<div dir="ltr"><p class=""><span style="font-size:18pt;font-family:'Times New Roman',serif">SEMINARIO
DI MATEMATICA</span></p>
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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Martedì 27 gennaio 2015</span><span style="font-size:16pt;font-family:'Times New Roman',serif"></span></p>
<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">ore 16:00</span></p>
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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><u><span style="font-size:16pt;font-family:'Times New Roman',serif">Scuola Normale Superiore</span></u></p>
<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Pisa</span></p>
<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Aula Mancini</span></p>
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<pre style="text-align:center"><b><span style="font-size:22pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Ziyang Gao</span></b></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Université Paris Sud</span></i></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial"> </span></i></pre>
<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:'Times New Roman',serif">Terrà un
seminario dal titolo:</span></p>
<p class="MsoNormal"><b><span style="font-size:16pt;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:22pt;font-family:'Times New Roman',serif">“<span class=""><span style="background-image:initial;background-repeat:initial"> </span></span><span style="background-image:initial;background-repeat:initial">Polarized isogeny orbits in families of
abelian varieties</span></span>”</b></p>
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<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-family:'Times New Roman',serif">Abstract:</span></b></p>
<p class="MsoNormal" style="text-align:justify"><i><span lang="EN-US" style="background-image:initial;background-repeat:initial"><font face="arial, helvetica, sans-serif">The Andre-Pink-Zannier
conjecture predicts that a subvariety of</font></span></i><i><font face="arial, helvetica, sans-serif"><span lang="EN-US"> <span style="background-image:initial;background-repeat:initial">a mixed
Shimura variety is weakly special if its intersection with the</span></span> <span style="background-image:initial;background-repeat:initial">generalized Hecke orbit of a point is Zariski dense.
When the ambient</span> <span style="background-image:initial;background-repeat:initial">mixed Shimura
variety is the universal abelian scheme, the generalized</span> <span style="background-image:initial;background-repeat:initial">Hecke orbits are precisely the polarized isogeny
orbits and weakly special</span> <span style="background-image:initial;background-repeat:initial">subvarieties
also have good geometric interpretation. In my talk I will</span> <span style="background-image:initial;background-repeat:initial">describe the Andre-Pink-Zannier conjecture for the
universal abelian</span> <span style="background-image:initial;background-repeat:initial">scheme in the
geometric term and explain the outline of its proof by the</span> <span style="background-image:initial;background-repeat:initial">Pila-Zannier method. I will then prove the conjecture
when the subvariety</span> <span style="background-image:initial;background-repeat:initial">is a curve</span>. </font></i></p>
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<p class=""><i><span lang="EN-US" style="font-family:'Times New Roman',serif"> </span></i></p>
<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif">Tutti gli interessati
sono invitati a partecipare.</span></p>
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<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif">Classe di Scienze
Matematiche e Naturali</span></p>
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<p class=""><span style="font-size:18pt;font-family:'Times New Roman',serif"> </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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