKZg&ab_channel=HarvardMath) [B站](https://www.bilibili.com/video/BV1BW411N7HA?p=1) Recommended to watch B站 53 | 17. **[Talk]** [Number of points modulo p when p tends to infinity by Serre](https://www.youtube.com/watch?v=CoGMWDCmfUQ&ab_channel=InstituteforMathematicalSciences) 54 | 18. **[Talk]** [Modularity of Galois Representations by Chandrashekhar Khare](https://www.youtube.com/watch?v=USwJHdGBh1M&list=PLcuoUv-DLxG8kxKa7NE6tDacJ_4BqMVcT&ab_channel=InstituteforAdvancedStudy) 55 | 19. **[Talk]** [Even Galois Representations and the Fontaine-Mazur conjecture by Frank Calegari](https://www.ias.edu/video/nt/calegari) 56 | 20. **[Talk]** [Local ($\ell = p$) Galois Deformation Rings by Ashwin Iyengar](https://www.youtube.com/watch?v=gSX787mLFSs&ab_channel=InstituteforAdvancedStudy) 57 | 21. **[Talk]** [On local Galois deformation rings by Vytautas Paskunas](https://www.youtube.com/watch?v=IiCIiRoCrTU&ab_channel=ColumbiaUniversityDepartmentofMathematics) 58 | 22. **[Minicourse]** An introduction to deformation of Galois Representations by Ehsan Shahoseini [1](https://www.youtube.com/watch?v=Fe27gnX_jr4&ab_channel=BhaskaracharyaPratishthana%2CPune) [2](https://www.youtube.com/watch?v=vj7YntHMdVU&t=10s&ab_channel=BhaskaracharyaPratishthana%2CPune) 59 | 23. **[Talk]** [Moduli Stacks of Galois Representations by Matthew Emerton](https://www.youtube.com/watch?v=hvNoxEFEgfU) 60 | 24. **[Talk]** [Moduli stacks of $(\varphi,\Gamma)$-modules by Toby Gee](https://www.youtube.com/watch?v=mDo1axGnHYs&ab_channel=Centrederecherchesmath%C3%A9matiques-CRM) 61 | 25. **[Lecture]** [Deformation Theory and Moduli in Algebraic Geometry](https://www.msri.org/summer_schools/419#) [B站](https://www.bilibili.com/video/BV154411c7tn?p=1) [Note](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.642.1989&rep=rep1&type=pdf) 62 | 26. **[Talk]** [Compatible systems of Galois representations of global function fields by Gebhard Böckle](http://www.birs.ca/events/2017/5-day-workshops/17w5118/videos/watch/201710020906-Boeckle.html) 63 | 27. **[Talk]** [A step-by-step introduction to p-adic Hodge theory by Jared Weinstein](https://researchseminars.org/talk/AutomorphicProject/41/) 64 | 28. **[Talk]** [Deforming Galois representations by Ashwin Iyengar](https://zoom.us/rec/play/BcLt0H3fxs2VPQAFKDo2bLI0rQQ2-uIZBEKu1BLULcDxayKXy2E-cedWkBfJH3zapQ7wK_u8E6zyLt8o.95ko9Sy0fO7V5fDk?startTime=1652185989000&_x_zm_rtaid=8Y5aKal0SISod4LD4nfTJQ.1652253718459.3031e0c27ba0d7ca8f748acee9d56673&_x_zm_rhtaid=488) 65 | 29. **[Talk]** [$p$-adic Langlands by Matthew Emerton](https://www.bilibili.com/video/BV1Th411o73H?spm_id_from=333.337.search-card.all.click&vd_source=b105b6f89f1b8aa3ba97b66e064ddc68) 66 | 30. **[Lecture]** [Franco-Asian Summer School on Arithmetic Geometry](https://www.ihes.fr/~abbes/Luminy/luminy2022.html) [B站](https://www.bilibili.com/video/BV1AB4y1W75n?spm_id_from=333.999.list.card_archive.click&vd_source=b105b6f89f1b8aa3ba97b66e064ddc68) 67 | 31. **[Talk]** [Adjoint Selmer groups for polarized automorphic Galois representations