Geometry Research Group at the University of São Paulo

The Geometry Research Group at IME USP

Events

Symposium on Contemporary Differential Geometry at USP

Organized by	Prof. Marcos Alexandrino (IME), Prof. Xiaobo Liu (Peking University) and Dr. Patricia Marçal (pos-doc IME)
Supported by	Projeto Temático (coord. Paolo Piccione) Fapesp 2022-16097-2 / BRICS- 2026 (SBM)
Date:	19 to 21 August 2026
venue:	Auditório Antonio Gilioli

	Wednesday (26.08.19)	Thursday (26.08.20)	Friday (26.08.21)
11:15-12:15	Prof. Andre Gomes Talk: Curvature Bounds of Isometric Actions via Optimal Transport	Dr. Marcelo Miranda Talk: Embedded contact homology of the unit cotangent bundle of the Klein bottle	Prof. Marcos Alexandrino Talk: Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities
14:00-15:00	Prof. Brayan Ferreira Talk: Max-min energy of pseudoholomorphic curves and periodic Reeb flows in dimension $3$	Prof. Dorel Fetcu Talk: Biconservative submanifolds in complex space forms	Prof. Fabricio Valencia Quintero Talk: Some topological aspects of orbifolds
15:00-16:00	Prof. Renato Vianna: Talk: Open-string Quantum Lefschetz formula	Prof. João Henrique Santos de Andrade Talk: Nonhomothetic periodic metrics with constant scalar curvature and conformally variational invariants	Prof. Cristian Ortiz Talk: Equivariant cohomology of stacky Lie group actions
16:30-17:30	Prof. Xiaobo Liu Talk: Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces.	Prof. Ivan Struchiner Talk: Lie Theory and Cartan's Realization Problem	Prof. Dirk Töben Talk: Polar and Toric Manifolds
17:30-18:30	Prof. Marcelo Atallah Talk: An overview of Hamiltonian cyclic and circle actions	Dra. Patrícia Marçal Talk: When is a singular Finsler foliation actually Riemannian? The case of $(\alpha,\beta)$ spaces.	Prof Michel F. C. Haddad Talk: Spherical Intersection Dissimilarity: A Geometric Alternative to Minkowski Metrics".
18:30-19:30	Prof. Leonardo Biliotti Talk: Reduction Principles for Proper Actions.	Profa. Clarice de Souza Ferreira Netto Talk: Multiplicative sections of CA-groupoids

Wednesday (26.08.19)

Wednesday (26.08.19) 11:15-12:15
Prof. Andre Gomes (IME-USP)
Title: Curvature Bounds of Isometric Actions via Optimal Transport
Abstract: Spaces with symmetry can be "divided" by that symmetry to produce a smaller quotient space, and a classical formula of O'Neill relates the curvature of the two: the quotient is more curved, because the symmetry twists the geometry and this twisting adds curvature. In parallel, a major development of recent decades reinterprets curvature through optimal transport — the problem of moving one distribution of mass onto another as efficiently as possible — showing that a space has positive Ricci curvature precisely when a natural entropy is convex along optimal transport paths. This talk brings the two viewpoints together. For distributions respecting the symmetry, optimal transport descends to the quotient, now carrying a natural weight that records the size of the symmetry orbits, and the convexity of entropy in this weighted quotient reproduces O'Neill's formula — twisting term included — from an entirely transport-theoretic route. The geometric and probabilistic faces of curvature meet, and the effect of the symmetry appears on both.

