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Workshop Inaugural do Centro Brasileiro de Geometria (CBG)

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Workshop Inaugural do Centro Brasileiro de Geometria (CBG)

17–20 de março de 2026

Local: Auditório do IMECC–UNICAMP, Campinas, SP, Brasil

O Workshop Inaugural do Centro Brasileiro de Geometria (CBG) marca a inauguração do CBG como um Centro de Pesquisa, Inovação e Difusão (CEPID) apoiado pela FAPESP. O encontro foi concebido como um momento de integração entre os participantes do Centro e convidados, incluindo membros de seu Conselho Consultivo Internacional, com o objetivo de promover a troca de ideias dentro de cada vertical e também entre as verticais.

O CBG reúne pesquisadores em quatro áreas temáticas:

A programação combina palestras plenárias, seminários por verticais, discussões e uma sessão de pôsteres integrada aos coffee breaks, além de atividades sociais.

FORMATO (DURAÇÕES)

  • Palestras plenárias (PP): 40 minutos + 10 minutos de perguntas
  • Seminários em sessões temáticas: 25 minutos + 5 minutos de perguntas
  • Discussões por vertical: 45 minutos

PÔSTERES

Teremos sessões de pôsteres.

Os interessados em participar devem enviar título e resumo de sua proposta de pôster através do formulário de inscrição até o dia 1° de Março.

DISCUSSÕES

As Sessões de Discussão têm como propósito reunir pesquisadores das Verticals em torno de temas de interesse comum e fomentar o diálogo, de modo a fortalecer a integração do CBG, tendo como primeiro objetivo o planejamento para 2026–2027.

Prazo para inscrições: 10 de Março.

Acesse o formulário para inscrição 

SPEAKERS — SESSÕES TEMÁTICAS / SEMINÁRIOS

  • Carlile Lavor (UNICAMP) — “Different Models for 3D Space in Molecular Geometry”
  • Carolina Araujo (IMPA) — “Birational Geometry and Moduli Spaces”
  • Dahisy Lima (UFABC) — “Cancellation of Invariant Sets via Spectral Sequences”
  • Ethan Cotterill (UNICAMP) — “Quadratically-enriched algebraic enumerative geometry”
  • Fernando Manfio (ICMC – USP) — “Complete cohomogeneity one hypersurfaces in space forms”
  • Herivelto Martins Borges Filho (ICMC – USP) — “Curvas de Artin-Schreier e o número de elementos com norma e traço prescritos”
  • Ivan Struchiner (IME – USP) — “Chern-Weil Classes of Cartan Connections”
  • Juliana Marta (Gestora Executiva do CBG) — “CBG: Como Funciona”
  • Leonardo Barichello (UNICAMP) — “Inovação curricular para a matemática do Ensino Médio no Brasil”
  • Marcelo Firer (UNICAMP) — “O CBG e o ensino de matemática na Educação Básica”
  • Maurício Richartz (UFABC) — “Spacetime Geometry and Gravitational Phenomena at the CBG”
  • Paolo Piccione (IME-USP) — “Conformal Curvatures”
  • Patrícia Schultz (EAIP-IMECC) — “CBG: Como Funciona”
  • Rúbia Barcelos Amaral (UNESP, Rio Claro) — “Ações de difusão do CBG”
  • Sueli Irene Rodrigues Costa (UNICAMP) — “Geometry and Information”

