Seminário de Geometria e Topologia de São Carlos

Página do Seminário de Geometria e Topologia de São Carlos, organizado por docentes dos grupos de Geometria Diferencial do ICMC-USP e Geometria e Topologia do DM-UFSCar.

Organizadores:

Prof. Daniel Fadel [daniel.fadel (at) icmc.usp.br]
Prof. Fernando Manfio [manfio (at) icmc.usp.br]
Prof. José Nazareno Vieira Gomes [jnvgomes (at) ufscar.br]
Prof. Luiz Roberto Hartmann Junior [hartmann (at) ufscar.br]

Contate um dos organizadores caso queira ser incluído(a) na lista de emails e receber avisos sobre os seminários.

Segundo Semestre de 2026

Frequência dos seminários: a cada duas semanas.

Dias da semana: Sextas-feiras.

Horário: 14:00 às 15:00.

07 de Agosto de 2026 - Aires Eduardo Menani Barbieri (University of Granada (IMAG))

Title: Complete elliptic Weingarten surfaces in $\mathbb{R}^3$

Abstract: An oriented surface in $\mathbb{R}^3$ is a Weingarten surface if its principal curvatures $\kappa_1 \geq \kappa_2$ satisfy a nontrivial relation $W(\kappa_1,\kappa_2)=0$. It is elliptic when the PDE governing its local graph is elliptic, in which case we can locally write $\kappa_2 = f(\kappa_1)$ with $f$ strictly decreasing. Minimal surfaces and CMC surfaces, which give rise to quasilinear PDEs, are classical examples. Therefore, studying elliptic Weingarten surfaces gives a natural generalization to the fully nonlinear setting. In this talk, we review key results on complete elliptic Weingarten surfaces in $\mathbb{R}^3$ and present recent joint work with José A. Gálvez, Yuanyuan Lian, and Kai Zhang, on the asymptotic behavior at infinity of uniformly elliptic Weingarten surfaces of minimal type and finite total curvature. We classify this behavior depending strongly on the value $f'(0)$ and establish a maximum principle at infinity.

Room: 3-102 (Bloco 3, ICMC)

Seminários anteriores

Primeiro Semestre de 2026

Frequência dos seminários: a cada duas semanas.

Dias da semana: Sextas-feiras.

Horário: 16:30 às 17:30.

03 de Julho de 2026 - Arpan Saha (IME-USP)

Title: Lefschetz structures on non-Kähler manifolds

Abstract: Being Kähler imposes severe constraints on the cohomology of compact complex manifolds such as the Hard Lefschetz property, and the question of how far this generalises beyond the class of Kähler manifolds has been of great interest for a while. In this talk, I shall report on ongoing joint work with Mario García Fernández and Raúl González Molina that abstracts out the definition of a variation of polarised Lefschetz structure and provides evidence that, under certain natural assumptions, such a structure exists more generally on distinguished subspaces within moduli spaces of Bismut--Ricci-flat metrics that are pluriclosed up to source terms. In particular, these distinguished subspaces may be regarded as replacements for the Kähler cone, with affine structure modelled on a subspace of the (1,1) Aeppli cohomology of the compact complex manifold.

Room: 3-102 (Bloco 3, ICMC)

12 de Junho de 2026 - Leandro Mauri (UFSCar)

Title: Tverberg-type problems

Abstract: Tverberg-type problems investigate the conditions under which the images of pairwise disjoint faces of a simplex must have a nonempty intersection under affine or continuous maps. The Tverberg Theorem states that every affine map $f:\Delta_{(r-1)(d+1)}\to\mathbb{R}^d$ admits $r$ pairwise disjoint faces whose images have a common point, while the Topological Tverberg Theorem establishes the same conclusion for continuous maps whenever $r$ is a prime power. When additional combinatorial constraints are introduced through a coloring of the vertices of the simplex, one obtains Colored Tverberg-type theorems, which seek to guarantee the existence of pairwise disjoint rainbow faces whose images have a common intersection. On the other hand, when restrictions are imposed on the dimensions of the faces under consideration, one obtains the class of results known as Van Kampen–Flores-type theorems.

Room: Auditório do Departamento de Matemática da UFSCar

29 de Maio de 2026 - Mateus Rodrigues (ICMC)

Title: Submanifolds with constant Moebius Ricci curvature

Abstract: In the Moebius geometry of submanifolds, there exists an important Moebius invariant tensor called the Moebius metric $g$, together with the Moebius second fundamental form, the Blaschke tensor, the Moebius form and the Moebius normal connection. These constitute a complete system of conformal invariants for umbilic-free submanifolds when the dimension $n \geq 3$.

