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<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman','serif'"><STRONG><U>SEMINARIO
DI <SPAN style="mso-no-proof: yes">MATEMATICA</SPAN><?xml:namespace prefix = o
ns = "urn:schemas-microsoft-com:office:office"
/><o:p></o:p></U></STRONG></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"></SPAN> </H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">mercoledì 06
Luglio 2011</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">15.00</SPAN><o:p></o:p></SPAN></P>
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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'"><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 lang=EN-US
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">(Aula
<SPAN style="mso-no-proof: yes">Fermi</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"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes; mso-ansi-language: EN-US"></SPAN></I></B> </P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes; mso-ansi-language: EN-US">Zinovy
Reichstein<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><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">University
of British Columbia, Canada</SPAN></I><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><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
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Terrà un
seminario dal titolo:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><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"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">“</SPAN></I></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">Versal
torsors with a twist</SPAN></B><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">”</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p></o:p></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">Abstract:<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><FONT
size=3><I style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Let G
be a linear algebraic group acting on an algebraic variety X. Informally
speaking, this action is versal if every G-torsor over a field can be obtained
by specialization from X. Here the term “versal” is best understood by
subtracting “unique” from both sides of the formula UNIVERSAL = UNIQUE + VERSAL.
The notion of versality and its variants play an important role in Galois
theory, in the theory of central simple algebras and in the theory of quadratic
forms. In this talk, based on joint work with Alex Duncan, I will address the
following ”recognition problem”: Determine whether or not a given G-action is
versal. The main idea is to relate versality to existence of rational points on
certain twisted forms of X. I will state a versality criterion based on this
idea and discuss a number of applications.</SPAN></I><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p></o:p></SPAN></I></B></FONT></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></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-GB
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></B></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=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=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=Corpodeltesto1 style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2"> </SPAN></SPAN><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=Corpodeltesto1 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=Corpodeltesto1 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></FONT><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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