IMPA - Seminário de Geometria Diferencial (REMOTO)
Organizador no período Março/2021
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Lucas Ambrozio (contato: l.ambrozio at impa dot br).
Horários
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Quintas-feiras, das 15:30h às 17h (GMT+3).
(Exceto quando indicado abaixo!).
Como acessar as palestras
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Link para a sala do GoogleMeets será divulgado
abaixo, e ativado meia hora
antes da palestra.
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Por segurança, o link será renovado a cada palestra.
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Por limitações do meio, a sala suporta no máximo 100 participantes.
Última atualização: 24 de junho de 2021.
Lembrete: Estamos vivendo uma
pandemia.
Cuidem-se, e cuidem dos outros!
Palestras
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18 de março de 2021
Khadim War (IMPA)
Título: Closed Geodesics on Surfaces without Conjugate Points
Resumo: We obtain Margulis-type asymptotic estimates for the number of free homotopy
classes of closed geodesics on certain manifolds without conjugate points. Our results
cover all compact surfaces of genus at least 2 without conjugate points.
This is based on a joint work with Vaughn Climenhaga and Gerhard Knieper.
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08 de abril de 2021
Diego Alonso Navarro Guajardo (IMPA)
Título: Sbrana-Cartan hypersurfaces in higher codimensions
Resumo: We will generalize the problem studied by Sbrana and Cartan of classifying the hypersurfaces
of the Euclidean space with genuine deformations, that is, classifying Riemannian manifolds M^n
with at least two non-congruent immersions in R^(n+1). In this presentation we will give a
characterization of some families of Euclidean hypersurfaces which possess genuine deformations
in higher dimensional flat spaces. As a consequence we will recover the classical Sbrana Cartan
classification and open the theory to higher dimensional studies.
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22 de abril de 2021
Baris Coskunuzer (UT Dallas)
Título: Minimal Surfaces in Hyperbolic 3-manifolds
Resumo: In this talk, we will show the existence of smoothly embedded closed minimal surfaces in infinite
volume hyperbolic 3-manifolds. The talk will be non-technical, and accessible to graduate students.
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06 de maio de 2021
Leonardo Cavenaghi (University of Freibourg - CH)
Título: On metric deformations and applications: the geometry of smooth structures
Resumo curto: We investigate several metric deformations, such as: Cheeger deformations, general vertical
warpings and conformal changes to construct/find obstructions for the existence of metrics with non-negative/positive
curvature properties, e.g, sectional, Ricci and scalar. Our focus relies on producing examples of exotic manifolds and
bundles with fibers/bases of exotic manifolds with such properties. We also solve the G-invariant Kazdan-Warner problem
to explore which smooth functions are the scalar curvature for Riemannian metrics on some exotic spaces obtained as
the orbit space of a G-principal bundle. Some of the presented results are obtained in collaboration with Prof.
Llohann D. Sperança and Prof. João Marcos do Ó.
Resumo longo e bibliografia: aqui
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20 de maio de 2021
Chao Li (Princeton University)
Título: Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Resumo: In this talk, I will discuss some recent developments on the topology of closed manifolds admitting
Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension
4 (resp. 5) has vanishing \pi_2 (resp. vanishing \pi_2 and \pi_3), then a finite cover of it is homotopy equivalent
to S^n or connected sums of S^{n-1}\times S^1. This extends a previous theorem on the non-existence of
Riemannian metrics of positive scalar curvature on aspherical manifolds in 4 and 5 dimensions,
due to Chodosh and myself and independently Gromov. A key step in the proof is a homological
filling estimate in sufficiently connected PSC manifolds. This is based on joint work with Otis Chodosh and Yevgeny Liokumovich.
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10 de junho de 2021
Marcos Cossarini (École Polytechnique Fédérale de Lausanne)
Título: Discrete length metrics and the filling area problem
Resumo: This talk is an invitation to imagine that every manifold with a Riemannian or Finsler length metric
is discrete at the small scale, structured as a simplicial set, thus made of simplices with directed edges. A path can
go along each edge in either way (positive or negative), and its length is defined as the number of positive steps.
The volume of the n-manifold is the number of n-simplices. We will see how to replace any Finsler metric on a compact
surface by a discrete structure whose lengths and area approximate arbitrarily well those defined by the continuous
metric.
This work is motivated by Gromov's filling area conjecture, suggesting that the Euclidean hemisphere has minimum
area among all surfaces that fill a given Riemannian circle isometrically. We propose a discrete version of the
conjecture: any discrete surface that fills a discrete circle C isometrically has area >= 2ab-a-b, where a and b
are the lengths of C oriented in the two possible ways. We will see why this discrete conjecture is equivalent to
Gromov's conjecture (for Finsler surfaces).
If time permits we will glimpse at a connection between this discrete model of space and the causal
sets model of spacetime.
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24 de junho de 2021
Gregory Cosac (IMPA)
Título: Closed geodesics on Semi-Arithmetic Riemann Surfaces.
Resumo: The goal of this talk is to introduce semi-arithmetic Riemann surfaces and present some geometric
aspects of these objects concerning their closed geodesics. In addition, we show the existence of infinite families of
semi-arithmetic surfaces with pairwise distinct trace fields.