The Geometry Seminar at IME-USP is organized by Prof. Marcos Alexandrino, Prof. Ivan Struchiner  and Prof. Paolo Piccione and  supported by Projeto Tematico-Fapesp of Prof.  Paolo Piccione ( Fapesp  22/16097-2;   2016/23746-6; Fapesp: 2011/21362-2)
  

• 2026.05.27 (17:30h)
  
• Speaker: Dr. Luca Accornero (IME-USP)
  
• Title:  Geometric structures on manifolds and integrability problems
  
• Abstract:  TBA
  
• venue: A249

• 2026.05.27
• Event: 3 Semana da Matematica Pura. 
• Speaker: Prof. Marcos. M. Alexandrino (IME-USP)
• Title: From Spectral Theorem to Polar Foliations
  
• Abstract:In this talk, we will take a geometric journey that will begin with the familiar Spectral Theorem
  and will take us to  current research topics. We will discuss how the structure of Lie Groups and the Maximum Torus Theorem exemplify  the theory of Polar Foliations—a theory that describes various mathematical objects, polar actions, isoparametric immersions, and wave fronts. To conclude, we will show how the presence of these foliations allows us to simplify complex problems of Partial Differential Equations originating in the Calculus of Variations. 
  
• venue: 

Previous talks and events:

• 2026.05.13 (17:30h)
  
• Speaker: Dr. Luca Accornero (IME-USP)
  
• Title: The geometry of jet spaces
  
• Abstract: The k-th jet prolongation of a submersion is a manifold consisting of the k-th order Taylor expansion of local sections. Jet prolongations provide a natural framework to study differential equations in a geometric way, by interpreting them as submanifolds.
  This talk will be an introduction to jet prolongations and their geometry, with a focus on the Cartan distribution - a canonical distribution whose integral submanifolds encode solutions of differential equations.
  The talk is meant to be accessible to students.
• venue: A249

• 2026.05.08
• Speaker: Victor Gustavo May Custodio (Universita degli Studi di Parma)
• Title: Coxeter Polar foliations and their invariants.
  
• Abstract: Singular Riemannian foliations (SRFs) generalize isometric group actions and encode rich transverse geometry. In the polar case, the leaf space carries a natural orbifold structure. We will see that all orbifold Riemannian metrics on the leaf space lift to Riemannian metrics on the ambient space that are adapted to the foliation. As an application, We will study the subclass of polar SRFs for which, in particular, the leaf space is a Coxeter orbifold. We show that the stratification of the leaf space and an appropiate choice of invariants completely determine the foliation up to foliated diffeomorphisms. This is part of an ongoing collaboration with Prof. Diego Corro.
  
• venue: A252

• 2026.04.26
• Speaker: Dr Marcelo José Miranda (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
  
• venue: 252-A
  

• 2026.04.10
• Speaker: prof. Rui Loja Fernandes (Illinois)
• Title: Resolutions of polar groupoids and their Weyl groups
  
• Abstract:A polar groupoid (a polaroid!) is a proper Lie groupoid whose isotropy representations are polar. This notion includes, as special
  cases, (infinitesimal) polar actions, as well as proper symplectic groupoids. It is also Morita invariant, so it leads to polar stacks.
  This class of proper groupoids exhibits a very rich structure, including a canonical Weyl resolution, from which it follows that the leaf space
  is an orbifold and that there is an associated Weyl group. I will illustrate the theory with several explicit examples, including
  toric symplectic manifolds. An important aspect of these constructions  is that they are canonical and, unlike existing approaches, do not
  require any choice of Riemannian metric. I will focus mainly on group actions to make the presentation accessible to those not familiar with
  Lie groupoids. This talk is based on joint ongoing work with Marius Crainic (Utrecht) and David Martínez-Torres (Madrid).
  
• venue: B143
  

• 2026.02.27
• Speaker: prof. Ricardo Mendes (University of Oklahoma)
• Title: Algebraicity of singular Riemannian foliations
  
• Abstract: Singular Riemannian foliations are certain partitions of Riemannianmanifolds, and the traditional sources of examples are isometric group actions and isoparametric hypersurfaces. When the ambient manifold is asphere, it has long been known that such examples are, in the appropriate sense, algebraic. In 2018, Lytchak and Radeschi have shownalgebraicity for a general singular Riemannian foliation in a sphere. In joint work with Samuel Lin and Marco Radeschi, we extend theLytchak-Radeschi theorem from spheres to any compact normal homogeneous space, a class that includes all compact symmetric spaces.Time-permitting, I'll comment on the ingredients of the proof(s).

