Título: FC-subspaces
Palestrante: Misha Belolipetsky, IMPA
Data: 13/07/2021
Horário: 10:30h
Local: Transmissão online
Confira AQUI o link para a transmissão.
Resumo: In a joint work with Nikolay Bogachev, Alexander Kolpakov, and Leone Slavich we discovered an interesting connection between totally geodesic subspaces of a hyperbolic manifold or orbifold and finite subgroups of the commensurator of its fundamental group. We call the totally geodesic subspaces associated to the finite subgroups by fc-subspaces. It appears that these subspaces have some remarkable properties. We show that in an arithmetic orbifold all totally geodesic subspaces are fc and there are infinitely many of them, while in non-arithmetic cases there are only finitely many fc-subspaces and their number is bounded in terms of volume. In the talk, I will discuss these results and if time permits will sketch some other applications of fc-subspaces.
Nesta tabela reunimos informações sobre todas as turmas de graduação ofertadas na segmentação 2021-1 pelo Instituto de Matemática, incluindo formulários de acesso, links para salas virtuais ou contato do professor ministrante conforme cada caso. Cada turma no sistema está associada a um número de controle que a identifica de forma única. Este número de controle é informado na sua CRID ao lado do código da disciplina. Tenha em mãos a sua CRID ao realizar a consulta, este documento pode ser emitido no portal do aluno pelo site ou pelo App.
Confira o quadro de horário das disciplinas oferecidas pelo IM em 2021.1
Clique AQUI e acesse.
Título: Sharp Ellipsoid Embeddings and Toric Mutations
Palestrante: Renato Vianna, Universidade Federal do Rio de Janeiro
Data: 29/06/2021
Horário: 10:30
Local: Transmissão online
Resumo: We will show how to construct volume filling ellipsoid embeddings in some 4-dimensional toric domain using mutation of almost toric compactification of those. In particular we recover the results of McDuff-Schlenk for the ball, Fenkel-Müller for the product of symplectic disks and Cristofaro-Gardiner for E(2,3), giving a more explicit geometric perspective for these results. To be able to represent certain divisors, we develop the idea of symplectic tropical curves in almost toric fibrations, inspired by Mikhalkin's work for tropical curves. This is joint work with Roger Casals.
Obs: The same result appears in "On infinite staircases in toric symplectic four-manifolds", by Cristofaro-Gardiner -- Holm -- Mandini -- Pires. Both papers were posted simultaneously on arXiv.
Acesse AQUI para mais informações.
Título: Finding real zeros a lot faster through an adaptive grid
Palestrante: Josué Tonelli Cueto (INRIA)
Data: 09/07/2021
Horário: 09:00h
Local: Transmissão via RNP e Youtube
Confira AQUI a transmissão pelo RNP.
Confira AQUI a transmissão pelo Youtube.
Resumo: An algorithm by Cucker, Krick, Malajovich and Wschebor finds all the real zeros of a dense real polynomial system. This algorithm has three very important properties for a numerical algorithm in algebraic geometry: 1) numerically stable, 2) parallelizable, and 3) good probabilistic run-time. Unfortunately, the algorithm does not have a finite expected run-time, a fact that has been inherited by all algorithms in real numerical algebraic geometry. In this talk, we show how by making this algorithm adaptive, we can obtain finite expected run-time while preserving all the nice features of the original algorithm.
Título: Revisiting the definition of stability of algorithms
Palestrante: Carlos Beltrán (Universidad de Cantabria)
Data: 25/06/2021
Horário: 10:00h
Local: Transmissão via RNP e Youtube
Confira AQUI a transmissão pelo RNP.
Confira AQUI a transmissão pelo Youtube.
Resumo: It is quite a tricky question to define what an algorithm is. It is even more tricky to give a sensible definition of what an stable algorithm is. Does there exist a good theory around this question? Well, it depends on what you call “good”. In this talk I will present some fundamental issues with the current standard viewpoint of stability and, hopefully, a theory which is called to become a solution to these issues.
The talk will be directed to a broad audience and, spoiler alert: could be polemic for experts.
