Workshop on modular curves


Monday, 17th of December

Lecture 1

10.30 - 11.45

(Maciej Ulas)

Contents: General definition of elliptic curves and basic facts about them. Reminder on algebraic number theory. Supersingular and ordinary elliptic curves. Hasse invariant. Definition of modular curves.

Lecture 2

13.00 - 14.15

(Joachim Jelisiejew)

Content: Formal groups as a local analogue of elliptic curves. Formal groups associated to elliptic curves. Examples with Lubin-Tate extensions. Lubin-Tate spaces.

Lecture 3

14.35 - 15.50

(Krzysztof Górnisiewicz)


Contents: Modular curves as a moduli problem. Vector bundles on modular curves and their sections- automorphic forms. Basic facts about the geometry of modular curves. Connections between Lubin-Tate spaces and modular curves.
Tuesday, 18th of December

Lecture 4

10.30 - 11.45

(Adrian Langer)

Contents: Complex and p-adic uniformisation of elliptic curves. Tate curve. Introduction to rigid analytic geometry of Tate.

Lecture 5

13.00 - 14.15

(Michał Zydor)

Contents: Why automorphic forms appear naturally in the context of Betti cohomology of modular curves. About Matsushima formula.

Lecture 6

14.35 - 15.50

(Przemysław Chojecki)

Contents: Reminder on etale cohomology in the context of elliptic and modular curves. Applications of I-adic cohomology in Matsushima formula.
Wednesday, 19th of December

Lecture 7

10.30 - 11.45

(Grzegorz Banaszak)

Contents: Why do we want to construct Galois representations? Applications.

Lecture 8

13.00 - 14.15

(Bartosz Naskręcki)

Contents: Construction of Galois representations associated to modular forms of weight 2.

Lecture 9

14.35 - 15.50

(Przemysław Chojecki)

Contents: Cohomology of modular curves in the context of Langlands program.