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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>
<DIV> </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><B>To:</B> <A title=docenti.scienze@sns.it
href="mailto:docenti.scienze@sns.it">Docenti Scienze</A> ; <A
title=ricercatori.scienze@sns.it
href="mailto:ricercatori.scienze@sns.it">Ricercatori Scienze</A> ; <A
title=perfezionandi.scienze@sns.it
href="mailto:perfezionandi.scienze@sns.it">Perfezionandi Scienze</A> ; <A
title=studenti.scienze@sns.it href="mailto:studenti.scienze@sns.it">Studenti
Scienze</A> ; <A title=borsisti.scienze@sns.it
href="mailto:borsisti.scienze@sns.it">borsisti.scienze@sns.it</A> </DIV>
<DIV><B>Cc:</B> <A title=segreteria.scienze@sns.it
href="mailto:segreteria.scienze@sns.it">Segreteria Classe di Scienze</A> ; <A
title=portineria.carovana@sns.it
href="mailto:portineria.carovana@sns.it">Portineria Carovana</A> ; <A
title=sitosns@sns.it href="mailto:sitosns@sns.it">Sito SNS</A> ; <A
title=curciare@dm.unipi.it href="mailto:curciare@dm.unipi.it">Curciarello
Giulia</A> ; <A title=laspina@dm.unipi.it
href="mailto:laspina@dm.unipi.it">Alessandra La Spina</A> ; <A
title=paoletti@dm.unipi.it href="mailto:paoletti@dm.unipi.it">Liviana
Paoletti</A> ; <A title=f.micheletti.arca@cooplarca.it
href="mailto:f.micheletti.arca@cooplarca.it">Micheletti</A> ; <A
title=v.quatrocchi.arca@cooplarca.it
href="mailto:v.quatrocchi.arca@cooplarca.it">valentina quattrocchi</A> ; <A
title=l.makhoul@sns.it href="mailto:l.makhoul@sns.it">leyla makhoul</A> ; <A
title=f.casacci.arca@cooplarca.it
href="mailto:f.casacci.arca@cooplarca.it">francesco casacci</A> ; <A
title=g.pinna.arca@cooplarca.it href="mailto:g.pinna.arca@cooplarca.it">gavina
pinna</A> </DIV>
<DIV><B>Sent:</B> Friday, June 11, 2010 10:33 AM</DIV>
<DIV><B>Subject:</B> avviso seminario di matematica prof. F.W. Lawvere
(18.06.2010)</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left" align=left><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'"><o:p><SPAN
style="TEXT-DECORATION: none"><STRONG><U></U></STRONG></SPAN></o:p></SPAN> </P>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman'"><STRONG><U>SEMINARIO DI
<SPAN
style="mso-no-proof: yes">MATEMATICA</SPAN><o:p></o:p></U></STRONG></SPAN></P>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><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">venerdì 18 giugno
2010</SPAN><SPAN style="FONT-FAMILY: 'Times New Roman'"><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'">ore
<SPAN style="mso-no-proof: yes">15.00</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: 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'">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'">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'">(Aula
Mancini)<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>
<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: 22pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">F.
William Lawvere<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><st1:place w:st="on"><st1:PlaceType w:st="on"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">University</SPAN></I></st1:PlaceType><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes; mso-ansi-language: EN-GB">
of <st1:PlaceName w:st="on">Buffalo</st1:PlaceName></SPAN></I></st1:place><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>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN lang=EN-GB
style="FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><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'">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'"><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
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'">“</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 24pt; FONT-FAMILY: 'Times New Roman'; mso-no-proof: yes">What
is a space</SPAN></B><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman'">”<o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB"><FONT
size=3>Abstract:<o:p></o:p></FONT></SPAN></I></B></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify; mso-layout-grid-align: none"><SPAN
lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">A
space is just an object in a category of spaces!<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify; mso-layout-grid-align: none"><SPAN
lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">The
implied further question is given a very general answer involving lextensivity,
as well as a much more structured answer involving dialectically coupled
(cohesive/discrete) pairs of toposes. Examples can be analyzed and constructed
using the simple geometric paradigm of figures and incidence relations, by which
any lextensive category can be embedded in a Grothendieck topos; more refined
subtoposes of the latter are specified by Grothendieck coverings that embody the
geometrical equivalent of existential/disjunctive conditions on these extended
spaces; a specific example involves a generalization of Maschke means. The
extended spaces always include the Hurewicz exponential spaces, for example,
spaces of functions and distributions equipped automatically with the ambient
sort of cohesion. Examples important for smooth, analytic, and algebraic
geometry are infinitesimally generated, pursuing an observation that goes back
to Euler. A smooth account of points and components for algebraic geometry over
a non</SPAN><FONT face="Times New Roman"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: Cambria; mso-ansi-language: EN-GB">‐</SPAN><SPAN
lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">algebraically
closed field is achieved by replacing Cantorian abstract sets with a
Galois</SPAN><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: Cambria; mso-ansi-language: EN-GB">‐</SPAN><SPAN
lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman'; mso-ansi-language: EN-GB">Barr
topos as the discrete aspect. The basic goal is to help make the advances in
Algebraic Geometry during the past 50 years more accessible to students and to
colleagues in related fields by utilizing the simplifying advances in
categorical foundations during the same 50 years, especially guided by proposals
made by Grothendieck in 1973.<B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></I></B></SPAN></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: 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: 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: 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"><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=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman'; 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 lang=EN-GB><SPAN style="mso-tab-count: 2"><FONT
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>
<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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