Teaching

2025 Spring:   Torsion on elliptic curves

Lecture notes  (I do NOT claim any originality of the material):

Lecture 1    Lecture 2    Lecture 3    Lecture 4    Lecture 5   Lecture 6   Lecture 7   Lecture 8   Lecture 9   Lecture 10

Lecture 11  Lecture 12  Lecture 13  Lecture 14  Lecture 15

References:  

1.  "Rational isogenies of prime degree" by Barry Mazur, Invent. Math.

2.  "Bornes pour la torsion des courbes elliptiques sur les corps de nombre" by Loïc Merel, Invent. Math.

2024 Fall:   Mazur's torsion theorem

Lecture notes  (I do NOT claim any originality of the material):

Lecture 1    Lecture 2     Lecture 3     Lecture 4    Lecture 5    Lecture 6    Lecture 7    Lecture 8    Lecture 9    Lecture 10

Lecture 11   Lecture 12  Lecture 13   Lecture 14  Lecture 15  Lecture 16  Lecture 17  Lecture 18  Lecture 19  Lecture 20

Lecture 21  Lecture 22  Lecture 23  Lecture 24

References:  

3. "Modular curves and the Eisenstein ideal" by Barry Mazur, Publ. Math. Inst. Hautes Etudes Sci.

4.  Snowden's course at Univ. of Michigan (2013 fall)

2024 Spring:   Diophantine problems and p-adic period mappings

Lecture notes  (I do NOT claim any originality of the material):

Lecture 1    Lecture 2    Lecture 3     Lecture 4     Lecture 5     Lecture 6     Lecture 7     Lecture 8     Lecture 9    Lecture 10

Lecture 11  Lecture 12  Lecture 13   Lecture 14   Lecture 15   Lecture 16   Lecture 17   Lecture 18   Lecture 19  Lecture 20

Lecture 21  Lecture 22  Lecture 23  Lecture 24

References:  "Diophantine problems and p-adic period mappings" by Lawrence and Venkatesh, Invent. Math.

2023 Fall:   Prismatic Dieudonné Theory

Lecture notes  (I do NOT claim any originality of the material): 

Lecture 1     Lecture 2     Lecture 3    Lecture 4    Lecture 5     Lecture 6    Lecture 7    Lecture 8    Lecture 9    Lecture 10

Lecture 11   Lecture 12   Lecture 13  Lecture 14  Lecture 15   Lecture 16   Lecture 17   Lecture 18   Lecture 19   Lecture 20

Lecture 21   Lecture 22   Lecture 23   Lecture 24

References:  "Prismatic Dieudonné Theory" by Anschütz and Le Bras, Forum Math. Pi

2023 Spring:   Eigenvarieties, families of Galois representations, p-adic L-functions

Lecture notes  (I do NOT claim any originality of the material): 

Lecture 1     Lecture 2     Lecture 3     Lecture 4    Lecture 5    Lecture 6    Lecture 7    Lecture 8    Lecture 9    Lecture 10

Lecture 11   Lecture 12   Lecture 13   Lecture 14  Lecture 15  Lecture 16  Lecture 17  Lecture 18  Lecture 19  Lecture 20

Lecture 21   Lecture 22   Lecture 23   Lecture 24   Lecture 25   Lecture 26   Lecture 27   Lecture 28 

References: "The Eigenbook" by Joel Bellaiche

2022 Fall:   Introduction to Prismatic Cohomology

Lecture Notes  (I do NOT claim any originality of the material):  

Lecture 1      Lecture 2     Lecture 3     Lecture 4     Lecture 5     Lecture 6     Lecture 7     Lecture 8     Lecture 9     Lecture 10

Lecture 11    Lecture 12   Lecture 13   Lecture 14   Lecture 15   Lecture 16   Lecture 17   Lecture 18   Lecture 19   Lecture 20

Lecture 21   Lecture 22  Lecture 23   Lecture 24  Lecture 25  Lecture 26   Lecture 27  Lecture 28

References: 

1. "Prisms and prismatic cohomology" by Bhatt and Scholze, Annals of Mathematics

2. Bhatt's Eilenberg lectures at Columbia University (2018 fall)

3. Kedlaya's course notes at UC San Diego (2021 spring)