Palestras de Geometria
Palestrantes: Daniel Fadel (IMPA), Matias del Hoyo (UFF) e Federico Quallbrunn (Universidad CAECE e CONICET, Arg.)
Data: 10/03/2023, às 10:30h
Local: Sala C116 do CT

Horários:
10:00h - Café
10:30h - Daniel Fadel (IMPA) - On the harmonic flow of geometric structures
11:30h - Café
13:30h - Matias del Hoyo (UFF) - Completeness of metrics and linearization of groupoids
14:30h - Café
15:00h - Federico Quallbrunn (Universidad CAECE e CONICET, Arg.) - Singularidades Persistentes de Folheações.
16:00h - Café

Resumos

Palestrante: Daniel Fadel (IMPA)
Título: On the harmonic flow of geometric structures
Resumo: In this talk, I will report on recent results of an ongoing collaboration with Éric Loubeau, Andrés Moreno and Henrique Sá Earp on the study of the harmonic flow of H-structures. This is the negative gradient flow of a natural Dirichlet-type energy functional on a given isometric class of H-structures on a closed Riemannian n-manifold, where H is the stabilizer in SO of a finite collection of tensors in Rn. Using general Bianchi-type identities of H-structures, we are able to prove monotonicity formulas for scale-invariant local versions of the energy, similar to the classic formulas proved by Struwe and Chen (1988-89) in the theory of harmonic map heat flow. We then deduce a general epsilon-regularity result along the harmonic flow and, more importantly, we get long-time existence and finite-time singularity results in parallel to the classical results proved by Chen-Ding (1990) in harmonic map theory. In particular, we show that if the energy of the initial H-structure is small enough, depending on the C^0-norm of its torsion, then the harmonic flow exists for all time and converges to a torsion-free H-structure. Moreover, we prove that the harmonic flow of H-structures develops a finite time singularity if the initial energy is sufficiently small but there is no torsion-free H-structure in the homotopy class of the initial H-structure. Finally, based on the analogous work of He-Li (2021) for almost complex structures, we give a general construction of examples where the later finite-time singularity result applies on the flat n-torus, provided the n-th homotopy group of the quotient SO/H is non-trivial; e.g. when n=7 and H=G2, or when n=8 and H=Spin(7). Reference: arXiv:2211.05197

Palestrante: Matias del Hoyo (UFF)
Título: Completeness of metrics and linearization of groupoids
Resumo: Every smooth fiber bundle admits a complete Ehresmann connection. I will talk about the story of this theorem and its relation with Riemannian submersions. Then, after discussing some foundations of Riemannian geometry of Lie groupoids and stacks, I will present a generalization of the theorem into this framework, which somehow answers an open problem on linearization. Talk based on collaborations with my former student M. de Melo.

Palestrante: Federico Quallbrunn (Universidade CAECE e CONICET, Arg.)
Título: Singularidades Persistentes de Folheações.
Resumo: Falaremos das propriedades notáveis de certos tipos especiais de singularidades de Folheações nas variedades algébricas que chamamos persistentes."

Ministrante: Prof. Régis Varão, idealizador do canal "Fantástico Mundo Matemático"
Data: 29 de março 2019, sexta-feira, às 14:15
Local: Auditório da Engenharia Naval, Bloco C - 2º andar

Resumo: Quais qualidades a matemática nos ensina e que podemos levar para a nossa vida diária? Em poucas palavras: rebeldia, coragem e criatividade. Ah sim, além de super-poderes. Sim, a matemática nos dá poderes! A boa notícia é que não é preciso ser matemático para desenvolver essas habilidades, apenas use a matemática como guia. Falarei também um pouco sobre o projeto de divulgação matemática: Fantástico Mundo Matemático (Youtube, Instagram e Facebook). O Joaquim pediu para avisar que a palestra é para todos os públicos, então só vem! Se não conhece o Joaquim, procura a gente no YouTube.

Palestra: The Future Quantum Internet: Research Challenges
Palestrante: D. Towsley - College of Information & Computer Sciences - UMass - Amherst. 

O Prof. Towsley é um dos mais renomados pesquisadores em Ciência da Computação atualmente. É membro Correspondente da Academia Brasileira de Ciências. Esse ano falará sobre Computação Quântica, tópico de interesse geral. 

Data: 21/08/2019
Horário: 10:30
Local: Auditório do Programa de Engenharia de Sistemas e Computação (PESC)

Resumo: Quantum information processing is at the cusp of having significant impacts on technology and society in the form of providing unbreakable security, ultra-high-precision distributed sensing with applications to metrology and science discovery (e.g., LIGO), much higher-rate deep space optical communications than possible with conventional systems, and polynomial speeds up on graphical search with implications to big data. Most of these applications are enabled by high-rate distributed shared entanglement between pairs and groups of users. A critical missing component that prevents crossing this threshold is a distributed infrastructure in the form of a world-wide "Quantum Internet"  to enable this. This motivates our study of quantum networks, namely what the right architecture is and how to operate it, i.e., route multiple quantum information flows, and allocate resources fairly and dynamically. In this talk we review a specific entanglement-based quantum network architecture and present opportunities and challenges related to resource sharing among multiple parties of users.  In particular, we focus on issues related to resource allocation based on global/local state information and the benefits of path diversity. Last, we evaluate the performance of an entanglement-based quantum switch.