by Patrick Allen](https://www.youtube.com/watch?v=HsuV4ajmM2g&ab_channel=InstituteforAdvancedStudy) 68 | 32. **[Lecture]** [Inverse Galois Problem by Tim Dokchitser](https://people.maths.bris.ac.uk/~matyd/InvGal/) 69 | 33. **[Talk]** [Counting Galois representations by Frank Calegari](https://www.youtube.com/watch?v=WbbhO-ERN0Q&t=3055s&ab_channel=InstituteforAdvancedStudy) 70 | 71 | 72 | 73 | ## Shimura Varieties 74 | 75 | 1. **[Minicourse]** Introduction to Shimura varieties by Liang Xiao 76 | [1](https://www.bilibili.com/video/BV1Gq4y1K7CA?spm_id_from=333.999.0.0) 77 | [2](https://www.bilibili.com/video/BV1ob4y127MC?spm_id_from=333.999.0.0) 78 | [3](https://www.bilibili.com/video/BV1cQ4y1k7Bf?spm_id_from=333.999.0.0) 79 | [4](https://www.bilibili.com/video/BV14g411c74Q?spm_id_from=333.999.0.0) 80 | [5](https://www.bilibili.com/video/BV1Wq4y1f75e?spm_id_from=333.999.0.0) 81 | [6](https://www.bilibili.com/video/BV18f4y1w7h1?spm_id_from=333.999.0.0) 82 | [7](https://www.bilibili.com/video/BV1sQ4y1r7dj?spm_id_from=333.999.0.0) 83 | [8](https://www.bilibili.com/video/BV16L411x7Pz?spm_id_from=333.999.0.0) 84 | [9](https://www.bilibili.com/video/BV1d64y1b7nG?spm_id_from=333.999.0.0) 85 | [10](https://www.bilibili.com/video/BV1bM4y1g7Xr?spm_id_from=333.999.0.0) 86 | [Note](https://bicmr.pku.edu.cn/cn/content/show/17-2528.html) 87 | 2. **[Minicourse]** [Counting points on Shimura Varieties by Yihang Zhu](https://www.bilibili.com/video/BV1HL4y1z7e2?spm_id_from=333.999.0.0) 88 | 3. **[Talk]** [On torsion in the cohomology of Shimura varieties by Ana Caraiani](https://www.youtube.com/watch?v=Gib2PDj8-qw&t=195s&ab_channel=InstituteforAdvancedStudy) 89 | 4. **[Minicourse]** [Perfectoid Shimura varieties by Ana Caraiani](https://www.math.arizona.edu/~swc/aws/2017/index.html) 90 | 5. **[Minicourse]** An example based introduction to Shimura varieties and their compactifications by Kai-Wen Lan [1](https://www.youtube.com/watch?v=3ESH9URO3G4&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) [2](https://www.youtube.com/watch?v=oSiM7wZo5Uc&list=PLCe-H2N8-ny6CuzEHzZshbqiuVVXIdVUe&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) [3](https://www.youtube.com/watch?v=5wNmy_FB5X0&list=PLCe-H2N8-ny6CuzEHzZshbqiuVVXIdVUe&index=2&ab_channel=MathematicsvideoVAROQUIHerv%C3%A9) 91 | 92 | ## Etale Cohomology, Perverse Sheaves and $p$-adic Cohomology 93 | 94 | 1. **[Lecture]** [Etale cohomology by Daniel Litt](https://www.daniellitt.com/tale-cohomology) 95 | 2. **[Talk]** [Finiteness Theorems for Etale Cohomology of Excellent Schemes by Ofer Gabber](https://www.ias.edu/video/geometry-and-arithmetic-finiteness-theorems-etale-cohomology-excellent-schemes) 96 | [Note](http://www.cmls.polytechnique.fr/perso/laszlo/gdtgabber/abelien.pdf) 97 | 3. **[Talk]** [The pro-etale site by Peter Scholze](https://www.youtube.com/watch?v=qL5uxXAeU00&ab_channel=HausdorffCenterforMathematics) 98 | 4. **[Minicourse]** [on perverse sheaves by Williamson](https://www.youtube.com/watch?v=HQxKjquwbz4&list=PLp4l8vpEC0G_dNZfHpeh1NefZo3v3O6XG&ab_channel=SNSChannelMathematicalandNaturalSciences) 