Título: Fluctuations of homology of diffusion processes on Riemannian manifolds
Palestrante: Mauro Mariani, HSE University, Moscow.
Data: 18/08/2021
Horário: 13:00h
Local: Transmissão online.
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ID da reunião: 958 0581 3232
Resumo: I will discuss the long time behavior and symmetry properties of the DeRham homology of Brownian curves on compact manifolds. Some basic results will be shown and open problems discussed.
Título: Local Symmetry in Erdős–Rényi Graphs
Palestrante: Jefferson Elbert Simões (DIA/UNIRIO)
Data: 16/08/2021
Horário: 15:00h
Local: Transmissão online.
Resumo: Real-world networks are often understood as being symmetrical, meaning that vertices can be found which perform similar or equivalent structural roles (such as hubs from different communities in social networks, or functional regions in neuronal networks). These roles are usually associated with their topological placement relative to its surroundings; however, traditional mathematical formulations of graph symmetry are based on automorphism groups, which depend fundamentally on global structure and do not account for similarities in local structures. In this work, we introduce the concept of local symmetry, which reflects the structural equivalence of vertices' egonets while generalizing classical conceptualizations of symmetry such as automorphism and isomorphism. We also study the emergence of local asymmetry in Erdős–Rényi graphs, identifying regimes of both asymptotic local symmetry and asymptotic local asymmetry. We find that local symmetry persists at least to an average degree of n^{1/3} and local asymmetry emerges at an average degree not greater than n^{1/2}, which are regimes of much larger average degree than for traditional, global asymmetry.
Joint work with Daniel Figueiredo (COPPE/UFRJ) and Valmir Barbosa (COPPE/UFRJ).
All the talks are held in English.
The videos of the online seminars are available:
2020
2021-1
For the second semester, a few days after each meeting the video should be available at HERE.
Título: Discrete-time evolution in recombination
Palestrante: Servet Martínez, Universidad de Chile
Data: 30/06/2021
Horário: 13:00h
Local: Transmissão online.
Confira AQUI o link para transmissão.
ID da reunião: 958 0581 3232
Resumo: We study the discrete-time evolution of a recombination transformation in population genetics acting on the set of measures on genetic sequences. The evolution can be described by a Markov chain on the set of partitions that converges to the finest partition. We describe the geometric decay rate to the limit and the quasi-stationary behavior when conditioned that the chain has not hit the limit.
Título: Generalised oriented site percolation
Palestrante: Réka Szabó (Université Paris Dauphine)
Data: 09/08/2021
Horário: 15:00h
Local: Transmissão online.
Confira AQUI o link para transmissão.
Resumo: We consider a generalised oriented site percolation model on Z^d with arbitrary neighbourhood. The key additional difficulties as compared to standard oriented percolation are the lack of symmetry and, in two dimensions, of planarity. We establish that, despite these deficiencies, in the supercritical regime GOSP behaves qualitatively like OP. Joint work with Ivailo Hartarsky. All the talks are held in English.
The videos of the online seminars are available:
2020
2021-1
For the second semester, a few days after each meeting the video should be available at HERE.
Título: Long-range Ising model and decaying fields- a contour approach
Palestrante: Lucas Affonso (IME-USP)
Data: 28/06/2021
Horário: 15:00h
Local: Transmissão online.
Confira AQUI o link para transmissão.
Resumo: In 1982, Fröhlich and Spencer solved a long-standing conjecture about phase transition in a one-dimensional long-range Ising model for 1/r^2 interaction energy. After that, Cassandro, Ferrari, Merola, and Presutti extended the contour argument for other decays \alpha. In this talk, we address the multidimensional long-range Ising model, showing that a contour argument holds for all decays \alpha> d. As an application, we will show how our techniques can be used to study phase transition when the model has a decaying magnetic field.
The talk is based on joint work with Rodrigo Bissacot, Eric O. Endo, and Satoshi Handa.
All the talks are held in English.
The videos of the online seminars held in 2020 are available at HERE.
For the 2021 series, a few days after each meeting the video should be available at HERE.