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<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Inoltro avviso
di Seminario a me pervenuto.</EM></FONT></DIV>
<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Cordiali
saluti</EM></FONT></DIV>
<DIV><FONT face="Bitstream Vera Serif" color=#000080 size=2><EM>Liviana
Paoletti</EM></FONT></DIV></FONT></DIV></FONT></DIV>
<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=giuliani@sns.it href="mailto:giuliani@sns.it">Valeria Giuliani</A> </DIV>
<DIV> </DIV>
<DIV><B>Sent:</B> Thursday, December 02, 2010 1:28 PM</DIV>
<DIV><B>Subject:</B> seminario di matematica Dr. Vincenzo Mantova
(9.12.2010)</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman','serif'"><STRONG><U>SEMINARI
DI MATEMATICA<o:p></o:p></U></STRONG></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left" align=left><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"><o:p> </o:p></SPAN></H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">Giovedì 9
dicembre 2010</SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></H2>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">ore <SPAN
style="mso-no-proof: yes">16.00</SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><U><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Pisa<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">(Aula <SPAN
style="mso-no-proof: yes">Tonelli</SPAN>)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'">Vincenzo
Mantova<o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'">Scuola Normale
Superiore di Pisa<B style="mso-bidi-font-weight: normal"><SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></B></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN lang=EN-US
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Terrà
un seminario dal titolo:<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><SPAN
lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">“</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">A
Differential Nullstellensatz and the Mordell-Lang Conjecture</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">”<o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes; mso-ansi-language: EN-US"><FONT
size=3>Abstract:<o:p></o:p></FONT></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes; mso-ansi-language: EN-US"><o:p><FONT
size=3> </FONT></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">The
Mordell-Lang Conjecture is a difficult statement about the rational points of
the subvarieties of semi-abelian varieties, and it has several consequences in
diophantine geometry, such as Faltings' Theorem and the Manin-Mumford
Conjecture. It has been proven with several methods, ranging from algebraic
geometry to model theory.We focus our attention on the relative Mordell-Lang
Conjecture for function fields of characteristic 0. Since in this case the
ground field is equipped with a differential operator, it is possible to embed
it in a so-called "differentially closed field": in such fields, a weak form of
Nullstellensatz holds (i.e., varieties defined as zeroes of differential
polynomials have rational points in the fields).We will see how this
differential Nullstellensatz can be axiomatized, and we will show some basic
consequences that establish analogies between the structure of differential
varieties and algebraic varieties. We will then discuss some of the ideas behind
exploiting differentially closed fields in order to give a relatively simple
proof of the Mordell-Lang Conjecture for function fields (from works of Buium,
Pillay and Ziegler)."<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Tutti gli
interessati sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><FONT
face="Times New Roman"><SPAN style="mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2"><FONT
size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT">Classe
di Scienze<o:p></o:p></SPAN></FONT></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P></FONT></DIV>
<DIV><FONT face=Arial
size=2>--------------------------------------------------------------------------------<BR>Valeria
Giuliani<BR>Scuola Normale Superiore<BR>Servizio Supporto Attività Didattiche -
Scienze<BR>Tel. 050-509260<BR>Fax. 050-509045<BR>Piazza dei Cavalieri,
7<BR>56126 Pisa<BR>E-Mail: <A
href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</A> <BR>E-Mail: <A
href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</A></FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Le informazioni contenute nella presente e-mail e
nei relativi allegati possono essere riservate e sono, comunque, destinate
esclusivamente al destinatario in indirizzo.<BR>E’ vietata, pertanto, la
diffusione, distribuzione e/o copiatura di tali informazioni da parte di
qualsiasi soggetto diverso dal destinatario. <BR>Chiunque abbia ricevuto o letto
questa e-mail per errore o senza esserne legittimato è invitato a darne
immediatamente notizia al mittente tramite fax o e-mail e a
distruggerla.<BR>Grazie.</FONT></DIV>
<DIV> </DIV>
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