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<DIV><FONT face=Arial size=2>Gentile Prof./dott.,</FONT></DIV>
<DIV><FONT face=Arial size=2>la avvertiamo che nei prossimi giorni alla Scuola
Normale si terrà, nell'ambito del Colloquio De Giorgi, il seguente seminario di
Matematica:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Giovedì 22 maggio 2003, ore 15:00 Aula
Mancini,</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Prof. D. Zagier</STRONG> </FONT><FONT
face=Arial size=2>(College de France and Max Planck Institute, Bonn)<BR>"Modular
forms and their periods"</FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>
Abstract:<BR>Classical modular forms, which are a certain
class of transcendental functions which transform nicely with respect to an
infinite group of symmetries, have been studied for 200 years and are now one of
the most important tools in number theory. It turns out that one can
associated to each modular form a certain polynomial, called its ``period
polynomial,'' which encodes completely all the information contained in the
modular form itself. This gives a beautiful and very elementary approach
to the theory of modular forms, with many connections to other classical
number-theoretical topics such as continued fractions and Dedekind sums.
The talk will explain how this goes and, if time permits, also about analogous
constructions for other kinds of automorphic functions which lead to surprising
connections with topics from quite different branches of mathematics such as
spectral theory, dynamical systems, and quantum invariants of knots and
3-manifolds.</FONT></FONT></DIV>
<DIV><FONT><FONT face=Arial size=2></FONT></FONT> </DIV>
<DIV><FONT><FONT face=Arial size=2>Cordiali saluti</FONT></FONT></DIV>
<DIV><FONT><FONT face=Arial size=2>SEGRETERIA DELLA CLASSE DI SCIENZE</DIV>
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