<div dir="ltr"><p class=""><span style="font-size:18pt;font-family:'Times New Roman',serif">SEMINARI
MATEMATICA</span></p>
<pre><b><span style="font-size:22pt;font-family:'Times New Roman',serif"> </span></b></pre><pre style="text-align:center"><b><span lang="EN-US" style="font-size:20pt;font-family:'Times New Roman',serif">Il dr. <span style="background-image:initial;background-repeat:initial">Lars Kuehne</span></span></b><b><span lang="EN-US" style="font-size:22pt;font-family:'Times New Roman',serif"> </span></b></pre><pre style="text-align:center"><i><span lang="EN-US" style="font-size:12pt;font-family:'Times New Roman',serif">(SNS)</span></i></pre>
<p class="MsoNormal" align="center" style="text-align:center"><span lang="EN-US" style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:'Times New Roman',serif">Terrà due
seminari dal titolo:</span></p>
<p class="MsoNormal" align="center" style="text-align:center"><b><span style="font-size:22pt;font-family:'Times New Roman',serif"> </span></b></p>
<p class="" align="center" style="text-align:center"><b><i><span style="font-size:20pt;font-family:'Times New Roman',serif">“</span></i></b><b><span style="font-size:20pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Modular forms</span></b><b><i><span lang="EN-US" style="font-size:20pt;font-family:'Times New Roman',serif">”</span></i></b><b><span lang="EN-US" style="font-size:20pt;font-family:'Times New Roman',serif"></span></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><b><span lang="EN-US" style="font-size:20pt;font-family:'Times New Roman',serif"> </span></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:14pt;font-family:'Times New Roman',serif">secondo il
seguente calendario:</span></p>
<p class="MsoNormal"><span style="font-size:14pt;font-family:'Times New Roman',serif"> </span></p>
<p class="MsoNormal" style="margin-left:9pt;line-height:18pt"><span style="font-size:14pt;font-family:'Times New Roman',serif">Lunedì 24 novembre 2014</span><span style="font-size:14pt;font-family:'Times New Roman',serif"></span></p>
<p class="MsoNormal" style="margin-left:9pt;line-height:18pt"><span style="font-size:14pt;font-family:'Times New Roman',serif">ore 14:00, Aula Mancini</span></p>
<p class="MsoNormal" style="margin-left:9pt;line-height:18pt"><span style="font-size:14pt;font-family:'Times New Roman',serif"> </span></p>
<p class="MsoNormal" style="margin-left:9pt;line-height:18pt"><span style="font-size:14pt;font-family:'Times New Roman',serif">Lunedì 1
dicembre 2014</span></p>
<p class="MsoNormal" style="margin-left:9pt;line-height:18pt"><span style="font-size:14pt;font-family:'Times New Roman',serif">Ore 14:00, Aula
Mancini</span></p>
<p class="MsoNormal" style="text-align:justify;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>
<p class="MsoNormal" style="text-align:justify;line-height:18pt"><b><span lang="EN-US" style="font-family:'Times New Roman',serif">Abstract: </span></b><font face="arial, helvetica, sans-serif"><i><span lang="EN-US" style="background-image:initial;background-repeat:initial">In these two talks, a
quick introduction to modular forms and some of their arithmetic utilizations
shall be given. On the one hand, basic facts about modular forms (e.g.
Atkin-Lehner theory) are given to promote a better understanding of an upcoming
talk of Rafael van Känel about modularity and the S-unit equation. On the other
hand, I highlight some more advanced aspects of this ever-growing area of
mathematical research, which hopefully present good motivation to the novice.</span></i><i><span lang="EN-US"><br style="text-align:start">
<span style="background-image:initial;background-repeat:initial">The relation between modular forms and Dirichlet
series as well as the construction of Galois representations associated with
modular forms is covered (without complete proofs, of course). As far as time
permits, I indicate how these representations are used, in particular if they are
combined with modularity results. Such applications include congruences of
arithmetic functions, diophantine equations (Hellegouarch-Frey, Bennett-Dahmen)
and the Sato-Tate conjecture for elliptic curves. However, the modularity
results (Wiles-Taylor et al.) will be used solely as a blackbox, avoiding a
rather intricate part of modern arithmetic."</span></span></i></font><b><i><span lang="EN-US" style="font-family:'Times New Roman',serif"></span></i></b></p>
<p class=""><span lang="EN-US">Classe di Scienze Matematiche e Naturali</span><span style="font-family:'Times New Roman',serif;font-size:16pt;text-align:center"> </span></p><div><div class="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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