Expository notes

These are notes that for topics that I studied during my Ph.D.

• Notes on Abel-Jacobi maps (Typeset Notes (PDF)).
• Notes on Grothendieck topologies (Typeset Notes (PDF)).
• Notes on Katz’s modular forms, written for the Graduate student seminar organized by H.Darmon.
• Serre’s p-adic modular forms. A summary of Serre’s Antwerp paper, featuring the results and most of the definitions.
• Coleman’s theory of p-adic integrals (Notes on a paper).

Lecture Notes

These are lecture notes of courses that I attended in the past. All errors are mine.

2010 - 2020

• Computational aspects of Shimura curves (Building Bridges 2018, by Drew Sutherland, John Voight) (Scan (PDF))
• The resolvent kernel and the Maass-Shimura-Shintani lifting (Building Bridges 2018, by Ozlem Imamoglu, Arpad Toth) (Scan (PDF))
• Theta liftings and modularity of abelian varieties (Building Bridges 2018, by Jens Funke, Lassina Dembélé) (Scan (PDF))
• Arithmetic of Euler Systems (workshop in Benasque, 2015) (Typeset by many of the participants (PDF))
• Euler Systems (Learning Seminar at Columbia U.) (Scan (PDF))
• Algebraic Cycles and p-adic L-functions (Scan (PDF))
• mod-p Langlands (R.Olivier) (Scan (PDF))

2007 - 2010

• p-adic Integration (A.Iovita) (Typeset Notes (PDF)) (jointly with Cameron Franc)
• p-adic Hodge Theory (B.Cais) (Scan (PDF))
• Geometric Modular forms (A.Iovita) (Typeset Notes (PDF))
• Etale Cohomology (A.Iovita) (Typeset Notes (PDF)) (jointly with Cameron Franc)
• Modular Forms (H.Darmon): (Scan (PDF))
• Algebraic Geometry (A.Iovita)(Typeset Notes (PDF))
• Modular Forms (E.Goren) (Scan (PDF))

2005 - 2007

• Representation Theory (A.Malkin) (Scan (PDF))
• Diophantine Approximation (C.Haesemeyer) (Scan (PDF))
• Modular Forms (S.Ahlgren) (Scan (PDF))
• Class Field Theory (S.Ullom) (Scan (PDF))
• Analytic Number Theory (K.Ford) (Scan (PDF))
• Riemann Surfaces and Algebraic Curves (S.Bradlow) (Scan (PDF))
• Arithmetic of Curves (H.Darmon) (Scan (PDF))
• Group Theory (D.Robinson)(Scan (PDF))
• Algebraic Number Theory (S.Ahlgren) (Scan (PDF))
• Abstract Algebra II (M.Bergvelt) (Scan (PDF))
• Commutative Algebra (C.Rezk) (Scan (PDF))
• Elliptic Curves (I.Duursma) (Scan (PDF))

2004

• Rational Points on Curves (B.Poonen) (Scan (PDF))
• Algorithms for Finite Fields (H.Lenstra) Scan (PDF
• Series de Dirichlet (D.Zagier) (Scan (PDF)) (in Catalan)
• Sobre la Mitjana Aritmetico-Geometrica (J-F.Mestre) (Scan (PDF)) (in Catalan)
• Comptatge de punts en Corbes sobre Cossos Finits (P.Gaudin) (Scan (PDF)) (in Catalan)