Among the relevant classes of umbilic-free submanifolds is that of submanifolds with constant Ricci curvature with respect to the Moebius metric, also called constant Moebius Ricci curvature. In this talk, the speaker will present the classification of umbilic-free submanifolds with constant Moebius Ricci curvature and flat normal bundle with two distinct principal normal vector fields. When the Moebius form vanishes identically on $M^n$, a classification result is also obtained for such submanifolds with at least three distinct principal normal vector fields.

Room: 4-005 (Bloco 4, ICMC)

15 de Maio de 2026 - Fabiani A. Coswosck (UFSCar)

Title: Hypersurfaces with two principal curvatures in Euclidean space

Abstract: In this talk, based on works by Alías and Meléndez and by Alías and García-Martínez, we discuss estimates for the infimum and supremum of the norm of the second fundamental form of a complete oriented hypersurface M^n, n \ge 3, in Euclidean space, where M has some constant higher order mean curvature and two principal curvatures, one of them simple. In collaboration with Roberto A. Núñez, we establish estimates for the k-th mean curvature and we show that, if the bounds are attained, the hypersurface is isometric to a cylinder.

Room: Auditório do Departamento de Matemática da UFSCar

17 de Abril de 2026 - Matheus Hudson Gama dos Santos (UFSCar)

Title: Yamabe problem for cornered asymptotically hyperbolic manifolds

Abstract: In this talk, we address the problem of prescribing scalar and mean curvatures on manifolds with two boundaries, one of them is an infinite boundary as usual in a conformally compact theory, and the other one is a finite boundary and a corner where the two meet. The case of negative scalar curvature and minimal finite boundary is treated. We show the existence and uniqueness result under suitable asymptotic assumptions on its scalar curvature and mean curvature of the finite boundary. Our strategy comes from the construction of barrier functions on noncompact setting and relies on a certain operator being an isomorphism. As an application, we discuss positive conformal mass theorems without a Spin approach using a resolution of this problem in this setting.

Room: 4-005.

Segundo Semestre de 2025

Frequência dos seminários: a cada duas semanas.

Dias da semana: Sextas-feiras.

Horário: 16:30 às 17:30.

28 de Novembro de 2025 - Jakob Stein (Unicamp)

Title: Nearly G2-structures and G2-Laplacian co-flows

Abstract: Nearly G2-structures in dimension seven are, up to scaling, critical points of a geometric flow called (modified) Laplacian co-flow. Moreover, since nearly G2-structures define Einstein metrics, they can also be associated to critical points of the volume-normalised Ricci flow. In this talk, we will discuss a recent joint work with Jason Lotay, showing that many of these nearly G2 critical points are unstable for the modified co-flow, and giving a lower bound on the index.

Room: 3-102.

07 de Novembro de 2025 - Luiz Hartmann (UFSCar)

Title: Rotational Surfaces with Second Fundamental Form of Constant Length

Abstract: I will present a classification of rotational surfaces in three-dimensional Euclidean space whose second fundamental form

has constant length equal to one at every point. This defines a class of non-linear Weingarten surfaces. The tools used to obtain the

classification involve classical differential geometry and ordinary differential equations.

Room: 3-102.

10 de Outubro de 2025 - José Nazareno V. Gomes (UFSCar)

Title: Gradient Einstein-type warped products: Rigidity, existence and nonexistence results via a nonlinear PDE

Abstract: We establish the necessary and sufficient conditions for constructing gradient Einstein-type warped metrics. One of these conditions leads us to a general Lichnerowicz equation with analytic and geometric coefficients for this class of metrics on the space of warping functions. In this way, we prove gradient estimates for positive solutions of a nonlinear elliptic differential equation on a complete Riemannian manifold with associated Bakry–Émery Ricci tensor bounded from below. As an application, we provide nonexistence and rigidity results for a large class of gradient Einstein-type warped metrics. Furthermore, we show how to construct gradient Einstein-type warped metrics, and then we give explicit examples which are not only meaningful in their own right, but also help to justify our results.

Room: 3-012.

26 de Setembro de 2025 - Udhav Fowdar (Unicamp)

Title: The holonomy of the Obata connection on Joyce hypercomplex manifolds

Abstract: The Obata connection is the hypercomplex analogue of the Levi-Civita connection on Riemannian manifolds. While a lot is known about Riemannian holonomy groups (including a full classification), very little is known about the Obata holonomy group. In this talk, I will present some new results exploring the Obata holonomy on compact Lie groups endowed with left invariant hypercomplex structures. The talk should be fairly non-technical and is based on a recent joint work with Beatrice Brienza, Giovanni Gentili and Luigi Vezzoni.

Room: 3-102.

