[CvGmt News] avviso Colloquio De Giorgi Prof. Fabrizio Catanese (28.02.2013)

[valeria.giuliani at sns.it]

Colloquio De Giorgi


    Giovedì 28 febbraio 2013

ore 16.00

_Scuola Normale Superiore_

Pisa

(Sala degli Stemmi)

*__*

*Fabrizio Catanese*

/Universitaet Bayreuth/

//

Terrà un seminario dal titolo:

*"Topological Methods in Algebraic Geometry"*

**

*Can the angel of topology live happily together with the devil of 
abstract algebra ?*//*

*//*

*/Abstract:/*

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.

* Historical note: In these days the angel of topology and the devil of 
abstract algebra fight for the soul of each individual 
mathematicaldomain. [Hermann  Weyl (1939), p.500 of "Invariants", Duke 
Mathematical Journal 5 (3): 489-502.]

Tutti gli interessati sono invitati a partecipare

Classe di Scienze

-- 
--------------------------------------------------------------------------------
Valeria Giuliani
Scuola Normale Superiore
Servizio Supporto Attività Didattiche - Scienze
Tel. 050-509260
Fax. 050-509045
Piazza dei Cavalieri, 7
56126 Pisa
E-Mail: v.giuliani at sns.it
E-Mail: segreteria.scienze at sns.it
  
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