99 | 5. **[Talk]** [Etale and crystalline companions by Kiran Kedlaya](https://www.ias.edu/video/members/2019/0415-KiranKedlaya) 100 | 6. **[Talk]** [Arithmetic D-modules and existence of crystalline companion by Abe, Tomoyuki](https://library.cirm-math.fr/Record.htm?record=19282450124910006329&lang=ES) 101 | 102 | 103 | ## $p$-adic Geometry, Perfectoid Spaces, Prismatic Cohomology and Geometrization of the Local Langlands Program 104 | 1. **[Lecture]** [$p$-adic geometry AWS2007](https://www.math.arizona.edu/~swc/aws/2007/notes.html) 105 | 2. **[Lecture]** [Perfectoid Spaces and the Weight-Monodromy Conjecture by Peter Scholze at IHES, 2011](http://www.ihes.fr/~abbes/CAGA/scholze.html) [B站](https://www.bilibili.com/video/BV1vs411E7wP) This is Scholze's interpretation of his own doctoral dissertation [perfectoid space](http://www.ihes.fr/~abbes/CAGA/PerfectoidSpaces.pdf) 106 | 3. **[Lecture]** [Overview: Perfectoid Spaces and their Applications](https://www.youtube.com/watch?v=CiN7X7V-HOE&t=2646s&ab_channel=xuan-gottfriedYANG), [Note](https://yufanluo.wpcomstaging.com/wp-content/uploads/2021/01/Overview.pdf) and [ICM 2014](https://www.youtube.com/watch?v=82nhZ1KtcQs&ab_channel=SeoulICMVOD),[Note](https://www.math.uni-bonn.de/people/scholze/ICM.pdf) 107 | 4. **[Lecture]** [Berkeley lectures on $p$-adic geometry by scholze](https://www.bilibili.com/video/BV15s41147ke) [Note](https://www.math.uni-bonn.de/people/scholze/Berkeley.pdf) 108 | 5. **[Lecture]** [AWS2017,applications of perfectoid space](https://www.math.arizona.edu/~swc/aws/2017/index.html) 109 | 6. **[Lecture]** [Prismatic cohomology by Scholze](https://www.bilibili.com/video/BV1GJ41147a7?p=1&share_medium=iphone&share_plat=ios&share_source=COPY&share_tag=s_i×tamp=1611070488&unique_k=qsqSNZ) A great preview of those lectures was given by [Tao’s blog](https://terrytao.wordpress.com/2019/03/19/prismatic-cohomology/) a great [Note](http://www.math.columbia.edu/~chaoli/doc/BhattEilenberg.html) 110 | 7. **[Lecture]** [Geometrization of the local Langlands correspondence by scholze](https://www.bilibili.com/video/BV17y4y1B7vy?from=search&seid=11345345554728752100) [Course homepage](http://www.math.uni-bonn.de/people/scholze/Geometrization/) [Notes by Tony feng](https://www.mit.edu/~fengt/beyond.html) 111 | 8. **[Lecture]** [Workshop on “Perfectoid spaces”](https://www.icts.res.in/program/perfectoid2019/talks) [Course homepage](https://www.icts.res.in/program/perfectoid2019) [Note](https://www.icts.res.in/event/page/18447) 112 | 9. **[Lecture]** [prismatic cohomology by kedlaya](https://www.bilibili.com/video/BV1tX4y1G7bM) [Course homepage](https://kskedlaya.org/math206a-spr21/) [Note](https://kskedlaya.org/prismatic/sec_overview.html) 113 | 10. **[Lecture]** Simons Lecture Series：p-adic algebraic geometry by Bhargav Bhatt 114 | [1](https://www.youtube.com/watch?v=zVICcM8PUEI&t=79s&ab_channel=StonyBrookMathematicsStonyBrookMathematics) 115 | [2](https://www.youtube.com/watch?v=HyAZFB5niNM&ab_channel=StonyBrookMathematicsStonyBrookMathematics) 116 | [3](https://www.youtube.com/watch?v=oEebN8VCHEQ&ab_channel=StonyBrookMathematicsStonyBrookMathematics) [Note](http://www.math.stonybrook.edu/Videos/SimonsLectures/PDFs/20210415-Bhatt.pdf) 117 | 11. **[Lecture]** [p-adic Riemann-Hilbert functor and vanishing theorems by Bhargav Bhatt](https://www.bilibili.com/video/BV1P541157Np?p=1) 118 | 12. **[Lecture]** [四部曲](https://www.bilibili.com/video/BV1Gt4y1X7dq?p=1) 119 | 13. **ICM2018** [Perfectoid spaces and the homological conjectures](https://www.youtube.com/watch?v=U5MR7jy4Bwo&ab_channel=RioICM2018) 120 | 14. **[Minicourse]** [Bun_G, shtukas, and the local Langlands program](https://sites.google.com/view/rampageseminar/bun_g-minicourse) 121 | 15. **[Talk]** [Geometrization of the local Langlands correspondence by Laurent Fargues](https://www.youtube.com/watch?v=gq5vB2xbRv0&ab_channel=FieldsInstitute) 122 | 16. **[Lecture]** Fourier transform and the geometrization of local Langlands by Arthur-César Le Bras [1](https://www.youtube.com/watch?v=2E-Uz7yhpuA&list=PLAMniZX5MiiJWkTT5scA5hNUdOavlnuKf&index=2&ab_channel=GeoTopCPH) [2](https://www.youtube.com/watch?v=HI2v8U4zQy8&list=PLAMniZX5MiiJWkTT5scA5hNUdOavlnuKf&index=1&ab_channel=GeoTopCPH) [3](https://www.youtube.com/watch?v=4kXa6WKoVq8&list=PLAMniZX5MiiJWkTT5scA5hNUdOavlnuKf&index=3&ab_channel=GeoTopCPH) [4](https://www.youtube.com/watch?v=a66knWC0mCU&list=PLAMniZX5MiiJWkTT5scA5hNUdOavlnuKf&index=4&ab_channel=GeoTopCPH) [5](https://www.youtube.com/watch?v=zNfgK__-gY4&list=PLAMniZX5MiiJWkTT5scA5hNUdOavlnuKf&index=5&ab_channel=GeoTopCPH) 123 | 17. **[Talk]** [The Fargues-Fontaine curve and local Langlands by Arthur-César Le Bras](https://researchseminars.org/talk/AutomorphicProject/47/) 124 | 18. **[Talk]** [Overview of the Fargues–Fontaine curve by Gabriel Dospinescu](https://researchseminars.org/talk/AutomorphicProject/43/) 125 | 19. **[Talk]** [Vector bundles on the Fargues-Fontaine curve by Gabriel Dospinescu](https://researchseminars.org/talk/AutomorphicProject/49/) 126 | 20. **[Workshop]** [Workshop on Geometrization of Local Langlands Correspondence](https://mp.weixin.qq.com/s/K2xI5oSA3wdNw6sSChGxoQ) [video](https://cloud.tsinghua.edu.cn/d/f75955eab0514a48b446/) 127 | 128 | ## $L$-functions 129 | 130 | 1. **[Lecture]** [Arithmetic of Elliptic curves and special values of L-functions](https://www.icts.res.in/program/ecl2022) 131 | 2. **[Lecture]** [Analytic Aspects of L-functions and Applications to Number Theory](https://mathtube.org/conference/Analytic%20Aspects%20of%20L-functions%20and%20Applications%20to%20Number%20Theory) 132 | 133 | ## Langlands Program 134 | 135 | 1. **[Lecture]** [Automorphic Forms and the Langlands Program by Kevin Buzzard at the Summer Graduate School of MSRI](https://www.bilibili.com/video/BV1YW411L7Zr) [Course homepage](http://wwwf.imperial.ac.uk/~buzzard/MSRI/) (You can find the Latex notes below) 136 | 2. **[Lecture]** The local Langlands correspondence and local-global compatibility for $GL_2$ by Sug Woo Shin 137 | [1](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_134l1psy/1_47ritgx2) 138 | [2](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_134l1psy/1_0ijb4ug0) 139 | [3](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_134l1psy/1_g6ortsdt) 140 | [4](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_134l1psy/1_nt9wgc27) 141 | [5](https://mediaspace.unipd.it/playlist/dedicated/119214951/1_d8zm99gi/1_y4s3ep5b) 142 | 3. **[Lecture]** [Representation theory and number theory by Benedict Gross](https://www.bilibili.com/video/BV1d441147Lz?p=1) [Note](http://www.math.columbia.edu/~chaoli/docs/EilenbergLectures.html#sec10) 143 | 4. **[Lecture]** [Langlands correspondence and Bezrukavnikov’s equivalence by Geordie Williamson](https://www.youtube.com/watch?v=9icAHvcVRAc&list=PLtmvIY4GrVv9kMZmf4Fm1mHUGYzTPY8pV&ab_channel=SydneyMathematicalResearchInstitute-SMRI) [Note](https://arxiv.org/pdf/2103.02329.pdf) 144 | 5. **[Lecture]** [Relative aspects of the Langlands program by Farrell Brumley](https://www.bilibili.com/video/BV19f4y1478E?p=1&share_medium=iphone&share_plat=ios&share_source=GENERIC&share_tag=s_i×tamp=1615239713&unique_k=yvhg3e) [Course homepage](https://www.math.univ-paris13.fr/~brumley/M2-2021.html) 145 | 6. **[Lecture]** [Sato-Tate distributions](https://www.math.arizona.edu/~swc/aws/2016/index.html) 146 | 7. **[Lecture]** An introduction to the Langlands correspondence by Matthew Emerton 147 | [1](https://www.youtube.com/watch?v=oXQvcNdu-b8&t=520s&ab_channel=MathsVideos) 148 | [2](https://www.youtube.com/watch?v=EjewLsTU8Dw&t=508s&ab_channel=MathsVideos) 149 | 8. **[Lecture]** Motives and L-functions by Frank Calegari 150 | [1](https://www.youtube.com/watch?v=hKpbvq7HsZo&ab_channel=HarvardMath) 151 | [2](https://www.youtube.com/watch?v=NN3Gt6iBj3w&ab_channel=HarvardMath) 152 | [Note](http://www.math.uchicago.edu/~fcale/papers/CDM.pdf) 153 | 9. **[Popular science]** [Modular forms and Galois representations by Sug Woo Shin](https://www.youtube.com/watch?v=2cGTHuiRo3E&ab_channel=MathnetKorea) 154 | 10. **[Talk]** [The local Langlands conjecture by Richard Taylor](https://www.youtube.com/watch?v=xwPwDAMzWlc&ab_channel=InstituteforAdvancedStudy) 155 | 11. **[Talk]** [Local Langlands correspondence for $GL_n$ over $p$-adic fields by Michael Harris](http://www.birs.ca/events/2008/summer-schools/08ss045/videos/watch/200808121600-Harris.html) 156 | 12. **[Lecture]** [Between electric-magnetic duality and the Langlands program](https://web.ma.utexas.edu/users/vandyke/notes/langlands_sp21/langlands.pdf) 157 | by David Ben-Zvi 158 | 13. **[Lecture]** [IHES Summer School on the Langlands Program](https://indico.math.cnrs.fr/event/6909/timetable/) 159 | 14. **[Workshop]** [Langlands correspondence for function fields-explain Vincent Lafforgue's ground breaking work](https://www.msri.org/workshops/855) [B站](https://www.bilibili.com/video/av55649612/) 160 | 15. **[Mini course]**[Introduction to Langlands-Shahidi Method by Dongming