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<p class="MsoTitle"><span style="font-family:"Times New
Roman","serif"">Colloquio
De Giorgi<o:p></o:p></span></p>
<h2><span style="font-family:"Times New
Roman","serif";mso-no-proof:yes"><o:p> </o:p></span></h2>
<h2><span style="font-family:"Times New
Roman","serif";mso-no-proof:yes">Giovedģ
28 febbraio 2013</span><span style="font-family:"Times New
Roman","serif""><o:p></o:p></span></h2>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;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-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><u><span
style="font-size:16.0pt;
font-family:"Times New Roman","serif"">Scuola
Normale Superiore<o:p></o:p></span></u></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">Pisa<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:9.0pt;text-align:center;
line-height:18.0pt;tab-stops:324.0pt" align="center"><span
style="font-size:16.0pt;font-family:
"Times New Roman","serif"">(Sala degli
Stemmi)<o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><b><u><span
style="font-size:10.0pt;
font-family:"Times New Roman","serif""><o:p><span
style="text-decoration:none"> </span></o:p></span></u></b></p>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><span style="font-size:26.0pt;font-family:"Times
New Roman","serif"">Fabrizio
Catanese<o:p></o:p></span></b></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif"">Universitaet
Bayreuth<o:p></o:p></span></i></p>
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align="center"><i style="mso-bidi-font-style:normal"><span
style="font-size:11.0pt;font-family:
"Times New
Roman","serif";mso-no-proof:yes"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="text-align:center;tab-stops:324.0pt"
align="center"><span
style="font-size:16.0pt;font-family:"Times New
Roman","serif"">Terrą un
seminario dal titolo:<o:p></o:p></span></p>
<p class="MsoNormal" style="tab-stops:324.0pt"><span
style="font-size:8.0pt;
font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<pre style="text-align:center"><b style="mso-bidi-font-weight:normal"><span style="font-size:22.0pt;font-family:"Times New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">“Topological Methods in Algebraic Geometry”<o:p></o:p></span></b></pre>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><span style="font-size:18.0pt;font-family:"Times
New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US"><o:p> </o:p></span></b></p>
<p class="MsoNormal" style="text-align:center" align="center"><b
style="mso-bidi-font-weight:
normal"><span style="font-size:18.0pt;font-family:"Times
New Roman","serif";
mso-ansi-language:EN-US" lang="EN-US">Can the angel of
topology live happily together with
the devil of abstract algebra ?*<i
style="mso-bidi-font-style:normal"><o:p></o:p></i></span></b></p>
<p class="MsoNormal" style="text-align:justify"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><b
style="mso-bidi-font-weight:
normal"><i style="mso-bidi-font-style:normal"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">Abstract:<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">Algebraic
topology flourished from some of its applications (such as
Brouwer's
fixed point theorem, or the theorem of Borsuk-Ulam) showing
the non existence of certain continuous maps since they would
imply the
existence of homomorphisms satisfying algebraic properties
which
are manifestly impossible. Conversely, the theory of fibre
bundles and homotopy
theory give a topological incarnation of a group G through its
classifying
space BG. The theory of classifying spaces translates then group
homomorphisms
into continuous maps to classifying spaces. In algebraic
geometry, the theory
of Albanese varieties can be understood as dealing with the case
where G is
free abelian. For more general G, an important question is the
one of the
regularity of these classifying maps, and their complex
analyticity. These
questions, which were addressed in the last 40 years, have
powerful
applications to moduli theory. After this general introduction,
I shall
concentrate on some classes of projective varieties which are
classifying
spaces for some group, and on their rigidity and quasi-rigidity
properties. I
shall show how the investigations of their moduli spaces lead to
some group
theoretical questions, and to theinvestigation of moduli spaces
of curves with
symmetries. Key examples are: varieties isogenous to a product,
and the
Inoue-type varieties introduced in recent work with Ingrid
Bauer: for these the
moduli space is determined by the topological type. I shall
devote the
final part to recent joint work with Michael L\"onne and Fabio
Perroni,
dealing with the irreducible components of moduli spaces of
curves with
symmetries, with stabilization results and open questions.<o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="mso-ansi-language:EN-US" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">*
Historical note: In these days the angel of topology and the
devil of abstract
algebra fight for the soul of each individual mathematical</span><span
style="mso-ansi-language:EN-US" lang="EN-US"> </span><span
style="font-family:"Times New
Roman","serif";mso-ansi-language:EN-US"
lang="EN-US">domain.
[Hermann Weyl (1939), p.500 of "Invariants", Duke Mathematical
Journal 5 (3): 489-502.]<o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:18.0pt;font-family:"Times New
Roman","serif";mso-ansi-language:
EN-US;mso-no-proof:yes" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:18.0pt;
font-family:"Times New
Roman","serif";mso-no-proof:yes">Tutti gli
interessati
sono invitati a partecipare<o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify"><span
style="font-size:18.0pt;
font-family:"Times New
Roman","serif";mso-no-proof:yes"><o:p> </o:p></span><span
style="font-size:18.0pt;font-family:"Times New
Roman","serif""><o:p></o:p></span><span
style="font-size:18.0pt;font-family:"Times New
Roman","serif"">Classe di
Scienze<o:p></o:p></span>
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<pre class="moz-signature" cols="72">--
--------------------------------------------------------------------------------
Valeria Giuliani
Scuola Normale Superiore
Servizio Supporto Attivitą Didattiche - Scienze
Tel. 050-509260
Fax. 050-509045
Piazza dei Cavalieri, 7
56126 Pisa
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</a>
E-Mail: <a class="moz-txt-link-abbreviated" href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</a>
Le informazioni contenute nella presente e-mail e nei relativi allegati possono essere riservate e sono, comunque, destinate esclusivamente al destinatario in indirizzo.
E’ vietata, pertanto, la diffusione, distribuzione e/o copiatura di tali informazioni da parte di qualsiasi soggetto diverso dal destinatario.
Chiunque abbia ricevuto o letto questa e-mail per errore o senza esserne legittimato č invitato a darne immediatamente notizia al mittente tramite fax o e-mail e a distruggerla.
Grazie.
</pre>
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