TeXed notes for personal study. Comments are welcome!
For web, use this link: here
List of notes:
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Number theory
- How automorphic forms and elliptic curves fly?
- Arithmetic of Function Fields (v1.0)
- Proof of $L(2, \chi_{-3}) \not \in \mathbb{Q}$ by Calegari-Dimitrov-Tang
- Modular forms on $G_2$
- Automorphic forms on GL(2)
- Structure of $(\mathbb{Z}/p^{n}\mathbb{Z})^{\times}$
- Nontrivial examples of ideal class groups
- Hilbert's theorem 90
- Some properties of $p$-adic numbers
- Automorphic induction from GL(1) to GL(2)
- Irrationality measure
- Unramified extension of $\mathbb{Q}(\sqrt{3})$
- Langlands functoriality (ongoing)
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Geometry
- Singular algebraic curves (follow Chapter 4 of Serre's Algebraic Groups and Class fields)
- $\mathbb{S}^2$ is not a Lie group
- Low-dimensional complex Spin groups
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Representation theory
- Bruhat-Tits buildings, Moy-Prasad filtration, and Yu's construction
- Littlewood-Richardson rule (ongoing)
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Miscellaneous
I re-TeXed some of the existing articles with old typesets or non-English (e.g. French) for my own study. Let me know if there are any issues, errors, or possible improvements.
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I. Piatetski-Shapiro, Work of Waldspurger, Lie group representations, II (College Park, Md., 1982/1983), 280–302. Lecture Notes in Math., 1041 Springer-Verlag, Berlin, 1984
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R. Beuzart-Plessis, PROGRÈS RÉCENTS SUR LES CONJECTURES DE GAN-GROSS-PRASAD (d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.). Séminaire BOURBAKI (2018): 70e.
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J. Bourgain, L. Clozel, J-P. Kahane, Principe d'Heisenberg et fonctions positives, Annales de l'institut Fourier, Tome 60, no 4 (2010), p. 1215-1232.
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J-P. Labesse, L-indistinguishable representations and trace formula for SL(2), Lie Groups and their Representations (I. M. Gelfand, ed.), Wiley, New York, 1975.
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F. Beukers, Irrationality proofs using modular forms, Astérisque, tome 147-148 (1987), p. 271-283
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P. Colmez, Le Rubik's Cube, Groupe de Poche, ENS Ulm, may (2010).