Uniqueness and nondegeneracy for fractional Dirichlet problems.
January 23, at 11:00 a.m. (Rio de Janeiro local time)
Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.
Speaker: Isabella Ianni (Sapienza Università di Roma)
Abstract: We discuss some recent uniqueness and nondegeneracy results for non-negative solutions of some fractional semilinear problems in bounded domains with Dirichlet exterior condition.
In particular we can consider least energy solutions in balls or in more general symmetric domains, for problems with power nonlinearities. The symmetry properties of the solutions of the associated linearized equation are also investigated.
The talk is mainly based on the following joint works:
[1] A. Dieb, I. Ianni, A. Saldaña, Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods, Nonlinear Analysis, 236, 2023,
https://doi.org/10.1016/j.na.
[2] A. Dieb, I. Ianni, A. Saldaña, Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems, preprint arXiv:2310.01214
Título: “A basis for certain spaces of overconvergent modular functions”
Palestrante: Cláudio da Silva Velasque
Data: 15/12/2023
Horário: 10:00h
Local: C-116 e Transmissão online
Clique AQUI para acessar a transmissão
Banca:
Aftab Pande (presidente) - IM/UFRJ
Ian Kiming - University of Copenhagen
João Pedro dos Santos - Université de Montpellier/IMPA
Francesco Noseda - IM/UFRJ
Ariel Molinuevo - IM/UFRJ
Baskar Balasubramanyam - IISER Pune (Suplente)
100º EDAÍ, 10/11 no CBAE em Flamengo
Local: Colégio Brasileiro de Altos Estudos, Av. Rui Barbosa, 762 - Flamengo
Data e hora: 10 de novembro de 2023, das 10:30 às 18:30
10h30 – 11h30: Katrin Gelfert (UFRJ)
Ergodic recycling of heterodimensional cycles
We define the concept of heterodimensional cycles between hyperbolic ergodic measures of different indices. We study what impact the existence of such a cycle has on the topological properties of the space of invariant measures and present some examples. This is joint work with L. Díaz and Ch. Bonatti.
11h45 - 12h45: Carlos H. Vásquez (PUC Valparaíso)
Measures of maximal entropy for partially hyperbolic diffeomorphisms.
A central problem in dynamics is being able to determine the existence of measures that capture relevant dynamic information. One of these measures is the one that maximizes entropy. In this talk, we will explore the problem of establishing the existence and uniqueness of this measure in partially hyperbolic systems.
14h30 - 15h30: Luna Lomonaco (IMPA)
The Mandelbrot set and its Satellite copies
For a polynomial on the Riemann sphere, infinity is a (super) attracting fixed point, and the filled Julia set is the set of points with bounded orbit. Consider the quadratic family P_c(z)=z^2+c. The Mandelbrot set M is the set of parameters c such that the filled Julia set of P_c is connected.
Computer experiments quickly reveal the existence of small homeomorphic copies of M inside itself; the existence of such copies was proved by Douady and Hubbard. Each little copy is either primitive (with a cusp on the boundary of its main cardioid region) or a satellite (without a cusp). Lyubich proved that the primitive copies of M satisfy a stronger regularity condition: they are quasiconformally homeomorphic to M. The satellite copies are not quasiconformally homeomorphic to M (as we cannot straighten a cusp quasiconformally), but are they mutually quasiconformally homeomorphic? In joint work with C. Petersen we prove that the answer is negative in general, but positive in the case the satellite copies have rotation number with same denominator (this last part is work in progress).
15h40 - 16h40: Cecilia González Tokman (University of Queensland - UQ)
Lyapunov–Oseledets spectrum for transfer operator cocycles under perturbations
In recent years, the study of transfer operators has been combined with multiplicative ergodic theory to shed light on ergodic-theoretic properties of random dynamical systems. The so-called Lyapunov– Oseledets spectrum associated to the transfer operator cocycle contains fundamental information about invariant measures, exponential decay rates and coherent structures which characterize dominant global transport features of the system. While the scope of this framework is broad, it is challenging to identify and approximate this spectrum. In this talk, we present examples of maps where the Lyapunov– Oseledets spectrum can be understood and analyzed under perturbations. This talk is based on joint work with Anthony Quas.
17h10 – 18h10: Enrique Pujals (City University of New York - CUNY)
From zero to positive entropy
We will discuss the mathematical processes by which a system evolves from one whose recurrent set is finite towards another one exhibiting chaotic behavior as parameters governing the behavior of the system are varied. In that direction, we will present a tentative global framework toward describing a large class of two-dimensional dynamics (that includes the Henon family), inspired partially by the developments in the one-dimensional theory of interval maps. More precisely, we present a class of intermediate smooth dynamics between one and higher dimensions where it is possible to describe the transition from zero to positive entropy.
De 4 a 8 de dezembro de 2023 ocorrerá o minicurso The cutoff phenomenon for stochastic Langevin equations, ministrado pelo Professor Michael Högele, da Universidad de Los Andes, Bogotá.
Para saber mais, clique AQUI.
De janeiro a março de 2024 acontecerá o Escola de verão - IM-UFRJ
Minicursos Confirmardos:
Introdução na teoria de controle ótimo e equações de Hamilton - Jacobi - Erwin Topp (IM-UFRJ)
Um breve passeio pelas interseções entre música, matemática e estatistica - Hugo Tremonte de Carvalho (IM-UFRJ)
Introdução às matemágicas - Bernardo Nunes Borges de Lima (ICEX - UFMG)
Superficies minimas - Haimer Alexander Trejos Serna (UERJ)
Activated Random Walks on Z°- Leonardo Trivellato Rolla (IME-USP)
Confira a Programação completa AQUI.