Confira a programação completa aqui

CONTATO

E-mail: workshop.cbg@ime.unicamp.br

Informações do Evento

Data

17 a 20 de março de 2026

Local

Auditório do IMECC - UNICAMP

Contato

workshop.cbg@ime.unicamp.br

Faça sua inscrição

Programação do evento

Programação preliminar, sujeita a ajustes

WP Table Builder
TERÇA (17/03)
  • 14:00–15:00 Cerimônia de abertura
  • 15:00–15:30 Coffee break
  • 15:30–16:00 Seminário – Ethan Cotterill
  • 16:00–16:30 Seminário – Ivan Struchiner
  • 16:30–17:00 Seminário – Herivelto Martins Borges Filho
  • 17:15–18:00 Discussão (GA + GD) - sala 253
QUINTA (19/03)
  • 09:00–10:00 Palestra Plenária – Ugo Bruzzo
  • 10:00–10:30 Coffee break + Sessão de pôsteres
  • 10:30–11:00 Seminário – Rúbia Amaral
  • 11:00–11:30 Seminários – Marcelo Firer
  • 11:30–12:00 Seminários – Leonardo Barichello
  • 12:00–14:00 Almoço
  • 14:00–15:00 Palestra Plenária – Zsolt Lavicza
  • 15:00–15:30 Coffee break + Sessão de posteres
  • 15:30–16:00 Seminário – Carlile Lavor
  • 16:00–16:30 Seminário – Carolina Araujo
  • 16:30–17:00 Seminário – Sueli Irene Rodrigues Costa
  • 17:15–18:00 Discussão (AG + GA) - sala 253
  • 18:30–22:00 Coquetel CPV
QUARTA (18/03)
  • 09:00–10:00 Palestra Plenária – Bobby Acharya
  • 10:00–10:30 Coffee break + Sessão de pôsteres
  • 10:30–11:30 Palestra Plenária – Jorge Lauret
  • 11:30–12:00 Seminário – Patrícia Schultz e Juliana Marta
  • 12:00–14:00 Almoço
  • 14:00–15:00 Palestra Plenária – Oscar García-Prada
  • 15:00–15:30 Coffee break + Sessão de posteres
  • 15:30–16:00 Seminário – Dahisy Lima
  • 16:00–16:30 Seminário – Maurício Richartz
  • 16:30–17:00 Seminário – Fernando Manfio
  • 17:15–18:00 Discussão (GD + AG) - sala 253
SEXTA (20/03)
  • 09:00–10:00 Palestra Plenária – Alicia Dickenstein (Online)
  • 10:00–10:30 Coffee break
  • 10:30–11:30 Discussão (ED&I) - sala 253
  • 11:30–14:00 Almoço
  • 14:00–15:00 Palestra de Encerramento: Paolo Piccione (Online)
  • 15:00–15:30 Encerramento
  • 17:00–20:00 Happy hour

Palestras Plenárias

Bobby Acharya (King’s College London)

Classifying Special Holonomy Kummer Constructions

Ricci flat manifolds with special holonomy (Calabi-Yau, hyperKähler, G2- and Spin7-manifolds) play an important role in superstring/M-theory and many areas of mathematics. Whilst Yau’s proof of the Calabi conjecture enables one to construct compact examples readily as Kahler manifolds with vanishing first Chern class, compact hyperKähler, G2 and Spin7 holonomy manifolds are much more challenging to construct. The first examples of compact G2 and Spin7 manifolds were provided by Joyce in the 90’s who used a generalised Kummer construction to produce manifolds whose G2 and Spin7 structures were sufficiently close to being torsion free that one can perturb to genuine exceptional holonomy. In the G2 case, Joyce constructed of order 30 singular 7-orbifolds $T^7/\Gamma$ which gave rise to a few hundred topologically distinct compact G2-holonomy manifolds. We will report on recent work with Daniel Baldwin in which we classify ALL affine equivalence classes of G2 Kummer 7-orbifolds $T^7/\Gamma$. For 7-tori whose fundamental groups are indecomposable lattices we show that there are over 6000 inequivalent 7-orbifolds with torsion free G2-structures. Many of these can be desingularised using Joyce’s techniques. We also classify all compact flat manifolds admitting a torsion free G2-structure, this produces hundreds of new examples. Many examples of 7-orbifolds are given with codimension 7 singularities whose physical interpretations will likely to prove very interesting from a physical and mathematical point of view.

(PP1)

Jorge Lauret (Universidad Nacional de Córdoba)

On compact homogeneous complex manifolds

A compact complex manifold M is said to be homogeneous if there exists a compact Lie group G of biholomorphisms acting transitively on M.  This provides a presentation M=G/K as a homogeneous space that admits a G-invariant complex structure.  Such spaces were characterized by Wang and Tits in the fifties as follows: K is contained in the centralizer H of a torus and its semisimple part coincides with that of H.  They are called C-spaces.  Geometrically, any C-space is a holomorphic torus fibration over the flag manifold F=G/H, with fiber the torus A=H/K.  The G-invariant complex structures are all given by one of the finitely many G-invariant complex structures on F and any left-invariant complex structure on the torus A. In this talk, we will report on recent results obtained on the de Rham and complex cohomologies of complex C-spaces, as well as on the existence of distinguished Hermitian metrics like balanced, SKT, CYT, LCK and BTP.

(PP2)

Oscar García-Prada (ICMAT, Madrid)

Higher Teichmüller spaces and Higgs bundles

It is well-known that the Teichmüller space of a compact surface can be identified with a connected component of the character variety of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmüller spaces are generalizations of this, which exist in the character varieties for representations of the fundamental group of the surface into certain real simple non-compact Lie groups of higher rank. As for the usual Teichmüller space, these spaces consist entirely of discrete and faithful representations. In this talk, I will give a classification of all possible higher Teichmüller spaces, and a parametrization of them from a Higgs bundle perspective (based on joint work with Bradlow, Collier, Gothen and Oliveira).

