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).
On the p-adic variation of Heegner points
Based on the paper by Francesc Castellà, “On the p-adic variation of Heegner points”.
Iwasawa theory for the symmetric square of a modular form
Based on the article by D. Loeffler and S.L. Zerbes, “Iwasawa theory for the symmetric square of a modular form”. In J. Reine Angew. Math.
Heegner cycles and p-adic L-functions
Based on “Heegner cycles and p-adic L-functions” by Castellà and Hsieh.
The Rank of Mazur’s Eisenstein ideal
In his landmark 1976 paper “Modular curves and the Eisenstein ideal”, Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N.