Título: On Mean curvature flow of Singular Riemannian foliations: Non compact cases

Palestrante: Marcos Alexandrino (USP)
Data: 13/07/2021
Horário: 14:00h
Local: Transmissão online

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Resumo: In this talk we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Radeschi and first author. We show that, under bounded curvature conditions, any finite time singularity is a singular leaf, and the singularity is of type I. We also discuss the existence of basin of attractions, how cylinder structures can affect convergence of basic MCF of immersed submanifolds and make a few remarks on MCF of non closed leaves of generalized isoparametric foliation.We will introduce all the concepts targeting a wide audience in geometry. This talk is based on a joint work with Leonardo F. Cavenaghi, Icaro Gonçalves.

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Título: FC-subspaces

Palestrante: Misha Belolipetsky, IMPA
Data: 13/07/2021
Horário: 10:30h
Local: Transmissão online

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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.

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

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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.