Seminário de Geometria da UFRJ

Ano 2026

Escrever a geometria@im.ufrj.br para receber os anúncios do seminário e/ou outras questões.
Anos anteriores no link.

Próximo Encontro

Terça 25/Ago, 3:15 PM, Sala C116
Umberto Hryniewicz (RWTH Aachen)
Aspectos de teoria de Morse em dimensão infinita

Abstract. O objetivo desta palestra é discutir, em caráter de divulgação, a maneira encontrada por Floer nos anos 80 para construir homologias de Morse para certos tipos de funcionais em dimensão infinita. A ideia é dar diversos exemplos e discutir alguns detalhes da análise envolvida. Um pouco mais de ênfase será dada à “Seiberg-Witten-Floer homology”. Como aplicação, citaremos a resolução da conjectura “two or infinity” para fluxos geodésicos Finsler na 2-esfera (resultado em conjunto com Cristofaro-Gardiner, Hutchings e Liu).

Encontros anteriores

Terça 18/Ago, 3:15 PM, Sala C116
Matias del Hoyo (UFRJ)
The global quotient problem for orbifolds and beyond

Abstract. Orbifolds are spaces that are locally modeled as quotients of manifolds by finite group actions, but not every orbifold arises globally in this way. This leads to the notion of developable orbifolds, closely related to covering space theory in this setting. On the other hand, a classical construction (via the frame bundle) shows that every effective orbifold can be realized as a global quotient of a manifold by a compact Lie group. In this talk, I will briefly review orbifolds and their description in terms of étale Lie groupoids, and explain how the global quotient problem naturally appears. I will then discuss ongoing work extending this picture beyond the étale case, using ideas such as linearization and the strictification of representations up to homotopy.

Terça 4/Ago, 2:00 PM, Sala C116
Alejandro Cabrera (UFRJ e UPC - Barcelona)
Vortices in symplectic fluids and geodesics

Abstract. This talk is based on joint work with Umberto Hryniewicz and Jair Koiller involving the geometry behind certain fluid dynamical systems. We recall the notion of symplectic fluid which generalizes the standard Euler one from 2d to higher dimensions. We discuss the equations of motion for underlying point-vortex type of solutions and focus on the case of two opposite vortices. We show that, in the dipole limit in which the vortices are arbitrarily close, their mid-point follows a geodesic in the symplectic manifold, providing a far-reaching generalization of Kimura's conjecture for vortices on a surface. We also provide an asymptotic expansion with the leading correction to the geodesic motion, a regularization of the collision, and associated "magnetic" limits.

Terça 16/Jun, 3:15 PM, Sala C116
Ernani Ribeiro (UFC)
Rigidity of Compact Quasi-Einstein Manifolds with Boundary

Abstract. It is known from the classical book *Einstein Manifolds* (Besse, 1984) that quasi-Einstein manifolds correspond to the base of a warped product Einstein metric. Another important motivation for studying quasi-Einstein manifolds comes from the work of Bakry and Émery (1985) on diffusion operators, which is closely related to the theories of smooth metric measure spaces, static spaces, and Ricci solitons. In this talk, we show that a three-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature must be isometric either to the standard hemisphere (S^3_+) or to the cylinder (\mathbb{R} \times S^2) with the product metric. In dimension four, we prove that a four-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric either to the standard hemisphere (S^4_+), to the cylinder (I \times S^3) with the product metric, or to the product space (S^2_+ \times S^2) endowed with the product metric. This is joint work with D. Zhou (UFF) and J. Costa (UFPB).

Terça 26/Mai, 3:15 PM, Sala C116
Ivan Miranda de Almeida (IMPA)
Finite Index CMC Hypersurfaces in Low Dimensions

Abstract. We prove that every complete finite-index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. This answers affirmatively a question posed by do Carmo for this class of ambient spaces and extends known lower-dimensional results. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in positively curved space forms in dimension six. We also prove that a complete finite-index CMC hypersurface immersed in hyperbolic six-space with mean curvature (|H| > 7) is compact. This provides a partial answer to a question posed by Chodosh in his ICM survey.

Terça 19/Mai, 3:15 PM, Sala C116
Yuri Conrado (UFRJ)
Teorema de Batchelor

Abstract. O teorema de Batchelor é um resultado clássico da supergeometria que estabelece uma forma normal para supervariedades suaves. Embora existam diversas demonstrações na literatura, em geral não se enfatiza o caráter geométrico do resultado. Nesta palestra apresentaremos uma demonstração baseada no mapa exponencial de uma conexão, seguindo uma ideia inspirada pela geometria diferencial clássica.

Terça 5/Mai, 3:15 PM, Sala C116
Rui Loja Fernandes (UI - Urbana Champaign)
Totally Real Fibrations of Complex Manifolds

Abstract. Lagrangian fibrations of symplectic manifolds are abstract versions of integrable systems and play an important role in symplectic geometry, Kähler geometry, mirror symmetry, and related areas. An important class of examples is provided by symplectic toric manifolds. In this talk, I will discuss analogous fibrations in complex geometry, called totally real fibrations, which include the class of complex toric manifolds. One of the main goals of the talk is to explain the connection between such fibrations and log-integral affine manifolds, analogous to the relationship between Lagrangian fibrations and integral affine manifolds. The talk is based on ongoing joint work with Maarten Mol (Toronto) and Daniele Sepe (Medellín).

Sexta 10/Abr, 1:30 PM, Sala C116
Jakob Stein (Unicamp)
Instantons on Dk ALF Gravitational Instantons

Abstract. We discuss ongoing work with Foscolo, Ross, and Sotgiu on the construction of Yang–Mills instantons on noncompact hyperkähler four-manifolds with cubic volume growth of dihedral type, including the Atiyah–Hitchin metric on the moduli space of two monopoles. We focus on the moduli problem near the geometric limit arising from the Sen construction.

Terça 24/Mar, 3:00 PM, Sala C116
Maria Fernanda Elbert (UFRJ)
Estabilidade de Hipersuperfícies com Curvatura Média de Ordem Superior Constante

Abstract. Nesta palestra discutiremos o conceito de estabilidade para hipersuperfícies com curvatura média de ordem superior constante. Consideraremos os casos de hipersuperfícies compactas, completas e capilares, estabelecendo comparações com a teoria clássica das hipersuperfícies de curvatura média constante.

Terça 24/Mar, 1:30 PM, Sala C116
Valerio Assenza (IMPA)
Existence and Localization of Closed Magnetic Geodesics with Small Energy

Abstract. One of the classical and most celebrated problems in Hamiltonian dynamics is the existence of periodic orbits on a prescribed energy level. In the context of magnetic dynamics, and adopting a variational approach, this talk presents new results on the existence and localization of low-energy periodic magnetic orbits.A central role is played by the notion of magnetic curvature, recently formalized in full generality in [Ass24, AMRT25]. This work is part of a joint project with Leonardo Macarini and Gabriele Benedetti.