GAVRIL FARKAS, Humboldt Universitaet Berlin
THE BIRATIONAL GEOMETRY OF MODULI SPACES OF SPIN CURVES
Lunedì 14 Giugno 2010, ore 15:30
Università di Milano, Dipartimento di Matematica, Via Saldini, Sala di Rappresentanza | |
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JEAN-MICHEL CORON, Université Pierre et Marie Curie - Paris 6
CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS AND NONLINEARITY
Martedì 08 Giugno 2010, ore 16:30
Università di Milano, Dipartimento di Matematica, Via Saldini 50 | |
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GiUSEPPE ROSARIO MINGIONE, Università di Parma
ASPETTI NON LINEARI DELLA TEORIA DI CALDERON-ZYGMUND
Martedì 04 Maggio 2010, ore 16:00
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Aula 3014 | |
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CHARLES FEFFERMAN, Princeton University
EXTENSION OF FUNCTIONS AND INTERPOLATION OF DATA
Lunedì 03 Maggio 2010, ore 16:30
Università di Milano, Dipartimento di Matematica, Via Saldini 50 | |
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ANGELO VULPIANI, Università di Roma La Sapienza
FRONT PROPAGATION IN LAMINAR AND TURBULENT FLOWS
Lunedì 29 Marzo 2010, ore 17:00
Dipartimento di Matematica, Politecnico di Milano, Sala Consiglio VII piano | |
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P.M.H. WILSON, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
METRIC PROPERTIES OF CALABI-YAU MANIFOLDS
Lunedì 29 Marzo 2010, ore 15:00
Dipartimento di Matematica, Università di Milano |
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Abstract
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This talk aims to introduce some general ideas relating properties from algebraic
geometry to concepts from metric geometry, in particular that of Gromov-Hausdorff limits
of metric spaces.
Let $X$ be a Calabi-Yau manifold of dimension $n$, that is a complex projective manifold
which admits a nowhere vanishing holomorphic $n$-form, and no holomorphic $i$-forms for
$0 < i < n$. By a famous theorem of Yau, for each K"ahler class in the real second cohomology,
there exists a unique Ricci
at K"ahler metric on X with K"ahler form in the given
class, the Calabi Yau metric; hence there is a well-defined metric space structure on $X$.
A natural question then arises: if we degenerate either the complex or Kähler structures
on X in the sense of algebraic geometry, obtaining a singular projective variety, what
can be said about the metric limits (in the sense of Gromov-Hausdorff) of the corresponding Ricci
at K"ahler manifolds? We will suggest some answers to this question and explain
their relevance for the geometry of Calabi-Yau manifolds.
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