Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 30 ottobre al 5 novembre 2017
Lunedì 30 ottobre 2017
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Gabriele Mondello (Sapienza Università di Roma)
On the existence of spherical metrics with conical points
For every compact connected surface with negative Euler characteristic Koebe
and Poincaré proved the existence and uniqueness of a metric of finite
area and curvature -1 in each conformal class. McOwen and Troyanov proved an
analogous result for metrics with prescribed conical behavior at given marked
points. The analogous question for metrics of curvature 1 is subtler: in a
small range existence and uniqueness still holds (Troyanov), in another range
existence holds but uniqueness fails (Bartolucci-De Marchis-Malchiodi).
The aim of this talk is to discuss some results of existence and non-existence
of metrics of curvature 1 on surfaces with conical singularities.
This is joint work with Dmitri Panov.
Martedì 31 ottobre 2017
Ore 16:00, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata
seminario di Analisi Complessa
Christophe Mourougane (Rennes)
Asymptotics of L2 and Quillen metrics in degenerations
of Calabi-Yau varieties
It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.
Our first motivation is to give a metric analogue of Kodaira's canonical
bundle formula for elliptic surfaces, in the case of families of Calabi-Yau
varieties.
We consider degenerations of complex projective Calabi--Yau varieties and study
the singularities of L2, Quillen and BCOV metrics on Hodge and
determinant bundles. The dominant and subdominant terms in the expansions of
the metrics close to non-smooth fibres are shown to be related to well-known
topological invariants of singularities, such as limit Hodge structures,
vanishing cycles and log-canonical thresholds.
Giovedì 2 novembre 2017
Ore 14:30, aula di Consiglio
seminario PDN P(n)
Angela Pistoia (Sapienza Università di Roma)
On the existence of solutions to weakly coupled elliptic system with
critical growth
We consider a critical weakly coupled elliptic systems in a domain D in RN
with N=3,4. We prove the existence of positive solutions which blow-up at one or more points
in D provided some conditions are satisfied.
The results have been obtained in collaboration with Nicola Soave and Hugo Tavares.
Tutte le informazioni relative a questo notiziario devono pervenire
esclusivamente all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 24 del giovedì precedente la settimana interessata.
Le comunicazioni pervenute in ritardo potranno essere ignorate.
Tutti coloro che desiderano ricevere questo notiziario via e-mail sono
invitati a comunicare il proprio indirizzo di posta elettronica a
seminari@mat.uniroma1.it.
Il Direttore