Título: A Lower bound for set-colouring Ramsey numbers
Palestrante:Taísa Lopes Martins (IME-UFF)
Data: 19/06/2023
Horário: 15:30 às 16:30h
Local: C116 - Bloco C - CT – Instituto de Matemática – UFRJ.
Resumo: The set-colouring Ramsey number Rr,s(k) is defined to be the minimum n such that if each edge of the complete graph Kn is assigned a set of s colours from {1, . . . , r}, then one of the colours contains a monochromatic clique of size k. The case s = 1 is the usual r-colour Ramsey number, and the case s = r − 1 was studied by Erdős, Hajnal and Rado in 1965, and by Erdős and Szemerédi in 1972.
The first significant results for general s were obtained only recently, by Conlon, Fox, He, Mubayi, Suk and Verstraëte, who showed that Rr,s(k) = 2^{Θ(kr)} if s/r is bounded away from 0 and 1. In the range s = r − o(r), however, their upper and lower bounds diverge significantly. In this talk we introduce a new (random) colouring, and use it to determine Rr,s(k) up to polylogarithmic factors in the exponent for essentially all r, s and k.
This is a joint work with Lucas Aragão, Maurício Collares, João Pedro Marciano and Rob Morris.
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Título: Survival of Renewal Contact Process
Palestrante:Rafael Souza dos Santos (IM-UFRJ)
Data: 14/08/2023
Horário: 15:30 às 16:30h
Local: C116 - Bloco C - CT – Instituto de Matemática – UFRJ.
Resumo: The renewal contact process, introduced in 2019 by Fontes, Marchetti, Mountford, and Vares, extends the Harris contact process by allowing the possible cure times to be determined according to independent renewal processes (with some interarrival distribution mu) and keeping the transmission times determined according to independent exponential times with a fixed rate lambda. In this talk we will discuss conditions on mu to have a positive and finite critical parameter in the renewal contact process. Joint work with Maria Eulalia Vares.
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Título: "Oriented Percolation Models: Further improvement for the critical probability on regular trees"
Palestrante: Jaime Utria (IME-UFF)
Data: 10/04/2023
Horário: 15:30h
Local: C116 - Bloco C - CT – Instituto de Matemática – UFRJ.
Resumo: Let V be the vertex set of the regular tree of degree d + 1. We consider an oriented, dependent, and long-range bond percolation model. In this model, the underlying graph is the complete and oriented graph in which its vertex set is V. We derive a new upper bound for the critical probability of this model, and as a consequence, we retrieve and improve previous bounds for the critical probability of some particular models in the literature.
Todas as palestras são realizadas em Inglês.
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Título: "Oriented Percolation Models: Further improvement for the critical probability on regular trees"
Palestrante: Zoraida Fernandez Rico (Columbia)
Data: 24/04/2023
Horário: 15:00h
Local: Transmissão Online
Acesse a transmissão AQUI.
Resumo: We present an estimator of the covariance matrix of a random d-dimensional vector from an i.i.d. finite sample. Our only assumption is that this vector satisfies a bounded L^p-L^2 marginal moment for p greater or equal than 4, and we allow an adversary to modify arbitrary a fraction of the sample. Given this, we show that the covariance can be estimated with the same high-probability error rates that the sample covariance matrix achieves in the case of Gaussian data. This talk is based on a joint work with Roberto I. Oliveira (IMPA).
Todas as palestras são realizadas em Inglês.
Mais informações completas sobre os seminários estão disponíveis AQUI.
Título: "Noisy voters"
Palestrante: Rangel Baldasso (PUC-Rio)
Data: 27/03/2023
Horário: 15:30h
Local: C116 - Bloco C - CT – Instituto de Matemática – UFRJ.
Resumo: We study noise sensitivity of the consensus opinion of the voter model on finite graphs with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small perturbations of the initial configuration and is sensitive to perturbations of the dynamics governing the evolution of the process. This talk is based on a joint work with G. Amir, O. Angel, and R. Peretz.
Todas as palestras são realizadas em Inglês.
Informações mais completas sobre os seminários estão disponíveis AQUI.
