Análise Geométrica & Geometria Diferencial

On the geometry and topology of initial data sets in General Relativity

Palestrante: Gregory J. Galloway (University of Miami)
Local: meet.google.com/ujd-ndsi-hvw
Data: Quinta-feira, 18 de março de 2021
Hora: 15h00

Resumo:

A theme of long standing interest (to the speaker!) concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness). Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside of all black holes (and white holes) should be topologically simple. In this talk we present results which provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the theory of marginally outer trapped surfaces, which have played an important role in the theory of black holes, and which may be viewed as spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack.

Initial data rigidity results

Palestrante: Abraão Mendes do Rêgo
Local: 
meet.google.com/nkp-jdwx-cwr
Data:
Sexta-feira, 19 de fevereiro de 2021
Hora:
14h00

Resumo:

In this lecture we aim to present some rigidity results for initial data sets that are motivated by the spacetime positive mass theorem. A key step is to show that certain marginally outer trapped surfaces (MOTS) are weakly outermost. As a special case, our results include a rigidity result for Riemannian manifolds with a lower bound on their scalar curvature. 

Estimativa para o volume de ciclos em variedades hiperbólicas com bordo

Palestrante: Moreno Bonutti (UFAL)
Local: http://meet.google.com/wsj-qsrx-rcs
Data: Sexta-feira, 29 de janeiro de 2021
Hora: 14h00
Resumo

O índice de Morse e o primeiro número de Betti de subvariedades mínimas

Palestrante: Diego Alves Adauto (UERN/UFAL)
Local: Via Conferência Web em: http://meet.google.com/yfp-afeh-rwz 
Data: Quinta-feira, 14 de janeiro de 2021
Hora: 10h30
Resumo

Existência de hipersuperfícies mínimas de fronteira livre em domínios quádricos 

PalestranteRodrigo Fernandes de Moura Melo (UFAL)
Local: 
Via Conferência Web em: http://meet.google.com/yfp-afeh-rwz 
Data:
Sexta-feira, 12 de fevereiro de 2021
Hora: 
14h00