• 2025.12.12 (at  15h)
• Speaker: Prof. Dario Corona (University of Camerino -Italy)
  
• Title: Cohomogeneity One Minimal Hypersurfaces via Degenerate Geodesics
• Abstract: I will discuss recent progress on the construction and compactness of cohomogeneity one minimal hypersurfaces. Following the classical reduction theory of Hsiang–Lawson, a G-invariant minimal hypersurface in a manifold with a cohomogeneity two action corresponds to a geodesic, possibly with free boundary, for a degenerate metric on the quotient M/G. After establishing existence and uniqueness of geodesics issuing from the singular boundary, we obtain uniform length bounds for all simple geodesics of the reduced metric. As a consequence, we prove compactness of the space of embedded G-invariant minimal hypersurfaces, with no restriction on the ambient dimension.
  This is joint work with Renato G. Bettiol, Fabio Giannoni, and Paolo Piccione.
• B02

•  25.12.05. (15h)
• Speaker: Ivan Beschastnyi - Centre Inria d'Université Côte d'Azur
• Title: Jacobi curves in optimal control
  
•  Abstract: Jacobi fields is a classical object in the calculus of
  variations and Riemannian geometry, that can be seen as variations among
  not all possible curves, but only the extremal ones. Usually they are
  defined as solutions of a system of ODEs, and they can be used to
  determine local minimality of a given candidate curve. In many
  interesting examples there might be no ODE that captures local
  optimality of extremal curves (such as graph embeddings into length
  spaces). Interestingly enough, one can still define a geometric object,
  that captures information about local minimality and which can be
  extracted from it using tools of symplectic geometry. In particularly
  nice examples one recover the Jacobi equation or its suitable
  generalization. I will talk about this general object called the
  L-derivative and some applications obtained in collaboration with Andrei
  Agrachev and Stefano Baranzini.
   
  

• 2025.11.28 (at  15h)
• Speaker: prof. Marcelo Atallah (IME-USP)
• Title: Pontos fixos de difeomorfismos Hamiltonianos pequenos e as conjecturas do fluxo
• Abstract: Nesta palestra, descrevemos como as conjecturas do fluxo C^0 e C^1, que preveem que o grupo de difeomorfismos Hamiltonianos de uma variedade simplética é fechado, respectivamente, nas topologias C^0 e C^1, dentro do grupo de simpléctomorfismos isotópicos à identidade, se relacionam com certos casos da conjectura de Arnold, a qual estabelece uma cota inferior para o número de pontos fixos de um difeomorfismo Hamiltoniano. Por fim, apresentamos resultados recentes na direção da conjectura do fluxo C^0. Este é um trabalho em andamento em colaboração com Egor Shelukhin.
• A242

• 2025.11.07  (at 15h)
• Speaker: Prof. Umberto Leone Hryniewicz (wth-Aachen)
• Title:  Desigualdades sistólicas em superfícies Riemannianas
  
• Abstract:  Geometria sistólica é um tema clássico e fundamental em geometria Riemanniana. Dada uma n-variedade Riemanniana fechada, sua razão sistólica é definida pela n-ésima potência do comprimento da geodésica fechada não-constante mais curta dividido pelo volume total. O problema central desta área é encontrar cota superior ótima dentre todas as métricas Riemannianas em uma variedade fechada dada. No caso da 2-esfera este problema é muito difícil e está totalmente aberto. No entanto, foi conjecturado por Babenko e Balacheff que a geometria redonda é máximo local da razão sistólica. Nesta palestra descreverei solução da conjectura Babenko-Balacheff através de métodos simpléticos. Se o tempo permitir, discutirei a conexão com a noção de capacidade simplética e com desgigualdades sistólicas para sistemas Hamiltonianos.
  
• A242

• 2025. 09.19 (at 15h)
• Speaker: Profa. Cintia Pacchiano
• Title: Existence and regularity theory for variational solutions to the total variation flow on metric measure spaces
  
• Abstract:  
  
• A242

• 2025.09.05 (at 15h)
• Speaker:  Prof. Diego Corro (Cardi University -United Kingdom)
• Title: Deformations of metric foliations
  
• Abstract:  Given a closed singular Riemannian foliation on a compact manifold, i.e. a decomposition of
  the manifold into closed submanifolds called leaves, in this talk we present under the assumption that the
  leaves with the induced metric are at manifolds a deformation procedure along the leaves of the foliation
  that keeps the sectional curvature bounded. In particular this induces on a saturated compact subset of
  the manifold a sequence of foliated Riemannian metrics collapsing to the leaf space of this subset. This
  allows us to compare these at foliations to the so-called Nilpotent structures dened by Cheeger-Fukaya-
  Gromov. In the case when the original manifold is simply connected we can show that the regular part of
  the foliation is given by a torus action.
  
