This is the web page for the seminar "moduli spaces and modular forms'' organised by Peter Bruin and Marco Streng at Universiteit Leiden during the fall semester of 2007.

Location: room 403 of the Snellius building, Universiteit Leiden.

Description

The seminar is aimed at Ph. D. students and possibly also Master students with the goal of understanding moduli spaces and modular forms. The exact program will depend on the wishes of the participants, but we will start with moduli spaces of elliptic curves and with modular forms, both in a complex analytic and a more algebraic geometric setting.

If you are interested in participating, then please let us know. We also welcome all suggestions for the content of the seminar.

Schedule

September 12:

In the week of 17 - 21 September, there is a workshop on Galois Theory and Explicit Methods at the Lorentz Center in Leiden. At this workshop, there are several talks related to moduli spaces and modular forms. We list them here, although they are not a part of our seminar. (abstracts) September 26: October 10: October 24: On Thursday November 1, Bas Edixhoven will speak in the general colloquium in Leiden on an interesting computational application of modular forms. The talk will be for a general mathematical audience, so much of what he will say has already been covered in the seminar. In particular, there is an overlap with Lenny's talk of a few weeks back. November 7: November 21: December 5: On Thursday December 13, Eyal Goren will give a lecture which is related to moduli of curves of genus two. December 19:

Literature

For the basic theory of elliptic curves, we refer to [Sil86] and for algebraic geometry to [Liu06] and [Har77].

Introductions to modular forms include [DS05], [Lan76] and [Gun62].

Further good references include the survey article [DI95], which contains many references itself, and Bas Edixhoven's notes [Edi97].

For an application of modular functions and complex multiplication to representability of primes by quadratic forms, see [Cox89]. For an application of modular forms and L-series to a problem from elementary number theory, see [Kob84].

[Cox89]David A. Cox, Primes of the form x^2+ny^2 (Fermat, Class Field Theory, and Complex Multiplication), 1989
[DI95]Fred Diamond and John Im, Modular forms and modular curves, in V. Kumar Murty, Seminar on Fermat's last theorem, 1995. A scanned copy of the article (36 MB and bad quality) is available here.
[DS05]Fred Diamond and Jerry Shurman, A First Course in Modular Forms, 2005
[Edi97]The notes of Bas Edixhoven's series of lectures The modular curves X_0(N) at the ICTP Summer school on rational torsion of elliptic curves over number fields in Trieste, 1997
[Gun62]R.C. Gunning, Lectures on Modular Forms, 1962
[Har77]Robin Hartshorne, Algebraic Geometry, 1977
[Kob84]Neal Koblitz, Introduction to Elliptic Curves and Modular Forms, 1984
[Lan76]Serge Lang, Introduction to Modular Forms, 1976
[Liu06]Qing Liu, Algebraic Geometry and Arithmetic Curves, 2006
[Sil86]Joseph H. Silverman, The Arithmetic of Elliptic Curves, 1986
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