(PP3)

Ricci flat manifolds with special holonomy (Calabi-Yau, hyperKähler, G2- and Spin7-manifolds) play an important role in superstring/M-theory and many areas of mathematics. Whilst Yau’s proof of the Calabi conjecture enables one to construct compact examples readily as Kahler manifolds with vanishing first Chern class, compact hyperKähler, G2 and Spin7 holonomy manifolds are much more challenging to construct. The first examples of compact G2 and Spin7 manifolds were provided by Joyce in the 90’s who used a generalised Kummer construction to produce manifolds whose G2 and Spin7 structures were sufficiently close to being torsion free that one can perturb to genuine exceptional holonomy. In the G2 case, Joyce constructed of order 30 singular 7-orbifolds $T^7/\Gamma$ which gave rise to a few hundred topologically distinct compact G2-holonomy manifolds. We will report on recent work with Daniel Baldwin in which we classify ALL affine equivalence classes of G2 Kummer 7-orbifolds $T^7/\Gamma$. For 7-tori whose fundamental groups are indecomposable lattices we show that there are over 6000 inequivalent 7-orbifolds with torsion free G2-structures. Many of these can be desingularised using Joyce’s techniques. We also classify all compact flat manifolds admitting a torsion free G2-structure, this produces hundreds of new examples. Many examples of 7-orbifolds are given with codimension 7 singularities whose physical interpretations will likely to prove very interesting from a physical and mathematical point of view.

(PP1)

A compact complex manifold M is said to be homogeneous if there exists a compact Lie group G of biholomorphisms acting transitively on M. This provides a presentation M=G/K as a homogeneous space that admits a G-invariant complex structure. Such spaces were characterized by Wang and Tits in the fifties as follows: K is contained in the centralizer H of a torus and its semisimple part coincides with that of H. They are called C-spaces. Geometrically, any C-space is a holomorphic torus fibration over the flag manifold F=G/H, with fiber the torus A=H/K. The G-invariant complex structures are all given by one of the finitely many G-invariant complex structures on F and any left-invariant complex structure on the torus A. In this talk, we will report on recent results obtained on the de Rham and complex cohomologies of complex C-spaces, as well as on the existence of distinguished Hermitian metrics like balanced, SKT, CYT, LCK and BTP.

(PP2)

It is well-known that the Teichmüller space of a compact surface can be identified with a connected component of the character variety of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmüller spaces are generalizations of this, which exist in the character varieties for representations of the fundamental group of the surface into certain real simple non-compact Lie groups of higher rank. As for the usual Teichmüller space, these spaces consist entirely of discrete and faithful representations. In this talk, I will give a classification of all possible higher Teichmüller spaces, and a parametrization of them from a Higgs bundle perspective (based on joint work with Bradlow, Collier, Gothen and Oliveira).

(PP3)

Ugo Bruzzo (SISSA)

An introduction to algebraic supergeometry

I will give an introduction to algebraic supergeometry, starting with some physical motivations coming for supersymmetry and superstring theory. After briefly discussing the foundations of the theory, I will treat some relevant examples, such as supersymmetric curves and stable supermaps, and their moduli spaces.

(PP4)

Zsolt Lavicza (Johannes Kepler University Linz)

Innovating in STEAM and Exploring the Future of Learning with Technology and Creativity

This presentation outlines the evolving landscape of STEAM education at the Linz School of Education, where technology and pedagogy intersect to spark creativity and deepen learning. With a special focus on mathematics education, we explore how innovative teaching strategies and interdisciplinary approaches foster creative thinking. Key collaborations, including those with the Experience Workshop Movement and GeoGebra, will showcase emerging technologies such as Augmented Reality, 3D Printing, Machine Learning, and Mobile experiments. We will also examine the transformative potential of 3D technologies in enhancing mathematical understanding and bridging the gap between digital and physical learning. Additionally, we will highlight how Big Data and AI can be leveraged to uncover and nurture creative thinking processes. By embracing these advancements, we open new pathways for innovation, collaboration, and the future of STEAM education. Furthermore, I will outline the initiatives and facilities we are developing at Johannes Kepler University.

(PP4)

Alicia Dickenstein (Universidad de Buenos Aires)

Toric Euler-Jacobi vanishing theorem and zeros at infinity

Residues appear naturally in various questions in complex geometry: interpolation, duality, representation problems, and obstructions. The first global vanishing result in the projective plane, known as the Euler-Jacobi theorem, was established by Jacobi in 1835. In fact, he did not explicitly state the hypotheses of his result. In the toric case, the input is a system of n Laurent sparse polynomials with fixed Newton polytopes, and the first version of the Euler-Jacobi toric vanishing theorem for residues in the n-torus is due to Khovanskii in 1978, under restrictive genericity assumptions. In collaboration with Carlos D'Andrea, we provide geometric conditions on the input Newton polytopes to ensure that this global vanishing is equivalent to the existence of zeros at infinity in the associated compact toric variety. We relate these conditions to the dimension at the toric critical degree of the quotient of the Cox ring by the ideal generated by the multi-homogenizations of the input polynomials. We also relate the existence of zeros at infinity to interpolation issues. We will give a gentle introduction to these questions.

