Picard modular surfaces and families of automorphic forms (II)
p-adic families of modular forms as constructed first by Hida and in greater generality by Coleman and their generalizations are a great tool in modern number theory that appears in different parts of the Langlands program.
Gross-Kudla-Schoen diagonal cycles
Refined conjectures of the Birch and Swinnerton-Dyer type
Based on: B. Mazur, J. Tate, Refined conjectures of the Birch and Swinnerton-Dyer type, Duke Math Journal, vol. 54 1987.
Elliptic units for real quadratic fields
Based on the paper H. Darmon, S. Dasgupta. “Elliptic units for real quadratic fields”.
Applications of Goncharov’s conjectures to point-counting
The classical theory of multiple polylogarithms found a wealth of interesting relations between interesting transcendental numbers.
p-adic Banach spaces and families of modular forms
Based on the paper by Robert Coleman, “p-adic Banach spaces and families of modular forms”, Invent. Math. 127, 417-479 (1997).
p-adic Banach spaces and families of modular forms (II)
Second talk. Based on the paper by Robert Coleman, “p-adic Banach spaces and families of modular forms”, Invent. Math. 127, 417-479 (1997).
Limites de représentations crystallines
Based on the paper by Laurent Berger, “Limites de représentations crystallines”.
On the p-adic periods of X0(p)
Based on the paper by Ehud de Shalit, “On the p-adic periods of X_0(p)”. Mathematische Annalen (1995). Volume: 303, Issue: 3, page 457-472.
On number fields with given ramification
Based on the paper by Gaétan Chenevier, “On number fields with given ramification”, Compositio Mathematica 143 no 6, 1359-1373 (2007).