Wednesday (26.08.19) 14:00-15:00
Prof. Brayan Cuzzuol Ferreira (UFES)
Title: Max-min energy of pseudoholomorphic curves and periodic Reeb flows in dimension $3$
Abstract: Pseudoholomorphic curves were introduced by Mikhail Gromov in his seminal 1985 paper. Since then, their theory has been extensively developed and applied to a wide range of problems in symplectic geometry and dynamics. In this talk, we will introduce the basic ideas of the theory and explain how elementary spectral invariants, defined via the max-min energy of pseudoholomorphic curves by Michael Hutchings, can be used to characterize periodic three-dimensional Reeb flows.
We will show that Zoll contact forms on S^3 are characterized by the equalities c_1=c_2=A_min. This characterization fails for the lens spaces L(p,1) with p>1. Nevertheless, we characterize Zoll contact forms on L(p,1) in terms of embedded contact homology (ECH) spectral invariants. We will also present a characterization of Besse contact forms in terms of elementary spectral invariants, analogous to the one obtained by Dan Cristofaro-Gardiner and Marco Mazzucchelli. This is joint work with Rafael Fernandes.

Wednesday (26.08.19) 15:00-16:00
Prof. Renato Vianna (IME-USP)
Title: Open-string Quantum Lefschetz formula
Abstract: Let Y be a symplectic divisor of X, \omega. In the Kahler setting, Givental's (closed-string) Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, \omega|Y), we can lift it to a Lagrangian L' in neighbourhood NY \subset X. We will introduce the notion of the potential of a Lagrangian, which encodes information of Maslov index 2 J-holomorphic disks with boundary on it. From the work of Biran-Khanevski, we can extract a formula for when (X,L',Y,L) forms a monotone tuple (we will define this notion), and the minimal Chern number of Y is 2. We generalise the formula in this setting when we allow the minimal Chern number to be 1. We can use this to show the existence of infinitely many Lagrangian tori in CP^n, Quadrics, Cubics, and other symplectic manifolds, among other results.
Following the work of Tonkonog on gravitational descendants, we recover an explicit Quantum Lefschetz formula appearing in the work of Coates-Corti-Galkin-Kasprczyk. Interestingly, their formula applies in a different context--specifically when X is toric -- which neither contains nor is contained in the monotone tuple setting. Motivated by this, we introduce an alternative set of hypotheses, typically satisfied when X degenerates to a toric manifold, under which a broader open-string Quantum Lefschetz formula applies. The differences between these sets of hypotheses will be discussed. This is joint work with Luis Diogo, Dmitry Tonkonog and Weiwei Wu.

Wednesday (26.08.19) 16:30-17:30
Prof. Xiaobo Liu (Peking University)
Title: Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces.
Abstract: Mean curvature flow (MCF) of isoparametric submanifolds in Euclidean spaces and spheres have been studied by Liu and Terng. They have been used to give explicit ancient solutions of MCF with complicated topological type and study rigidity of ancient solutions of MCF for hypersurfaces in spheres. In this talk, I will describe behavior of MCF of isoparametric submanifolds in hyperbolic spaces. This talk is based on a joint work with Wanxu Yang.

Wednesday (26.08.19) 17:30-18:30
Prof. Marcelo Atallah (IME-USP)
Title: An overview of Hamiltonian cyclic and circle actions
Abstract: A symplectic structure on a smooth manifold is a non-degenerate closed 2-form. It is a natural generalization of an area form on an oriented surface. In this talk, we discuss actions of finite cyclic groups and of the circle group on a closed symplectic manifold, preserving the symplectic form. We shall be particularly interested in the case where the action is Hamiltonian, a notion of great importance in the field of symplectic geometry and dynamics. We explore how the topology of the manifold and the presence of holomorphic spheres are related to the existence of such actions. In the case of symplectic circle actions, we discuss how the presence of a fixed point is often sufficient to guarantee that the action is Hamiltonian. The more recent developments are from joint work with Egor Shelukhin.

Wednesday (26.08.19) 18:30-19:30
Prof. Leonardo Biliotti (Università degli studi di Parma)
Title: Reduction Principles for Proper Actions.
Abstract: In this talk, we review some fundamental aspects of proper group actions on smooth manifolds and describe the construction of the core. We demonstrate that many properties of a proper action can be understood and characterized through the corresponding action on the core.Joint work with Gustavo May Custodio e Alessandro Minuzzo.