• A 242

• 2025.08.29 (at 15h)
• Speaker:  prof. Paul Schwahn (Unicamp)
• Title: Einstein deformations 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.
  
• 259A

• 2025.08.18 to 2025.08.22
• Title: Workshop: Fun with Finsler  and Foliations (F.F.F. 2025)
• Dra. Patrícia Marçal
• Prof. Marcos Alexandrino
• Prof. Miguel Angel Javaloyes  
• Monica M. F. Drechsler
• Prof. José Barbosa Gomes
• Prof. Francisco Carlos Caramello Junior Junior
• Prof. Benigno Oliveira Alves
• Prof. Hengameh R. Dehkordi
• Profa. Viviana del Barco

• 2025.08.08 (at 15h)
• Speaker: Dr. Jonathan Trejos (Impa)
• Title: Capacidades ECH em domínios tóricos côncavos singulares
  
• Abstract:  No estudo de mergulhos de variedades simpléticas, existem duas abordagens possíveis.
  Uma é a abordagem construtiva, na qual se mostra explicitamente que uma variedade simplética pode ser mergulhada dentro de outra.
  A outra é a abordagem obstrutiva, em que se identificam propriedades entre as variedades que impedem a existência do mergulho.
  Em dimensão quatro, as capacidades ECH constituem um exemplo particularmente interessante na direção obstrutiva.
  Nesta palestra, descreveremos brevemente a relação entre as capacidades ECH e uma classe de variedades simpléticas de dimensão quatro conhecidas como domínios tóricos singulares. Em particular, abordaremos as capacidades ECH de domínios tóricos côncavos e sua relação com certos problemas de ball packing. Ao final, discutiremos brevemente a demonstração de algumas dessas relações.
  
• A249

• 2025. July  21th ,22th  , 23th  (15-17)
• Speaker: Prof. Luciano Mari (Universita degli Studi di Milano)
• Title: Short course: Splitting theorems in Riemannian Geometry old new old
  
• Abstract:  The minicourse aims to introduce some rigidity results in Riemannian geometry known as splitting theorems. The general philosophy is that by coupling a curvature control on a manifold $M$ with suitable topological (or geometric, or variational) properties one is able to characterize $M$ as a member of certain families of symmetric examples (warped products). Starting from the classical Cheeger-Gromoll's splitting theorem for manifolds with nonnegative Ricci curvature, the course will focus on analogous results in the case where the Ricci curvature may be negative but controlled in a suitable (spectral) sense. Such spectral Ricci bounds are strongly motivated by the theory of stable minimal and CMC hypersurfaces, which gained new impetus in the past years. The problem serves as a thread to describe some techniques in Riemannian Geometry with vast applicability, including the theory of harmonic functions developed by P. Li, L.F. Tam and J. Wang and recent new insights on a ``conformal geodesic" method, obtained in collaboration with P. Mastrolia, G. Catino and A. Roncoroni. We will discuss applications to the topology of minimal hypersurfaces in non-negatively curved spaces, and a characterization of the higher-dimensional catenoid in $\R^4$.
  
• B139

• 2025.07.18  
• Speaker: prof. Sebastián Herrera-Carmona (UFPR)
• Title:  Vector Fields on Lie groupoids and its Lie Rinehart structure
  
• Abstract:   The aim of this talk is to explore the Lie-Rinehart algebra structure associated with the 2-algebra of multiplicative vector fields on a Lie groupoid. To this end, we will start by presenting examples of Lie-Rinehart structures on manifolds and Lie algebroids. Next, we will discuss the notions of Lie groupoids and multiplicative vector fields on them, accompanied by illustrative examples. Finally, we will examine the Lie-Rinehart structure underlying the 2-algebra of multiplicative vector fields. This is joint work with Cristian Ortiz and James Waldron.
• A241
  

• 2025.05.23  (at  15h)
• Speaker: Prof. Aldo Pratelli (Prof. Titular da Universidade de Pisa, Itália)
• Title: Connectedness properties of small minimal clusters in manifolds.
• Abstract: In this talk we will show that in a compact Riemannian manifold, the $m$-minimal clusters of
  sufficiently small total volume are connected and with small diameter. We discuss also the situation in non-Riemannian manifolds.
  
• A259.

