Grupo de Trabalho: Análise Topológica de Dados

Organizer: Carlos Meniño Cotón, UFF.

Date: 24 sep 2020, 16h.

Place: contact organizer at This email address is being protected from spambots. You need JavaScript enabled to view it..

Abstract: Neste grupo de trabalho nos reuniremos para estudar trabalhos relevantes sobre Análise Topológica de Dados, tanto na parte teórica como aplicada.

Neste primeiro encontro, começaremos lembrando os conceitos básicos de homologia persistente e diagrama de persistência associados a um conjunto de dados assim como o conceito de estabilidade. Daremos alguns exemplos das suas aplicações. Seguidamente estudaremos os trabalhos de Bubenik e Y. Umeda et al. sobre paisagens persistentes e classificação de séries temporais:

P. Bubenik. Statistical Topological Data Analysis using Persistence Landscapes. Journal of Machine Learning Research 16 (2015) 77-102

Y. Umeda, J. Kaneko, H. Kikuchi. Topological Data Analysis and Its Application to Time-Series Data Analysis. FUJITSU Sci. Tech. J., Vol. 55, No. 2 (2019).

On Undirected Two-commodity Integral Flow, Disjoint Paths and Strict Terminal Connection Problems

Speaker: Alexsander A. de Melo, COPPE-UFRJ.

Date: 30 sep 2020, 16h.

Place: Google Meet: meet.google.com/ost-kzem-mqk.

Abstract: Even, Itai and Shamir (1976) proved simple two-commodity integral flow is NP-complete both in the directed and undirected cases. In particular, the directed case was shown to be NP-complete even if one demand is unitary, which was improved by Fortune, Hopcroft and Wyllie (1980) who proved the problem is still NP-complete if both demands are unitary. The undirected case, on the other hand, was proved by Robertson and Seymour (1995) to be polynomial-time solvable if both demands are constant. Nevertheless, the complexity of the undirected case with exactly one constant demand has remained unknown. We close this forty year complexity gap, by showing the undirected case is NP-complete even if exactly one demand is unitary. As a by-product, we obtain the NP-completeness of determining whether a graph contains 1 + d pairwise vertex-disjoint paths, such that one path is between a given pair of vertices and d paths are between a second given pair of vertices. Additionally, we investigate the complexity of another related network design problem called Strict Terminal Connection.

Obs.: This is a joint work with Celina M. H. de Figueiredo (PESC/COPPE/UFRJ) and Uéverton dos Santos Souza (IC/UFF).

Defesa de Dissertação: A Desigualdade de Bourgain-Milman e outras desigualdades clássicas da geometria convexa

M.Sc. Candidate: Erick Cargnel Borges Barreto

Thesis Committee: Prof. Vitor Balestro Dias da Silva (Supervisor, UFF)
Prof. Ralph Costa Teixeira (Co-supervisor, UFF)
Prof. Julián Eduardo Haddad, UFMG
Prof. Marcos da Silva Montenegro, UFMG
Prof. Carlos Hugo Jiménez Gómez, PUC-Rio
Prof. Marcos Craizer, PUC-Rio

Date: 23 sep 2020, 15h.

Place: Google Meet: meet.google.com/amk-foaf-pay

Abstract: A desigualdade de Bourgain-Milman estabelece uma cota inferior (que depende somente da dimensão do Rⁿ) para o produto de Mahler de um corpo convexo, isto é: vol_n(K) · vol_n(K^o) ≥ cⁿ.Vol(Bⁿ)² onde Bⁿ é a bola unitária euclideana em dimensão n e c é uma constante universal. O objetivo desta dissertação é estudar a demonstração de tal desigualdade, através do método da simetrização isomórfica. Para tal, utilizamos diversos resultados importantes, como o Teorema de John, a desigualdade de Sudakov para números de cobertura, e outras desigualdades clássicas da geometria convexa, como as desigualdades de Brunn-Minkowski e Blaschke-Santaló.

Seminars 2020

Brazilian Algebraic Geometry Seminar

Weekly on Wednesdays, 15h30m, online via Google Meet. See event's website.

Organizers: Carolina Araujo e Eduardo Esteves (IMPA), Ethan Cotterill e Marco Pacini (UFF), Maurício Corrêa e Renato Vidal Martins (UFMG), Marcos Jardim (UNICAMP).

Cibercoloquio Latinoamericano de Matemáticas

Fridays, 14h-15h, online via Webex: see event's site.

Contact at UFF: This email address is being protected from spambots. You need JavaScript enabled to view it..

Organizers: Daniel Campos Salas (Costa Rica), Manuel Rivera (Purdue), María Amelia Salazar (UFF), José Alejandro Samper (Puc-Chile), José Simental Rodríguez (UC Davis), Soledad Villar (John Hopkins).

