Seminário Simplético do Rio
O Seminário Simplético Conjunto é uma iniciativa de pesquisadores do IMPA, PUC-RJ, UFF e UFRJ. As palestras envolvem pesquisadores locais ou convidados, em temas relacionados à geometria simplética e de Poisson. Alunos são particularmente encorajados a participar.
The Joint Symplectic Seminar is organized by IMPA, PUC-RJ, UFF and UFRJ. The talks involve topics related to symplectic and Poisson geometry. Students are particularly encouraged to attend the seminars.
Em 2023, voltando ao formato usual, o seminário será presencial e itinerante, com frequência aproximada de 1 vez por mes.
Para receber anúncios e os links, entrar em contacto com:
contact: semsimp (arr) impa (pont) br
- Seminários de 2023: -
# Sex 8/Dez, 14hs: 2 palestras
IM-UFRJ (Fundão), sala C116
[14-15hs] Higher vector bundles
Matias del Hoyo (UFF)
Abstract: Joint with G. Trentinaglia, we establish a correspondence between representations up to homotopy of Lie groupoids and simplicial vector bundles equipped with a cleavage. Our result generalizes the work of Gracia-Saz and Mehta, and it can be seen both as a relative version of the Dold-Kan correspondence and as a higher generalization of the Grothendieck construction. I will describe the main definitions, ideas, and constructions, trying to avoid the technical issues. I will also discuss connections to Vaintrob’s theory of A-modules and to Lurie’s homotopy colimit equivalence. Finally, I will outline several applications and plans for future investigation.
[15:30-16:30hs] Integration of Poisson homogeneous spaces and shifted symplectic geometry
Henrique Brusztyn (IMPA)
Abstract: A central problem in Poisson geometry concerns the integrability of Poisson manifolds to symplectic groupoids. In this talk, I will show that every Poisson homogeneous space of any Poisson Lie group is integrable in this sense (joint work with Iglesias and Lu). This result is obtained through a concrete construction and the main tools come from Dirac geometry. I will then explain how this construction can be naturally understood in terms of "shifted symplectic geometry", which provides a general framework for such integration problems.
# Sex 3/Nov, 15hs: 2 palestras
IMPA, sala 236
[15-16hs] Invariant Kähler metrics: toric actions
Rui Loja Fernandes (U. Illinois at Urbana-Champaign)
Abstract: In the late 1990s, Guillemin and Abreu described all invariant, compatible, Kähler metrics for symplectic toric manifolds. They used singular Hessian metrics in the associated Delzant polytopes. Abreu's work also include a fourth-order nonlinear PDE expressing the condition for an invariant Kähler metric to be extremal, in the sense of Calabi. Later, Donaldson developed various estimates for solutions of Abreu's equation, sparking a series of subsequent research works in the subject. In this talk, I'll discuss invariant Kähler metrics for toric actions of symplectic torus bundles. This extends the theory to non-toric manifolds and allows us to discover many more examples of invariant (extremal) Kähler metrics, including, for instance, the case of complex ruled surfaces over elliptic curves, as studied by Apostolov et al.
This presentation is based on ongoing joint work with Miguel Abreu (IST-Lisbon) and Maarten Mol (Max Planck-Bonn). It will be related to, but independent of, [my earlier talk this week at UFRJ].
[16:30-17:30hs] Relative Quantum Lefschetz formula
Renato Vianna (UFRJ)
Abstract: Given an Lagrangian L in (Y, \omega|Y), we can lift it to a Lagrangian L' in neighbourhood NY \subset X. Recall that a potential of a Lagrangian encodes information of Maslov index 2 J-holomorphic disks with boundary on it. We will discuss the conditions in which the potential for L' relates with the potential for L according to a lifting formula. In particular, this formula involves counts J-holomorphic spheres with certain tangency on Y (part of relative Gromov-Witten invariants). It generalizes a formula that can be extracted from Biran-Khanevski, under some more restrictive assumptions on Y. As applications, we recover some Lefschetz formulas appearing in the work of Coates-Corti-Galkin-Kasprczyk and show the existence of infinitely many Lagrangian tori in CP^n, Quadrics, Cubics, among other symplectic manifolds. This is joint work with Luis Diogo, Dmitry Tonkonog and Weiwei Wu.
# 4-6 Out: X Workshop on Poisson geometry and related topics
@ IME-USP
https://www.xwpgrt.com.br/home
The Workshop on Poisson Geometry and related topics is an annual event of the Brazilian Poisson Geometry community. The first edition took place in Rio de Janeiro in 2013, and this year we are celebrating the 10th edition. The main goal of the event is to gather researchers working in Poisson Geometry and related subjects, including: Lie groupoids, Lie algebroids, foliations, quantization, mathematical physics, homotopy structures, geometric mechanics, among others. This year the conference will take place at the Auditório Antonio Giglioli, Bloco A, Instituto de Matemática e Estatística da Universidade de São Paulo (IME-USP) on October 04-06.
# Seg 8/Mai, 14hs: 2 palestras
IM-UFRJ, sala C119
[14-15hs] The periodic Toda lattice, some integrable billiards in simplices and some symplectic images of the ball
Daniele Sepe (UFF)
Abstract: Motivated by seminal work of Gromov and Viterbo, an important question in symplectic topology is to understand the orbit of a ball under the action by symplectomorphisms of the standard symplectic vector space. In this talk, we illustrate a strategy to identify certain symplectic images of a ball using integrability of the periodic Toda lattice. As part of this strategy, we show that some integrable billiards in simplices can be seen as suitable limits of the periodic Toda lattice. This is ongoing joint work with Yaron Ostrover and Vinicius G. B. Ramos.
[15:30-16:30hs] Local forms on the category of Loday brackets
Hudson Lima (UFAM)
Abstract: [see the PDF with the abstract]
# Qua 8/Mar, 14hs: 2 palestras
IMPA, sala 224
[14-15hs] Conjecturas e Resultados em Dinâmica Conservativa em baixas dimensões
Umberto Hryniewicz (Aachen)
Abstract: A conjectura de Weinstein pede pelo menos uma órbita periódica em níveis de energia com tipo de contato. Embora extremamente difícil de ser verificada, pode-se argumentar que a validade desta conjectura não nos ensina muito sobre a estrutura global da dinâmica de um dado sistema. Em dimensão três espera-se que existam exatamente duas ou infinitas órbitas periódicas (conjectura “2/infinity”). Também a validade desta conjectura não nos ensina muito sobre a estrutura da dinâmica no caso em que o número de órbitas periódicas é infinito; em contraste, os níveis com exatamente duas órbitas periódicas são extremamente rígidos, e a dinâmica/geometria simplética dos mesmos é totalmente compreendida. Nesta palestra serão discutidos refinamentos qualitativos da conjectura “2/infinity”. Um destes refinamentos é o enunciado de que todo compacto invariante e isolado de um fluxo de Reeb em dimensão 3 possui pelo menos uma órbita periódica. Um resultado obtido em colaboração com Patrice Le Calvez verifica este enunciado quando o número de componentes conexas (do compacto invariante isolado) é finito.
[15:30-16:30hs] Symplectic geometry of the classifying stack BG
Miquel Cueca (Gottingen)
Abstract: I will explain how for a Lie group G with an Ad-invariant and non-degenerate pairing one can construct a symplectic structure on the classifying stack BG. Then I will study their lagrangian structures and use them to produce integrations of Dirac structures. This is joint work with Chenchang Zhu, Daniel Alvarez and Henrique Bursztyn.