• 2025.05.16 (at  15h)
• Speaker: Daniel Álvarez (IMPA)
• Title: Generalized geometry and shifted symplectic structures
• Abstract: We revisit the role of Courant algebroids in generalized Kähler and Poisson geometry, and show how the framework of shifted symplectic geometry offers a unifying perspective that both illuminates classical results and inspires new directions. In particular, we explain how this global viewpoint leads to a solution of the long-standing problem of establishing the existence of a generalized Kähler potential. We also highlight recent developments in the integration of action Courant algebroids, revealing promising avenues for future applications. This is based on work in progress with Marco Gualtieri.
• A242

• 25-04-29 (16h - 16h30)
• Dr. Luca Accornero (IME-USP)
• Pseudogroups and geometric structures (Encontro de Pós-Doutorandos do IME-USP)

• 25-04-29 (16h30 - 17h)
• Dra Clarice Netto
• Geometria de Dirac e estruturas relacionadas (Encontro de Pós-Doutorandos do IME-USP)

• 25-04-29 (17h - 17h30)
• Patrícia Marçal
• Submanifolds and Submersions in Finsler Geometry (Encontro de Pós-Doutorandos do IME-USP)

• 21.02.25 (at15h)
• Speaker: dr Camilo Ângulo (pos-doc Universidade de Jilin / Universidade de Göttingen)
• title: Examples of Poisson manifolds with compactness properties
• Abstract: Poisson geometry lies in the intersection of symplectic geometry, foliation theory and Lie theory. As in each of these areas compactness hypotheses yield a wealth of results, it would be desirable to have a notion of compactness in Poisson geometry that simultaneously subsumes the theory of compact semisimple compact Lie groups and compact symplectic manifolds. This goal has been recently achieved by Crainic, Fernandes and Martinez-Torres, who defined a Poisson manifold of compact type (PMCTs) to be a Poisson manifold whose integrating symplectic groupoid is proper. The wonderful properties of these PMCTs lie in contrast to their relative scarcity. The geometric and topological constraints that go into building a PMCT make their definition rather demanding, and in so, constructing a PMCT beyond the trivial case of a compact symplectic manifold with finite fundamental group has proven a challenging problem. In this talk, after properly explaining the elements that go into play, we explain how by allowing for other geometric structures to “integrate” Poisson manifolds, one can get more examples while preserving most of the compactness properties.
• venue B143

• 2025.02-15 (at  15h)
• Prof. Luca Vitagliano (University of Salerno)
• Title: Homogeneous Boundaries of Geometric Structures
• Abstract: Under appropriate homogeneity conditions, a hypersurface in a symplectic manifold inherits a contact or a cosymplectic structure from the ambient space. There are similar statements for Poisson manifolds as well as for complex manifolds. Using ideas coming from the homogenization trick in Contact Geometry, we present a very general theorem putting all these statements under the same umbrella. This also allows generalizations, e.g., to Dirac Geometry, Generalized Complex Geometry and G-structures.
• venue: A242

• 2024.09.27  (at 15h)
• Title:   Reduction of 0-shifted contact structures
  
• Speaker:Antonio Maglio - Universitá degli Studi di Salerno
• Abstract:  Contact structures are the odd-dimensional analogue of symplectic structures. According to a principle formulated by Arnold, any result and construction in Symplectic Geometry has a counterpart in Contact Geometry and vice versa. One example is the contact version of the Marsden-Weinstein reduction, proved twenty years ago by Loose. Differentiable stacks, which generalize manifolds, serve as models for singular spaces like orbifolds and orbit spaces. Due to their categorical structure, geometric objects defined on differentiable stacks come together with a shift. For instance, shifted symplectic structures generalize the classical symplectic structures in this context. Recently, together with Tortorella and Vitagliano, we introduced the contact analogue, shifted contact structures. A few years ago Hoffman and Sjamaar generalized the Marsden-Weinstein reduction to differentiable stacks equipped with 0-shifted symplectic structures. In this presentation, we will first review the Marsden-Weinstein reduction for 0-shifted symplectic structures and the notion of shifted contact structures, before discussing the Marsden-Weinstein reduction for 0-shifted contact structures. This is joint work with F. Valencia.
  
• venue:  B3 (IME-USP) 

• 2024.06.21  (at 15h)
• Title:   A condição de Ricci para métrica warped
  
• Speaker: Dr. Roney Santos (IME-USP)
• Abstract:  Gostaríamos de introduzir e discutir brevemente o conceito recente de superfície de Ricci. Essas superfícies abstratas têm a propriedade de admitir imersão isométrica local no espaço Euclidiano tridimensional R^3 como superfície mínima quando sua curvatura Gaussiana é não-positiva, o que faz das superfícies de Ricci uma "maneira intrínseca" de olhar para superfícies mínimas do R^3. Discutiremos sobre a classificação de superfícies de Ricci que admitem métricas warped e sobre a relação entre superfícies de Ricci regradas e curvas de torção constante no R^3. Por fim, se ainda tivermos tempo, gostaríamos de explorar rapidamente uma definição de Lucas Ambrozio que estende o conceito de superfícies mínimas com bordo livre na bola Euclidiana unitária tridimensional para o contexto intrínseco das superfícies de Ricci.
  
