2025 Fall: Chabauty-Kim method in Diophantine geometry
References:
R. Coleman. "Effective Chabauty", "Torsion points on curves and p-adic abelian integrals"
M. Kim. "The motivic fundamental group of the projective line minus three points and the theorem of Siegel", "The unipotent Albanese map and Selmer varieties for curves"
J. Balakrishnan - N. Dogra. "Quadratic Chabauty and rational points I: p-adic heights", "An effective Chabauty-Kim theorem"
More references from Arizona Winter School 2020
2025 Spring: Torsion on elliptic curves
References:
"Rational isogenies of prime degree" by Barry Mazur, Invent. Math.
"Bornes pour la torsion des courbes elliptiques sur les corps de nombre" by Loïc Merel, Invent. Math.
2024 Fall: Mazur's torsion theorem
References:
"Modular curves and the Eisenstein ideal" by Barry Mazur, Publ. Math. Inst. Hautes Etudes Sci.
Snowden's course at Univ. of Michigan (2013 fall)
2024 Spring: Diophantine problems and p-adic period mappings
References: "Diophantine problems and p-adic period mappings" by Lawrence and Venkatesh, Invent. Math.
2023 Fall: Prismatic Dieudonné Theory
References: "Prismatic Dieudonné Theory" by Anschütz and Le Bras, Forum Math. Pi
2023 Spring: Eigenvarieties, families of Galois representations, p-adic L-functions
References: "The Eigenbook" by Joel Bellaiche
2022 Fall: Introduction to Prismatic Cohomology
References:
"Prisms and prismatic cohomology" by Bhatt and Scholze, Annals of Mathematics
Bhatt's Eilenberg lectures at Columbia University (2018 fall)
Kedlaya's course notes at UC San Diego (2021 spring)