Thursday (26.08.20)

Thursday (26.08.20) 11:15-12:15
Dr. Marcelo Miranda (IME-USP)
Title: Embedded contact homology of the unit cotangent bundle of the Klein bottle
Abstract: Michael Hutchings introduced embedded contact homology (ECH), a Floer homology theory for contact 3-manifolds that has become a powerful tool in low-dimensional symplectic and contact topology. In this talk, we give a combinatorial description of the ECH chain complex of the unit cotangent bundle of any flat Klein bottle. Using this description, we derive a combinatorial formula for its ECH spectrum and apply it to compute the Gromov width of the disk cotangent bundle of certain flat Klein bottles.

Thursday (26.08.20) 14:00-15:00
Prof. Dorel Fetcu (Gheorghe Asachi Technical University of Iasi)
Title:: Biconservative submanifolds in complex space forms
Abstract: We first consider PMC surfaces in complex space forms, and discuss about the interaction between the notions of PMC, totally real and biconservative. We will see that PMC surfaces in a non-flat complex space form are biconservative if and only if totally real. Then, we present a Simons type formula for a well-chosen vector field constructed from the mean curvature vector field and then a rigidity result for CMC biconservative surfaces in 2-dimensional complex space forms. We also present a reduction of codimension result for PMC biconservative surfaces in non-flat complex space forms. We conclude by constructing examples of CMC non-PMC biconservative submanifolds from the Segre embedding, and discuss when they are proper-biharmonic. This is a joint work with H. Bibi, B.-Y. Chen, and C. Oniciuc.

Thursday (26.08.20) 15:00-16:00
Prof. João Henrique Santos de Andrade (IME-USP)
Title:: Nonhomothetic periodic metrics with constant scalar curvature and conformally variational invariants
Abstract: Given a closed Riemannian manifold, two conformal metrics with the same constant scalar curvature may still be geometrically distinct, that is, not related by a conformal diffeomorphism followed by a rescaling. We prove that products of spheres with hyperbolic manifolds admit countably many pairwise nonhomothetic complete periodic metrics with constant scalar curvature. The key principle is that the properness of the conformal group action, guaranteed by the Ferrand-Obata theorem, combined with a volume shrinkage argument along a tower of finite coverings, provides an obstruction to conformal homothety. We then extend this framework to conformally variational invariants, obtaining nonuniqueness theorems for curvature prescription problems, including $Q$-curvatures, $sigma_k$-curvatures, and renormalized volume coefficients. Joint work with J. S. Case, P. Piccione, and J. Wei.

Thursday (26.08.20) 16:30-17:30
Prof. Ivan Struchiner (IME-USP)
Title:: Lie Theory and Cartan's Realization Problem
Abstract: This talk focuses on the Lie theoretic objects controlling moduli problems for G-structures with connections satisfying diffeomorphism-invariant PDEs. While finite-type realizations are governed by G-structure algebroids with connections (joint with R. L. Fernandes), infinite-type problems for coframes are controlled by relative Lie algebroids, as established by Fernandes and Smilde. Finally, we report on ongoing research putting both frameworks together via relative G-structure algebroids with connections to attack general infinite-type problems.

Thursday (26.08.20) 17:30-18:30
Dra. Patrícia Marçal (IME-USP)
Title:: When is a singular Finsler foliation actually Riemannian? The case of $(\alpha,beta)$ spaces.
Abstract: Singular Riemannian foliations (SRFs) provide a unifying language for isometric group actions, Riemannian submersions, and partitions by holonomy groupoids of a metric connection, and their study has been central to submanifold and metric geometry for decades. Their natural Finslerian counterparts, singular Finsler foliations (SFFs), arise as orbits of Finsler isometric actions, fibers of Finsler submersions, and level sets of some transnormal functions. A natural question in this area, going back to a problem of Ghys, asks under which conditions a singular Finsler foliation coincides with a singular Riemannian foliation with respect to some Riemannian metric. In this talk I will discuss recent joint work with M. M. Alexandrino and B. O. Alves, where we answer this question for singular Finsler foliations of (α,β)-spaces, i.e. manifolds equipped with (α,β)-metrics. These are among the most tractable and widely used non-Riemannian Finsler metrics, with applications ranging from Zermelo navigation to wildfire-spread modeling. Time permitting, I will explain how this characterization led us to extend Molino's conjecture (closure of the leaves of an SRF remains an SRF) to singular Finsler foliations that are simultaneously SRFs, and establish equifocality of regular leaves of such foliations with respect to the Finsler metric itself.