• venue: B 139  (IME-USP) 

• 
  
• Title:  Singular Riemannian Foliations, variational problems and Principles of Symmetric Criticalities,
  
• Speaker:  Prof. Marcos Alexandrino (IME-USP) 
• Abstract:  A singular foliation F on a complete Riemannian manifold M is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of M into orbits of an isometric action. In this talk, we discuss variational problems in compact Riemannian manifolds equipped with SRF with special properties, e.g. isoparametric foliations, SRF on fibers bundles with Sasaki metric, and orbit-like foliations. More precisely, we prove two results analogous to Palais' Principle of Symmetric Criticality, one is a general principle for basic symmetric operators on the Hilbert space W1,2(M), the other one is for basic symmetric integral operators on the Banach spaces W1,p(M). These results together with a basic version of Rellich Kondrachov Hebey Vaugon Embedding Theorem allow us to circumvent difficulties with Sobolev's critical exponents when considering applications of Calculus of Variations to find solutions to PDEs. We  exemplify this brielfy discussing the  existence of weak solutions to a class of variational problems which includes p-Kirschoff problems. This talk is based on a joint work with: Leonardo F. Cavenaghi, Diego Corro, Marcelo K. Inagaki.
  
• venue:   (IME-USP) 

• 2024.06.07 (at 15 h)
• Title:  Closures of Riemannian groupoids
  
• Speaker: Prof. Mateus Moreira de Melo  (ufes)
• Abstract:  From the Myers-Steenrod theorem, actions of closed subgroups of the isometry group are proper. Based on the previous example and the results of Molino, Salem, and Alexandrino-Radeschi, we address the problem of obtaining a proper groupoid from a Riemannian groupoid. As part of the ingredients of our proof, we will discuss the conditions for a foliation in a bundle to be a Riemannian foliation.
  
• venue:  B09  (IME-USP) 

• 2024.05.17 (at 15 h)
• Title:  Geometry over algebras
  
• Speaker: Dr Hugo Cattarucci Botós (IME-USP)
• Abstract:  We discuss how geometric structures arise from Hermitian forms on linear spaces over real algebras.
  Traditionally, the real algebras used are R, C, and H, representing real, complex, and quaternionic numbers. Structures like real/complex/quaternionic hyperbolic spaces are obtained naturally from this approach. Fubini-Study geometry and Riemannian structures for Grassmanians as well. One nice feature of the linear algebraic approach is that we can express geometric objects in a linear algebraic fashion, which is advantageous, for instance, for computational reasons. We extend the discussion to the dual numbers D=R+ϵ R, with ϵ² = 0, the split-complex numbers SC = R+j R, with j² = 1, and the split-quaternions SH=R+iR+jR+kR, with  i² = -1, j² = 1, k² = 1, ij = k = -ji. We present the projective geometry for these algebras and their pseudo-Riemannian geometries. We express their geodesics and curvatures as linear algebraic objects. We also describe the transition of geometries between projective lines over C, D, and SC. Additionally, we naturally interpret these projective lines as the configuration spaces for the oriented geodesics on the 2-sphere, the Euclidean plane, and the hyperbolic plane.  For the real algebra CxC, we also obtain a natural projective model for the hyperbolic bidisc, the product of two Poincaré discs.
  
• venue:  139 B  (IME-USP) 

• 2024.05.24  (at 15h)
• Title:  Algebricidade de folheações Riemannianas singulares
  
• Speaker: Prof. Ricardo Mendes (Oklahoma State Univ)
• Abstract: As folheações Riemannianas singulares são certas partições de variedades Riemannianas, e as fontes tradicionais de exemplos são ações isométricas e hipersuperfícies isoparamétricas. Se a variedade ambiente é uma esfera, esses exemplos são, no sentido apropriado, algébricos, o que segue de resultados clássicos de Hilbert, Cartan, e Münzner. Em 2018, A. Lytchak e M. Radeschi mostraram algebricidade para uma foliação Riemanniana singular geral em uma esfera. Em trabalho em andamento, em colaboração com S. Lin e M. Radeschi,  generalizamos o teorema de Lytchak--Radeschi das esferas para qualquer espaço homogêneo normal compacto, uma classe que inclui todos os espaços simétricos compactos.
  