Geometry, Dynamics and Mechanics Seminar

Every 2 weeks on Tuesdays, 15:00 GMT (12:00 Brasilia). A series of online seminars aiming at maintaining and reinforcing collaboration and connection among researchers working in the broad field of Geometry, Dynamics and Mechanics. Further info: https://events.math.unipd.it/GDMSeminar/.

Organizers: Paula Balseiro (UFF), Francesco Fassò (Padova), Luis García-Naranjo (UNAM), David Iglesias-Ponte (La Laguna), Tudor Ratiu (Shanghai), Nicola Sansonetto (Verona).

Latin American Real and Tropical Geometry Seminar

Bi-weekly on Fridays, 11:00. See event's website.

Organizers: Alicia Dickenstein (AR); Ethan Cotterill, Oliver Lorscheid and Marco Pacini (BR); Johannes Rau (CO); Fuensanta Aroca and Cristhian Garay López (MX).

Seminário de Combinatória

Last Wednesday of each month, 13:00, remotely via Google Meet. Further info: http://www.antenabrasil.uff.br/index.php/pt-br/acoes/seminario-combinatoria.

Organizer: Simone Dantas (UFF).

Seminário de EDP e Matemática Aplicada

Biweekly on Wednesdays, 14h, via Google Meet. See website.

Organizers: Juan Limaco (UFF), Mauro Rincon (UFRJ) and Max Souza (UFF).

Seminário Simplético do Rio

Tuesdays, 14h-15h, online via Google Meet: see event's calendar.

Organized by IMPA, PUC-RJ, UFF and UFRJ. Contact at UFF: This email address is being protected from spambots. You need JavaScript enabled to view it..

Seminário em Teoria Espectral de Grafos

Biweekly on Mondays, 15h. Contact organizers for specific info.

Organizer: This email address is being protected from spambots. You need JavaScript enabled to view it. (UFF).

Web-Seminar on Geometric Analysis

Thursdays, 14h, throughout August 2020, online via Google Meet: http://meet.google.com/zzy-pdjp-zmu.

Further info: https://sites.google.com/view/geometricanalysisbr/.

Organizers: Detang Zhou (UFF), Ernani Ribeiro Jr (UFC), Keti Tenenblat (UnB).

WorkGroup on Topological Data Analysis

Thursdays, 16h-18h.

Further info: contact the organizer by E-mail at This email address is being protected from spambots. You need JavaScript enabled to view it..

Organizer: Carlos Meniño Cotón (UFF).

Short Course: An introduction to the geometry of integrable Hamiltonian systems

Speaker: Daniele Sepe

Dates: to be confirmed.

Syllabus: An important question in Hamiltonian mechanics is to describe qualitative properties of the dynamics under consideration. In general, this is a hard problem but it can be tackled for those systems that are known to be integrable, i.e. that admit the "largest number" of constants of motion. In spite of their relatively simple dynamical behaviour, integrable Hamiltonian systems play a prominent role in Hamiltonian mechanics and beyond, ranging from symplectic geometry and Lie theory to quantum mechanics.

The aim of this course is to provide an introduction to the geometry of such systems from a symplectic perspective. After introducing the necessary tools from symplectic geometry, we will study the structure of integrable Hamiltonian systems near regular points and regular (connected components of) fibres, proving the Darboux-Carathéodory and the Liouville-Arnol'd theorems. The theory will be illustrated by some (simple) examples.

Possible extra topics (if time permits and/or the course is extended to 18 hours): Lagrangian fibrations and their global invariants, an introduction to singular orbits and fibres of integrable systems, the local and global geometry of non-commutative integrable Hamiltonian systems.

This is a joint course with Università di Verona, and it will be taught remotely and in English.

Our Calendar 2020 (modified)

Terms

Summer Program: 06/01 to 06/03

1st Term: 06/04 to 24/07

2nd Term: 24/08 to 18/12

Exams

Location

In 2015, we moved to our new campus, Gragoatá! Our new address is:

R. Prof. Marcos Waldemar de Freitas Reis, s/nº - Bloco H - 4º andar
Campus do Gragoatá
24210-201- Niterói - RJ
Tel: 55 - 21 - 2629-2171

Or on Google Maps:

Getting Here via Public Transportation

From Niterói's downtown: walk 16 minutes (map) or take buses 47, 47A or 47B (these buses are colored red).
From Rio's downtown: take the ferry from Praça XV towards Araribóia Niterói, and fall back to Case 1 (map).
From Santos Dumont Airport: walk 15 minutes (map) to Praça XV, and fall back to Case 2.
From South Zone in Rio: take one of the following buses Ipanema-Charitas (740D or 741D) or Gávea-Charitas (750D or 751D or 775D) and go to Case 1.
From International Airport Tom Jobim (a.k.a. Galeão): take bus Galeão-Charitas (760 or 761) and go to Case 1.