<div dir="ltr"><p class="" style="text-align:center"><span style="font-size:18pt;font-family:'Times New Roman',serif"><b>SEMINARIO
DI MATEMATICA</b></span></p>
<p class="" style="text-align:center"><span style="font-size:16pt;font-family:'Times New Roman',serif"><b> </b></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">Venerdì 27 marzo 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>
<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"> </span></p>
<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 Fermi</span></p>
<p class="MsoNormal"><b><u><span style="font-size:16pt;font-family:'Times New Roman',serif"><span style="text-decoration:none"> </span></span></u></b></p>
<pre style="text-align:center"><b><span style="font-size:22pt;font-family:'Times New Roman',serif;color:black;background-image:initial;background-repeat:initial">Jung Kyu CANCI</span></b><b><span style="font-size:22pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial"></span></b></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif">Universitat Basel<span style="background-image:initial;background-repeat:initial"></span></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:20pt;font-family:'Times New Roman',serif">“Quadratic maps with a marked periodic point of small
order”</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></b></p>
<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=""><i><span lang="EN-GB"><font face="arial, helvetica, sans-serif">In a
joint work with Jeremy Blanc and Noam Elkies we took in consideration the
variety Rat2(n) that parametrizes the pairs (f, P) where f is an endomorphism
of degree 2 of P1 and P is a periodic point for f of minimal period n, for an
arbitrary fixed integer n. One considers a canonical conjugation action of PGL2
on Rat2(n). The quotient M2(n) = Rat2(n)/PGL2 exists as a geometric quotient of
dimension 2. We proved that M2(n) is rational over Q when n ≤ 5 and is of
general type for n = 6. An explicit description of the surface with n = 6 lets
us find several infinite families of quadratic endomorphisms defined over Q
with a rational periodic point of order 6. We will see why this is in contrast
with the polynomial case, where it is conjectured that no polynomial
endomorphism defined over Q with degree 2 admits rational periodic points of
order n > 3.</font></span></i></p>
<p class=""><i><span lang="EN-US"><font face="arial, helvetica, sans-serif"> </font></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>
<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>
<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif">Classe di Scienze
Matematiche e Naturali</span></p>
<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>
<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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