She](https://bicmr.pku.edu.cn/content/show/70-2488.html) [B站](https://www.bilibili.com/video/BV1Xg411u7cH?spm_id_from=333.337.search-card.all.click) 161 | 162 | ## Algebraic Number Theory and Class Field Theory 163 | 164 | 1. **[Lecture]** An introduction to algebraic and analytic number theory by Kedlaya [Part I](https://www.bilibili.com/video/BV12X4y1K7Wn) [Part II](https://www.bilibili.com/video/BV1HT4y1K7RU) 165 | [Course homepageI](https://kskedlaya.org/math204a-fall20/) [II](https://kskedlaya.org/math204b-win21/) 166 | 2. **[Lecture]** [Algebraic Number Theory II by Johannes Sprang](https://homepages.uni-regensburg.de/~spj54141/teaching.html) 167 | 3. **[Lecture]** [Algebraic Number Theory by Howe](https://www.math.utah.edu/~howe/2021-fall/6370/) 168 | 4. **[Lecture]** [Class field theory standpoint and its so different three fundamental generalisation by Ivan Fesenko](https://www.bilibili.com/video/BV18A4y1X75i?spm_id_from=333.999.0.0) 169 | 170 | ## Geometric Langlands Program 171 | 172 | 1. **[Lecture]** [Langlangds program by Frenkel](https://www.bilibili.com/video/BV1XW411C7GN) P1:overview, P2-P5: langlands correspondence for function fields; P5: Deligne's proof of GCFT; P6: the case of over complex number and langlands correspondence for loop group 173 | 2. **[Talk]** [Geometric class field theory](https://www.msri.org/workshops/137/schedules/687) 174 | 3. **[Talk]** [Classical and geometric Langlands over function fields By Dennis Gaitsgory](https://www.bilibili.com/video/BV17Q4y1v734?spm_id_from=333.337.search-card.all.click) 175 | 4. **[Workshop]** [Towards the proof of the geometric Langlands conjecture](https://sites.google.com/site/geometriclanglands2014/) [B站](https://www.bilibili.com/video/av57651093/) 176 | 177 | ## Stacks and Moduli 178 | 179 | 1. **[Lecture]** [What is a Stack?](https://www.youtube.com/watch?v=91fJ3GTM7Dk&list=LL&index=2&ab_channel=TaylorDupuy) 180 | 2. **[Lecture]** [Introduction to stacks and moduli by Jarod Alper](https://sites.math.washington.edu/~jarod/math582C.html) 181 | 3. **[Lecture]** [Moduli spaces in algebraic geometry by Ravi Vakil](https://math.stanford.edu/~vakil/22-245moduli/) 182 | 183 | ## Higher Category Theory 184 | 185 | 1. **[Popular science]** [$ \infty $-Category Theory for Undergraduates](https://www.youtube.com/watch?v=A6hXn6QCu0k&feature=youtu.be&ab_channel=EmilyRiehl) 186 | 2. **[Lecture]** [Lecture course “Topological Cyclic homology”, WS 2020/21](https://www.uni-muenster.de/IVV5WS/WebHop/user/nikolaus/tc.html) 187 | 3. **[Lecture]** [Introduction to higher category theory by Tobias Dyckerhoff](https://www.math.uni-hamburg.de/home/dyckerhoff/inftycat2021/index.html) 188 | 4. **[Lecture]** [Introduction to Derived Geometry](http://bicmr.pku.edu.cn/content/show/70-2449.html) Password：Geometry 189 | 190 | ## Rational Points on Varieties 191 | 192 | 1. **[Lecture]** [Rational points on curves by Henri Darmon](https://www.bilibili.com/video/BV1M5411H7f5) [Note](http://www.claymath.org/library/proceedings/cmip08c.pdf) 193 | 2. **[Lecture]** [Faltings’ proof of the Mordell Conjecture by Jared Weinstein](https://www.bilibili.com/video/BV1Bt4y1B7VX) [Course homepage](https://sites.google.com/view/ma-842-spring-2021/home) 194 | 3. **[Lecture]** [Arizona Winter School 2015: Arithmetic and Higher-Dimensional Varieties](https://www.math.arizona.edu/~swc/aws/2015/index.html) 195 | 4. **[Talk]** [Introduction to the Mordell conjecture by Xinyi Yuan](https://www.bilibili.com/video/BV1534y1m7iy?spm_id_from=333.999.0.0) 196 | 197 | ## Iwasawa theory 198 | 199 | 1. **[Lecture]** [Iwasawa theory by Ted Chinburg](https://www2.math.upenn.edu/~ted/720F18/hw-720SchedTab.html) [1](https://www.bilibili.com/video/BV1854y1p7go) [2](https://www.bilibili.com/video/BV1tV411q7UM) 200 | [Course homepage](https://www2.math.upenn.edu/~ted/720F18/info.html#texts) 201 | 2. **[Lecture]** [Arizona Winter School 2018: Iwasawa Theory](https://www.math.arizona.edu/~swc/aws/2018/index.html) 202 | 203 | ## Ramification Theory and Geometry 204 | 205 | 1. **[Lecture]** [Arizona Winter School 2012: Ramification and Geometry](https://www.math.arizona.edu/~swc/aws/2012/index.html) 206 | 207 | 208 | 209 | ## Condensed Mathematics 210 | 211 | 1. **[Popular science]** [Condensed Mathematics](https://www.youtube.com/watch?v=pzq1FvmEjaM&feature=youtu.be&ab_channel=GraduateMathematics) 212 | 2. **[Lecture]** Masterclass in Condensed Mathematics [Bilibili](https://www.bilibili.com/video/BV1YD4y1X74T?p=1&share_medium=android&share_source=more&bbid=PAhsW2pYYQNnA2AGegZ6infoc&ts=1610875564950) 213 | [Note](https://www.math.uni-bonn.de/people/scholze/Condensed.pdf) 214 | 3. **[Seminar]** Condensed Seminar 215 | - [Who cares about pyknosis](https://www.msri.org/seminars/24809) 216 | - [Pyknotic sets](https://www.msri.org/seminars/24915#description) 217 | - [Pyknotic abelian groups](https://www.msri.org/seminars/24919) 218 | - [Animating pyknotic sets (AKA pyknotic spaces)](https://www.msri.org/seminars/24750) 219 | 4. **[Seminar]** Joint Seminar TUM/UR: [Condensed/Pyknotic Mathematics](http://www.mathematik.uni-regensburg.de/cisinski/condensed.html) 220 | 5. **[Seminar]** [Condensed Mathematics (in Chinese)](https://www.bananaspace.org/wiki/%E8%AE%B2%E4%B9%89:%E5%87%9D%E8%81%9A%E6%80%81%E6%95%B0%E5%AD%A6) 221 | 6. **[Lecture]** [Lecture (Summer 2022): Condensed Mathematics and Complex Geometry by Peter Scholze and Dustin Clausen](https://people.mpim-bonn.mpg.de/scholze/Course%20Summer%2022.html) [B站](https://www.bilibili.com/video/BV1XN4y1T7kz?mid=617908&p=1&share_from=ugc&share_medium=iphone&share_plat=ios&share_source=WEIXIN&share_tag=s_i×tamp=1658093210&unique_k=LnAT7dP&vd_source=b105b6f89f1b8aa3ba97b66e064ddc68) 222 | 223 | ## Deligne–Lusztig Theory 224 | 225 | 1. **[Lecture]** [Introduction to Deligne Lusztig Theory](https://www.youtube.com/watch?v=eQC9i4ul-K4&ab_channel=NingShan) 226 | -------------------------------------------------------------------------------- /LICENSE: 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No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------