  
  
• venue: 139 B   (IME-USP) 

• 2024.02.28 (Wed.)/  2024.03.01 (Fri.) /  2024.03.04 (Mon.)/ at  14h          
• Title:  Lectures: Metric aspects of buildings, by Linus Kramer
  
• Speaker:  prof. Linus Kramer (WWU Münster)
• Abstract:  Buildings are combinatorial metric structures. They come for example from simple algebraic groups. A fundamental result by Jacques Tits says that conversely, all spherical and euclidean buildings of higher dimension arise in this way. In my lectures I will give a manifold-style introduction
  to buildings, and highlight some of their properties.
  
• venue: Auditório Antonio Gilioli,  bloco A do IME.
  

• 2024.02.28 (Wed.) / 2024.02.29 (Thurs.). / 2024.03.01 (Fri..) / at 15.30h
• Title: Lectures:   Introduction to Kähler Geometry, 
  
• Speaker:  profa  Bianca Santoro  (WWU Münster)
• Abstract: 
  
• venue:  Auditório Antonio Gilioli,  bloco A do IME

• 2024.03.04   (Mon.)  / 2024.03.05 (Tues..) / 2024.03.06 (Wed..)  / at 15:30h.
• Title:  Lectures: A gluing construction for Kähler-Einstein metrics
  
• Speaker:  Prof.  Hans-Joachim Hein (WWU Münster)
• Abstract: 
  
• venue:   Auditório Antonio Gilioli,  bloco A do IME.

• 2023.03.08-15 h
• Title:  Special holomorphic gradients on K\"ahler manifolds
  
• Speaker: Prof. Andrzej Derdzinski (The Ohio State University)
• Abstract:  Two main results are presented. They deal with functions $\tau$ on K\"ahler manifolds $M$ of complex dimensions $m > 1$ satisfying
  a special Ricci-Hessian equation in the sense of Maschler (2008): $\alpha \nabla d\tau$ + Ric equals a function times $g$, for some
  function $\alpha$ of the real variable $\tau$, with $\alpha \nabla d\tau$ assumed nonzero almost everywhere. Examples are provided by the
  non-Einstein cases of CEKM, GKRS and SKRP (conformally-Einstein K\"ahler metrics, gradient K\"ahler-Ricci solitons, and special K\"ahler-Ricci
  potentials). If $\tau$ also happens to be transnormal (that is, the integral curves of its holomorphic gradient $v = \nabla \tau$ are reparametrized
  geodesics), the triple $(M,g,\tau)$ must represent one of the well-understood types GKRS and SKRP. We show that, in the non-transnormal case, one must have $m = 2$ and, up to normalizations, $\alpha/2$ equals $1$, or $1/\tau$, or $\cot \tau$, or $\coth \tau$ or, finally, $\tanh \tau$. Furthermore, we prove, using the Cartan-K\"ahler theorem, that each of these five options is actually realized by a non-transnormal function $\tau$ on a K\"ahler surface $M$. For $1$ and $1/\tau$ this last fact is already known due to two classic existence theorems, with $M$ equal to the two-point blow-up of $CP^2$, where $g$ is the Wang-Zhu toric K\"ahler-Ricci soliton or, respectively, the Chen-LeBrun-Weber
  conformally-Einstein K\"ahler metric. (Joint work with Paolo Piccione.)
  
• venue:   (IME-USP) 

• 2023.08.11 (15.15 h)     
• Title:  Revisiting Arnold's Topological Proof of the Morse Index Theorem
  
• Speaker: Eduardo Ventilari Sodre   (USP)
• Abstract:  We give an exposition of the Morse Index Theorem in the Riemannian case in terms of the Maslov Index, following and expanding upon Arnold's seminal paper. We emphasize the symplectic arguments in the proof and aim to be as self-contained as possible.
  
• venue:  B07    (IME-USP) 

• 2023.08.07 (15 h)     
• Title:  The bundle structure of compact rank-one ECS manifolds
  
• Speaker: Ivo Terek   (OSU-EUA)
• Abstract:  The local types of essentially conformally symmetric manifolds (i.e., pseudo-Riemannian manifolds with parallel Weyl tensor which are not locally symmetric or conformally flat) have been fully described by Derdzinski and Roter in 2009. They are distinguished by the rank, always equal to 1 or 2, of a certain null parallel D distribution associated with the Weyl tensor. Compact rank-one ECS manifolds exist in all dimensions starting from 5, and topological features common to all known examples are not accidental: we prove that a compact rank-one ECS manifold, if not locally homogeneous and replaced if needed by a two-fold isometric covering, must be the total space of a fiber bundle over the circle, with D^\perp appearing as its vertical distribution. This is joint work with Andrzej Derdzinski.

