<div dir="ltr"><br><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature" data-smartmail="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>
<br><div class="gmail_quote">2016-10-13 9:38 GMT+02:00 Valeria Giuliani <span dir="ltr"><<a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><p class="m_7712322143712033160gmail-MsoTitle" style="text-align:center"><span style="font-size:18pt;font-family:"times new roman",serif">SEMINARIO
DI MATEMATICA</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">Martedì 25 ottobre 2016</span><span style="font-size:16pt;font-family:"times new roman",serif"><span></span></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 16:30<span></span></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> </span></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></span></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></span></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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Aula Bianchi Scienze<span></span></span></p>

<p class="MsoNormal"><b><u><span style="font-size:16pt;font-family:"times new roman",serif"><span><span style="text-decoration:none"> </span></span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span style="font-size:22pt;font-family:"times new roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">David Masser</span></b><b><span style="font-size:22pt;font-family:"times new roman",serif"><span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="font-size:9.5pt;font-family:arial,sans-serif">(</span><i><span style="font-family:"times new roman",serif">University of Basel)</span></i><span style="font-size:9.5pt;font-family:arial,sans-serif"><span></span></span></p>

<pre style="text-align:center"><b><i><span style="font-size:12pt;font-family:"times new roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span> </span></span></i></b></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></span></span></p>

<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:22pt;font-family:"times new roman",serif;color:black">“</span></b><b><span lang="EN-US" style="font-size:22pt;font-family:"times new roman",serif">Elementary
integration and relative <span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:22pt;font-family:"times new roman",serif">Manin-Mumford<span style="color:black">”<span></span></span></span></b></p>

<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-size:22pt;font-family:"times new roman",serif"><span> </span></span></b></p>

<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-family:"times new roman",serif">Abstract:<span></span></span></b></p>

<p class="MsoNormal" style="text-align:justify"><i><span lang="EN-US" style="font-family:"times new roman",serif">In 1916 Hardy wrote “... no general method has been
devised by which we can always tell, after a finite series of operations,
whether any given integral is really elementary, or elliptic, or belongs to a
higher order of transcendents.” And 100 years later nothing has changed too
much. Every schoolgirl knows that R √ dx x(x−t) is elementary; that is, it can
be expressed with logarithms and exponentials. But not R √ dx x(x−1)(x−t)
unless t = 0, 1. In 1981 James Davenport asserted that if f is algebraic then R
f(x, t)dx is elementary for at most finitely many special complex values t
(unless it is elementary for a general value of t). I describe progress by
Umberto Zannier and myself on Davenport’s Assertion. The main tools are
suitable generalizations of the Manin-Mumford conjectures, in their very
simplest form about roots of unity, but here about torsion on families of group
varieties.<span style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span></span></span></span></i></p>

<p class="MsoNormal" style="text-align:justify"><span lang="EN-US" style="font-size:9.5pt;font-family:arial,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Tutti gli interessati sono invitati a
partecipare.<span></span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Classe di Scienze Matematiche e Naturali<span class="HOEnZb"><font color="#888888"><span></span></font></span></span></p><span class="HOEnZb"><font color="#888888">

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p><div><div class="m_7712322143712033160gmail_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>
</font></span></div>
</blockquote></div><br></div></div>