12 de Setembro de 2025 - Valter Borges (UFPA/UnB)

Title: Non-existence results for warped product shrinking Ricci solitons

Abstract: A warped product Ricci soliton is a gradient Ricci soliton which is isometric to a warped product $M^n\times_{h}F^m$, where $M$ is the base, $F$ is the fiber, and $h:M\rightarrow\mathbb{R}$ is the warping function. Through the work of Ivey, Dancer-Wang, and others, we have examples of complete gradient Ricci solitons with this geometry, which are either steady or expanding. However, no examples in the shrinking case have shown up until this moment.

This talk aims to present non-existence results concerning warped product shrinking gradient Ricci solitons, including contributions given by the speaker.

Room: 4-003.

22 de Agosto de 2025 - Tomás S. R. Silva (Unicamp)

Title: Machine Learning Ricci-Flat Metrics

Abstract: Artificial Intelligence has rapidly become a powerful tool in scientific discovery, with growing impact across many disciplines—including Pure Mathematics. In particular, Machine Learning offers promising approaches to tackling computationally intensive problems in fields such as Complex Differential and Algebraic Geometry.

In this talk, we will focus on recent advances in the use of supervised learning to approximate Ricci-flat metrics on Calabi–Yau manifolds, a central challenge in both Mathematics and Theoretical Physics. We will also explore how data-driven methods can reveal hidden structures and patterns in Differential and Algebraic Geometry.

Keywords: Ricci-flat metrics; Calabi–Yau manifolds; Machine Learning in Geometry

Room: 3-011

Primeiro Semestre de 2025

Frequência dos seminários: a cada duas semanas.

Dias da semana: Sextas-feiras.

Horário: 14:00 às 15:00.

23 de Maio de 2025 - Leonardo Francisco Cavenaghi (Unicamp)

Title: G-equivariant atoms

Abstract: In this talk, we introduce the concept of atoms developed by Katzarkov-Kontsevich-Pantev-Yu while presenting some generalizations, particularly in the G-equivalent context. We will discuss applications related to questions in G-equivariant birational geometry. This is based on two joint works (in progress) with Lino Grama, Ludmil Katzarkov, and Maxim Kontsevich.

Room: 3-102

09 de Maio de 2025 - Miguel Ibieta Jimenez (ICMC-USP)

Title: Subvariedades isométricas com aplicações de Gauss isométricas.

Abstract: Apresentarei um resultado recente sobre subvariedades isométricas do espaço Euclidiano, em codimensão 2, cujas aplicações de Gauss são também isométricas. Este é um trabalho em conjunto com M. Dajczer y Th. Vlachos.

Room: 3-102

25 de Abril de 2025 - Andrés Moreno (Unicamp)

Title: Invariant G2- instantons on homogeneous manifolds.

Abstract: In this talk, we will discuss recent advances on invariant G2-instantons on some particular homogeneous spaces. In the first part, we will consider 7-dimensional 2-step nilpotent Lie groups endowed with an invariant coclosed. For this case, we characterize the corresponding Lie algebras where the characteristic connection is a G2-instanton.

In the second part, we will consider the seven dimensional Stiefel manifold V^{5,2}=SO(5)/SO(3). According to the reductive decomposition of V^{5,2}, we provide an explicit description of all invariant G_2 structures on the Stiefel 7-manifold. As a consequence, we classify the invariant connections on homogeneous principal bundles over V^{5,2} with gauge group U(1) and SO(3), satisfying either the instanton condition.

Finally, as an application of both cases, we will analyze the heterotic G2-system which is the 7 dimensional analogue of the Hull-Strominger system in complex manifolds.This talk features two joint works, one with Viviana del Barco (Unicamp) and Andrew Clarke (UFRJ) and one with Luis Portilla (UBO).

Room: 3-102.

04 de Abril de 2025 - Diego Alonso Navarro Guajardo (ICMC-USP)

Title: Equivariant construction of spheres with Zoll families of minimal hypersurfaces.

Abstract: We studied a generalized notion of Zoll metric for the context of minimal surfaces. We construct examples of Euclidean spheres with such property.

We also showed that the real projective spaces RP^n are flexible with this extended notion of Zoll metrics. This contrasts with the classical theory of Zoll metrics where the real projective space only has the round metrics as Zoll metrics.

Our construction is equivariant with respect to the orthogonal group, and this gives us information even for classical Zoll metrics. In particular, given any discrete subgroup G of O(3) which does not contain the antipodal map, we show that there exists Euclidean Zoll 2-spheres with the group of isometries being precisely G.

Room: 5-003.

21 de Março de 2025 - Paul Schwahn (Unicamp)

Title: Rigidity of Einstein metrics and symmetric spaces

Abstract: The moduli space of Einstein metrics on a given closed manifold is not well-understood, even locally. I review the deformation theory of Einstein metrics and discuss some recent progress on compact symmetric spaces. In particular, I give a new conceptual description of their infinitesimal Einstein deformations. This is a joint effort with Stuart J. Hall and Uwe Semmelmann.

Room: 5-101.

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