• 2023.06.02 (15 h)     
• Title:  On the Multiplicity of the Brake Orbtis
  
• Speaker: prof. Dario Corona,  (University of Camerino -Italy)
• Abstract:  This seminar will show some recent developments in the study of the brake orbits of Hamiltonian systems. Roughly speaking, a brake orbit is a periodic solution that oscillates back and forth between two rest points, as a pendulum-like motion. In 1948, H. Seifert conjectured, under some hypotheses on the Hamiltonian function, that the number of geometrically distinct brake orbits is always greater than or equal to the degrees of freedom of the system. We show that if the Hamiltonian function is even and strictly convex with respect to the generalized momenta then the brake orbits are in one-to-one correspondence with orthogonal geodesic chords in a strongly concave Finsler manifold with boundary.Thus, the multiplicity of the brake-orbits can be obtained by appropriate refinements of mini-max methods and the Ljusternik and Schnirelmann category. The seminar is completed with a historical perspective and further developments of the subject.
  
• venue:  A243  (IME-USP) 

• 2023.05.26 (15 h)     
• Title:  Integration of generalized Kähler structures
  
• Speaker: Dr. Daniel Alvarez (University of Toronto)
• Abstract:  A generalized Kähler (GK) structure is a pair of commuting generalized complex structures  whose composite is a generalized metric, this is Gualtieri's reformulation of the concept of bihermitian  structure introduced in mathematical physics by Gates, Hull and Rocek.  We answer the question of what is the global meaning of GK potential by using the theory of symplectic double groupoids. We will review the ideas that led us to this general result by examining the situation of a Kähler metric from the viewpoint of Poisson geometry and double structures. This is based on work in progress with M. Gualtieri and Y. Jiang.
    
  
• venue: B143  (IME-USP) 

• 2023.05.19 (14 h)     
• Title:  Cofluxo do Laplaciano de G2 -estruturas cofechadas e seus solitons
  
• Speaker: Dr Andres Moreno - Unicamp
• Abstract: link
  
• venue: B16  (IME-USP) 

• 2023.05.19 (15:30 h)     
• Title:  Funções isoparamétricas e curvatura média em variedades com navegação de Zermelo
  
• Speaker: Profa Patrícia Marçal  (IME-USP)
• Abstract: O estudo de funções isoparamétricas surgiu a partir de uma pergunta simples em óptica geométrica: quais ondas tem velocidade constante em cada frente de onda? Por sua vez, o problema da navegação de Zermelo busca os caminhos que minimizem tempo em um ambiente, modelado por uma variedade Finsler (M,F), sob a influência de vento ou correnteza, expresso por um campo vetorial W. Nosso principal objetivo é investigar a relação entre as funções isoparamétricas na variedade M com e sem a presença do vento W. Para os casos positivos-definidos, também comparamos as curvaturas médias na variedade. Neste trabalho conjunto como Dr. Benigno Oliveira Alves (UFBA), buscamos seguir uma abordagem livre de coordenadas.
  
• venue: B16  (IME-USP) 

• 2023.04.19 (16 h)     
• Title:  Conical metrics with special holonomy.
  
• Speaker: Prof. Misha Verbitsky ( IMPA)
• Abstract: Metrics with special holonomy are well understood, thanks to Ambrose-Singer, de Rham and Berger theorems.I would present the classification of special holonomies on Riemannian cones and their correspondence to Weyl connections with special holonomy, appearing in conformal geometry. The main technical result presents a conical Riemannian metric in tensorial terms, and was used to define invariant locally conformal structures on Lie groups.
  
• venue: B101 (IME-USP) 

• 2023.01.06 (11-12)     
• Title: The topology of compact Weyl-parallel manifolds
  
• Speaker: Andrzej Derdzinski ( Ohio State University)
• Abstract: ECS manifolds are pseudo-Riemannian manifolds of dimensions n ≥ 4 which have parallel Weyl tensor, but not for one of two obvious reasons: conformal flatness  or local symmetry. They exist for every n ≥ 4, their metrics are always indefinite,  and their local structure has been completely described. Every ECS manifold has an invariant called rank, equal to 1 or 2. Known examples of compact ECS manifolds, representing every dimension n > 4, are of rank 1, and  none of them is locally homogeneous.  We prove that a compact rank-one ECS manifold, if not locally homogeneous, replaced if necessary by a two-fold isometric covering, must be the total space  of a bundle over the circle.(joint work with Ivo Terek)
  
  
• venue: ?? (IME-USP) 

• 2022.11.11     
• Title: An application of Finsler geometry in wildfire propagation modeling
  
• Speaker: Hengameh Raeisidehkordi (UFABC)
• Abstract: We will talk about some basic concepts in Finsler geometry and wave propagations. We provide some discussion about our methods in wildfire propagation modeling and, finally, see some examples showing the application of our methods.
  
