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<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman'"><STRONG><U>SEMINARIO DI
MATEMATICA</U></STRONG></SPAN></P>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt"><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'"><o:p><SPAN
style="TEXT-DECORATION: none"><STRONG><U></U></STRONG></SPAN></o:p></SPAN> </P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">lunedì 3 Maggio
2010</SPAN><SPAN style="FONT-FAMILY: 'Times New Roman'"><o:p></o:p></SPAN></H2>
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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'">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'"><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'"><o:p><SPAN
style="TEXT-DECORATION: none"></SPAN></o:p></SPAN></U> </P>
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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'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></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'">Pisa<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'">(Aula
<SPAN style="mso-no-proof: yes">Tonelli</SPAN>)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><B><U><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman'"><o:p><SPAN
style="TEXT-DECORATION: none"></SPAN></o:p></SPAN></U></B> </P>
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align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes"><o:p><FONT
size=3> </FONT></o:p></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
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">Brent
Doran<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
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">ETH
Zurigo</SPAN></I><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'"><o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN style="FONT-FAMILY: 'Times New Roman'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
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style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'">Terrà
un seminario dal titolo:<o:p></o:p></SPAN></P>
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style="FONT-FAMILY: 'Times New Roman'"><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'; mso-ansi-language: EN-GB">“</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">A
little taste of arithmetic geometric topology<I
style="mso-bidi-font-style: normal">”<o:p></o:p></I></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-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; 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'; 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"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">Topologists
developed powerful tools in the twentieth century with a focus on the
theory of manifolds. However, classical questions long solved in
topology, via fairly sophisticated techniques, have analogs which are
still open in algebraic geometry -- which, despite motivating dreams and
conjectures, lacks the precise analogs of those techniques. To cite
two simple concrete instances: (1) the cancellation problem, i.e., if X x
A^1 = A^n, then what is X, and (2) a theory of vector bundles via
classifying spaces, both have clean, complete topological stories.
We explore the rough question of what issues in algebraic geometry are
essentially topological, versus those which require hard geometry and
arithmetic, by illustrating some instances where A^1-homotopic thinking
(or ``motivic homotopy") clarifies matters. As an application, we
discuss the question "what is a sphere over Z", in a way that Heinz Hopf
would likely have appreciated.<o:p></o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></I></P>
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style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'"><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'">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'"><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'"><o:p> </o:p></SPAN></P>
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style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P>
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size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: IT">Classe
di Scienze<o:p></o:p></SPAN></FONT></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>
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