Faculty of Science AMSI Summer School 2013

AustMS SS2013 subject: Modular forms

Wadim Zudilin
The University of Newcastle


Synopsis

The lectures serve as an in introduction to the classical theory of modular forms and their applications. An impact of the theory on Fermat's Last Theorem will be discussed at the end of the course.

We will start with some useful facts from complex analysis and then go on in accordance with the following plan:


Contact hours

28 hours spread over the four weeks, with consultation upon request.


Prerequisites

Strong background in (complex) analysis, algebra and number theory is desirable. However the course itself will have a potential to create the required knowledge from the process of learning of its usefulness.


Assessment

Two homemade assignments worth 20% each, plus a 3-hour exam in class worth 60%.


Resources

Lecture notes are now available, these will be updated during the course

Recommended reading

  1. S. Lang, Elliptic functions, 2nd edn., Graduate Texts in Math. 112 (Springer, New York–Heidelberg 1987).
  2. J.-P. Serre, A course in arithmetic, Graduate Texts in Math. 7 (Springer, New York–Heidelberg 1973).
  3. E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th edn. (Cambridge, Cambridge University Press 1927).
  4. D. Zagier, Elliptic modular forms and their applications, in: The 1-2-3 of modular forms, Universitext (Springer, Berlin 2008), pp. 1–103.


About Wadim Zudilin

The major part of my education and academic career (1987–2008) is tied up with the Moscow Lomonosov State University (Moscow, Russia). I nevertheless managed to escape for research to Institut Henri Poincaré and Institut de Mathématiques de Jussieu in Paris (Ostrowski fellowship) in 1999, to the University of Cologne in Cologne (Alexander von Humboldt fellowship) in 2003, and to the Max Planck Institute for Mathematics in Bonn (Max Planck Society fellowships) several times from 2006 to 2009. My Australian adventure started in winter 2009 in Newcastle; this is a place where I am now. On the mathematics side, I have strong interests in number theory and its numerous relations with other pure maths subjects; check with my webpage for details.

top of page