• venue: B03 (IME-USP) 

• 2022.10.21
• Title: Completeness of metrics and linearization of groupoids
  
• Speaker:Prof.  Matias Luis del Hoyo (UFF)
• Abstract: Every smooth fiber bundle admits a  complete Ehresmann connection.  I will talk about the story of this theorem and its
  relation with Riemannian submersions.  Then, after discussing some foundations of Riemannian geometry
  of Lie groupoids and stacks, I will present a generalization of the theorem into this framework,  which somehow answers an open problem on the linearization of groupoids. Talk based on collaborations with M. de Melo (USP).
  
• venue: B06 (IME-USP) 

• 2022.10.07
• Title: A pesquisa vigente na área de curvaturas positivas e temas correlatos
  
• Speaker: Dr. Leonardo Francisco Cavenaghi (Imecc Unicamp)
• Abstract: Um fato bem conhecido em geometria consiste em seu próprio uso na compreensão de variedades como espaços topológicos. Por exemplo, teoremas como o Teorema da Esfera Diferenciável e o Programa de Geometrização de Thurston, classificam a topologia de algumas variedades Riemannianas de acordo com suas geometrias. Por outro lado, o problema inverso permanece sem solução para quase todas as variedades, sendo poucas as propriedades geométricas conhecidas que uma determinada variedade pode assumir.  Embora existam resultados como o Teorema de Preissman no cenário de variedades Riemannianas com curvatura seccional negativa, e o teorema de Bonnet-Meyers para variedades com curvatura de Ricci positiva limitada por baixo, não há teorema que distingue a classe de variedades simplesmente conectadas fechadas com curvatura seccional não negativa à de variedades simplesmente conectadas fechadas admitindo métricas com curvatura seccional positiva. De acordo com este fato, seria natural esperar que toda variedade da primeira classe mencionada admitisse uma métrica de curvatura seccional positiva. No entanto, a literatura apresenta uma enorme discrepância entre os exemplos dessas classes. Além disso, existem variedades suaves $\Sigma^n$ que são homeomórficas à esfera padrão $S^n$, mas não difeomorfas a ela. Existem também inúmeras estruturas suaves (em pares não difeomorfas) em $\mathbb{R}^4$, assim como existem toros exóticos, espaços projetivos exóticos e assim por diante. Isso naturalmente levanta a questão até que ponto a estrutura suave determina/obstrui a geometria? Mais especificamente, tais esferas exóticas admitem geometrias/dinâmicas semelhantes às geometrias padrão em $S^n$?
  
  Nessa palestra, iremos motivar a discussão acima por meio de trabalhos já desenvolvidos na área, discutindo também as técnicas comumente empregadas, bem como problemas atuais de relevância.
  
  
  
• venue: B03 (IME-USP) 

• 2022.09.16
• Title: Traçando Caminhos na Teoria de Transporte Ótimo
  
• Speaker:  Dr. André Gomes (Imecc Unicamp)
• Abstract: Apresentação do estado da arte da teoria de  ações lagrangianas na teoria de transporte ótimo  de Monge e Kantorovich, ressaltando o ponto de vista geométrico e seus vínculos com a análise.
  
• venue: B03 (IME-USP) 

• 2022.08.05
• Title: A geometric take on Kostant's Convexity Theorem
  
• Speaker:  Prof. Ricardo Mendes
• Abstract: We characterize convex subsets of R^n invariant under the linear action of a compact group G, by identifying their images in the
  orbit space R^n/G by a purely metric property. As a consequence, we obtain a version of Kostant's celebrated Convexity Theorem (1973)
  whenever the orbit space R^n/G is isometric to another orbit space R^m/H. (In the classical case G acts by the adjoint representation on
  its Lie algebra R^n, and H is the Weyl group acting on a Cartan sub-algebra R^m). Being purely metric, our results also hold when the
  group actions are replaced with submetries. 
  
• venue: B139  (IME-USP) 

• 2022.08.12
• Title:  Projective representations of real reductive Lie groups and the gradient map'
  
• Speaker:  Prof. Leonardo Billiotti
• Abstract: Let G=Kexp(p) be a connected semisimple noncompact real reductive Lie group acting linearly on a finite dimensional vector space V over R.  We assume that there exists a K-invariant scalar product g such that K\subset SO(V,g) and p \subset Sym_o (V,g), where Sym_o (V,g) is the set of symmetric endomorphisms with trace zero.  We also assume that the G-action on V and the G^C-action on V^C are irreducible. Using G-gradient map techniques we analyze the natural projective representation of G on P(V). ( arXiv:2205.15632)
  
• venue: B139  (IME-USP)