# Seminários

## PRÓXIMOS

Symplectomorphism problem for Hamiltonian reductions and phenomena related to size

Expositor: Hans-christian Herbig - UFRJ
Ter 26 Mar 2019, 15:30 - Room 236Geometria Diferencial

Resumo: I will explain how a Hamiltonian reduction (aka symplectic quotient) of a unitary representation of a compact Lie group at zero level of the moment map is defined. I will discuss what a (graded regular) symplectomorphism between such spaces is and present examples and general results. I will show how the Hilbert series can be used as an invariant under graded regular diffeomorphism. The role of the large-small dichotomy will be stressed. I will touch on a couple of open problems.

Tudo que você sempre quis saber sobre o Blender 2.8

Expositor: Dalai Felinto - Blender Foundation
Qua 27 Mar 2019, 13:30 - Auditorium 3Computação Gráfica

Resumo: Um passeio sobre o que há de novo no Blender 2.8. Funcionalidades novas, o paradigma de trabalho, questões técnicas de desenvolvimento, até o processo de decisões que fundamentaram as ferramentas novas e consolidaram as existentes. Esse panorama marca um ano da Blender 2.8 Code Quest, onde o palestrante trabalhou então como coordenador do projeto. A ocasião prepara a audiência sobre os temas que serão tratados no "Blender 2.8 Homestretch" em abril em Amsterdam.

Generators of Residual Intersections

Expositor: Vinicius Bouça - UFRJ
Qua 27 Mar 2019, 15:30 - Room 228Álgebra

Resumo: Residual intersections form a very important topic in Commutative Algebra and Algebraic Geometry, with applications in intersection theory (in the definition of the refined intersection product) and enumerative geometry, and were defined algebraically by Artin and Nagata as a generalization of the Linkage introduced by Péskine and Szpiro: if $R$ is a commutative ring and $I\subset R$ is an ideal, we say that $J$ is an $s$-residual of $I$, if $\mathrm{Ht} (J) \geq s\geq\mathrm{Ht}(I)$ and $J=\mathfrak a:I$, where $\mathfrak a$ is an ideal generated by $s$ elements.

In this talk I will give some historic background that motivates the study of residual intersections and the recent tools to study the Cohen-Macaulayness of such ideals, namely the residual approximation complexes and the disguised residual intersections. Later I will introduce a new construction that gives the explicit generators of the disguised residual intersection and prove that, in some cases, these are in fact the generators of the real residual intersection $J$.

This is a joint work with Hamid Hassanzadeh.

Continuidade dos expoentes de Lyapunov para cociclos lineares com somente uma holonomia.

Expositor: Catalina Freijo - IMPA
Qui 28 Mar 2019, 15:30 - Room 228Teoria Ergódica

Resumo: Consideramos uma dinâmica hiperbólica fixa na base e estudamos como os expoentes de Lyapunov variam em função ao cociclo. A continuidade dos expoentes de Lyapunov foi provada por Backes, Brown e Butler para cociclos que admitem holonomias uniformes estáveis e instáveis. Nesta palestra, apresentamos algumas soluções parciais para a conjectura de Marcelo Viana que propõe que somente uma holonomia uniforme (estável ou instável) já é suficiente para garantir a continuidade. Este é um trabalho em conjunto com Karina Marín (UFMG).

Irreducible components of space of foliations of degree three on $\mathbb{P}^3$

Expositor: Raphael Constant da Costa - UERJ
Qui 28 Mar 2019, 15:30 - Room 224Folheações Holomorfas

Resumo: We intend to show that the space of foliations of degree three on $\mathbb{P}^3$ has at least 27 distinct irreducible components, some of them being generically non-reduced. Joint work with Ruben Lizarbe and Jorge Vitório Pereira.

Higher Willmore energies, Q-curvatures, and related global geometry problems.

Expositor: Rod Gover - University of Auckland
Ter 02 Apr 2019, 15:30 - Room 236Geometria Diferencial

Resumo:

The Willmore energy and its functional gradient (under variations of embedding) have recently been the subject of recent interest in both geometric analysis and physics, in part because of their link to conformal geometry. Considering a singular Yamabe problem on manifolds with boundary shows that these these surface invariants are the lowest dimensional examples in a family of conformal invariants for hypersurfaces in any dimension. The same construction and variational considerations shows that (on even dimensional hypersurfaces) the higher Willmore energy and its functional gradient are analogues of the integral of the celebrated Q-curvature conformal invariant and its function gradient (now with respect to metric variations) which is known as the Fefferman-Graham obstruction tensor (or the Bach tensor in dimension 4). In fact the link is deeper than this in that the Willmore energy we consider is an integral of an invariant that actually generalises the Branson Q-curvature. This is part of fascinating unifying picture that includes some interesting open problems in global geometry.

Resíduos de folheções holomorfas de codimensão 1

Expositor: Arturo Fernández Pérez - UFMG
Qui 11 Apr 2019, 15:30 - Room 224Folheações Holomorfas

Resumo: Nesta palestra determinamos o resíduo de Lehmann-Suwa (via um número complexo e uma corriente de integração) de uma folheação holomorfa de codimensão 1 num espaço complexo de dimensão pelo menos 3. Veremos que para uma folheação Liouvilliana $\mathcal{F}$, este resíduo se relaciona com o índice de Baum-Bott de $\mathcal{F}$. Finalmente, daremos uma aplicação ao estudo de singularidades de hipersuperfícies Levi-flat.

The contribution of Jean François Le Gall to Brownian Geometry

Expositor: Hubert Lacoin - IMPA
Qua 15 Mai 2019, 15:30 - Room 228Probabilidade e Combinatória

Resumo: J.F. Le Gall has been awarded the Wolff prize in 2019 "for his profound and elegant works on stochastic processes". In this talk we wish to introduce to a large audience to Le Gall's contribution to the subject of Random Geometry (his main object of focus in the last 15 years). Our starting point is the following question:

"Is there a good notion of random sphere ?"

or more precisely:

"Is there a natural way to choose at random a manifold among all those that are homeomorphic to the sphere?"

In order to give a more precise meaning to the question and to explain the elegant answer brought to the above question by Le Gall and Miermont, we will make a detour to the world of discrete random geometry and the notion Quadragulations of the Sphere, and explore the path that lead to the construction of the Brownian Sphere via Brownian Motion, Brownian Tree, and Brownian Snake.