Thursday (26.08.20) 18:30-19:30
Profa. Clarice de Souza Ferreira Netto (IME-USP)
Title: Multiplicative sections of CA-groupoids
Abstract: A strong connection between differential geometric structures and category theory can be found in the literature, with several works spanning both areas. For example, by considering the complex of multiplicative sections of a VB-groupoid, we obtain an associated category of 2-vector spaces. In this talk, we will show that the category of 2-term $\infty$-Leibniz algebras is related to the complex of multiplicative sections of a twisted CA-groupoid. Furthermore, we will see how a morphism between twisted CA-groupoids allows us to construct a 2-term $\infty$-Leibniz algebra."

Friday (26.08.21)

Prof. Marcos Alexandrino 11:15-12:15
Talk: Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities
AbstractA Singular Riemannian foliation on a complete Riemannian manifold $M$ is called a Singular Riemannian foliation
(SRF for short) if its leaves are local equidistante, e.g., the partition of $M$ into orbits of na isometric
action. In this talk we investigate problems of Calculus of Varitions in compact Riemannian manifold equipped
with SRFs with special properties. Examples of such SRF being considered include isoparametric foliations, SRF on
Euclidean fiber bundles and the partition of M into the orbits of a Lie group acting by isometris. This lecture
is based on a joint work with Leonardo F. Cavanaghi, Diego Corro, Marcelo K. Inagaki. Its target audience is the
general public interested in Differential Geometry and Analysis.

Friday (26.08.21) 14:00-15:00
Prof. Fabricio Valencia Quintero (IME-USP)
Tilte: Some topological aspects of orbifolds
Abstract: The aim of this talk is to describe orbifolds in terms of Lie groupoids up to Morita equivalence. This perspective allows us to develop several topological tools and invariants, such as the fundamental group, de Rham cohomology, and the Euler class and Euler characteristic, in a natural and elegant way, avoiding the use of orbifold charts. If time permits, I will also present some recent results obtained within this framework.

Friday (26.08.21) 15:00-16:00
Prof. Cristian Ortiz (IME-USP)
Title: Equivariant cohomology of stacky Lie group actions
Abstract: There is a well-defined notion of action in the setting of higher categories. Specifically, weak 2-groups in a 2-category act on objects up to 2-isomorphism constrained by higher coherences. We unpack this notion for two main examples of 2-categories: Lie groupoids and differentiable stacks. We prove that both notions are naturally related, and we introduce their corresponding equivariant cohomology rings. As an application, we describe the equivariant cohomology of toric symplectic stacks. The talk is based on joint work with Daniel López (Niterói) and Roberto Villaflor (Valparaíso).

Friday (26.08.21) 16:30-17:30
Prof. Dirk Töben (UFSCar)
Talk: Polar and Toric Manifolds
Abstract: In this talk we want to relate group actions of two different areas. On the one hand there is the notion of a quasitoric manifold, a compact even-dimensional manifold equipped with a locally standard action of a compact half-dimensional torus whose orbit space is a simple convex polytope. It is a fundamental notion of toric topology that relates torus actions with the combinatorics of a polyhedra. On the other hand one has the notion of a polar action, an isometric Lie group actions admitting a section, an immersed submanifold that meets every orbit and always orthogonally. This type of action belongs to an area of Riemannian geometry that originated in the study of isotropy actions of compact Lie groups, symmetric spaces and of isoparametric submanifolds. We will show that a smooth quasitoric manifold is polar. This is a joint work with Francisco Caramello.

Prof Michel F. C. Haddad (Queen Mary University of London)
Talk:Spherical Intersection Dissimilarity: A Geometric Alternative to Minkowski Metrics".
abstract: TBA