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Modular forms are complex functions that have a great deal of symmetry. They are deeply connected to some of the most exciting current problems in number theory, and their study draws ideas from complex analysis, algebra and number theory. Their most famous application to date is to the proof of Fermat's Last Theorem. We will start with the basic theory and examples, and then look at applications to various areas of number theory. Possible topics include properties of the partition function, the congruent number problem and elliptic curves.
Last updated June 24, 2010 10:49:47 EDT