(PP6)

I will give an introduction to algebraic supergeometry, starting with some physical motivations coming for supersymmetry and superstring theory. After briefly discussing the foundations of the theory, I will treat some relevant examples, such as supersymmetric curves and stable supermaps, and their moduli spaces.

(PP4)

This presentation outlines the evolving landscape of STEAM education at the Linz School of Education, where technology and pedagogy intersect to spark creativity and deepen learning. With a special focus on mathematics education, we explore how innovative teaching strategies and interdisciplinary approaches foster creative thinking. Key collaborations, including those with the Experience Workshop Movement and GeoGebra, will showcase emerging technologies such as Augmented Reality, 3D Printing, Machine Learning, and Mobile experiments. We will also examine the transformative potential of 3D technologies in enhancing mathematical understanding and bridging the gap between digital and physical learning. Additionally, we will highlight how Big Data and AI can be leveraged to uncover and nurture creative thinking processes. By embracing these advancements, we open new pathways for innovation, collaboration, and the future of STEAM education. Furthermore, I will outline the initiatives and facilities we are developing at Johannes Kepler University.

(PP5)

Residues appear naturally in various questions in complex geometry: interpolation, duality, representation problems, and obstructions. The first global vanishing result in the projective plane, known as the Euler-Jacobi theorem, was established by Jacobi in 1835. In fact, he did not explicitly state the hypotheses of his result. In the toric case, the input is a system of n Laurent sparse polynomials with fixed Newton polytopes, and the first version of the Euler-Jacobi toric vanishing theorem for residues in the n-torus is due to Khovanskii in 1978, under restrictive genericity assumptions. In collaboration with Carlos D'Andrea, we provide geometric conditions on the input Newton polytopes to ensure that this global vanishing is equivalent to the existence of zeros at infinity in the associated compact toric variety. We relate these conditions to the dimension at the toric critical degree of the quotient of the Cox ring by the ideal generated by the multi-homogenizations of the input polynomials. We also relate the existence of zeros at infinity to interpolation issues. We will give a gentle introduction to these questions.

(PP6)

Sessões Temáticas

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Carlile Lavor (UNICAMP)

Different Models for 3D Space in Molecular Geometry

This talk will explore the utilization of two different geometric approaches (homogeneous and conformal models) for computing interatomic distances, and their derivatives, in terms of internal coordinates of molecules. While the traditional Euclidean model has long been employed to represent 3D space in molecular dynamics, the homogeneous coordinate system introduces an extra dimension that allows for a unified algebraic representation of molecular transformations, such as translations and rotations. The conformal model further extends this framework by adding an additional dimension for scale and uniquely enables the orthogonal representation of rotations and translations. We will discuss how these two models may enhance the efficiency of modeling molecular geometry and transformations.

Carolina Araujo (IMPA)

Birational Geometry and Moduli Spaces

Birational geometry and the theory of moduli spaces are two central topics in contemporary algebraic geometry. The interaction between these two theories has proved to be particularly fruitful: different birational models of the same moduli space reflect distinct geometric choices in the classification of the objects being parametrized. In this talk, we will discuss some instances of this interaction, exploring the birational geometry of moduli spaces of vector bundles on curves and surfaces.

Dahisy Lima (UFABC)

Cancellation of Invariant Sets via Spectral Sequences

In this talk, we explore geometric features of flow lines connecting isolated invariant sets in a dynamical system and encode them into a chain complex. An associated spectral sequence provides a systematic tool for detecting changes in the phase space under homotopical deformations. In particular, this framework captures bifurcation phenomena such as the cancellation of invariant sets, the birth and death of connections between them, and the emergence or disappearance of periodic orbits.

Ethan Cotterill (UNICAMP)

Quadratically-enriched algebraic enumerative geometry

In this talk we describe applications of the $A^1$-homotopy theory of Morel and Voevodsky (and more recently Levine, Kass, and Wickelgren) in algebraic geometry. It is often possible to promote a classical solution valued in integers to an enumerative problem over the complex numbers to a “quadratically-enriched” defined over an arbitrary base field F, and valued in the Grothendieck–Witt group of quadratic forms over F. We discuss broadly when this is feasible, along with some illuminating examples.

Fernando Manfio (ICMC – USP)

Complete cohomogeneity one hypersurfaces in space forms

Isometric actions establish a fundamental bridge between the algebraic structure of Lie groups and the intrinsic geometry of Riemannian manifolds. In the study of isometric immersions, these actions provide a powerful framework for classifying submanifolds that inherit the symmetries of their ambient space, such as space forms or symmetric spaces. In this talk, we will consider hypersurfaces $f\colon M^n \to \mathbb{Q}_c^{n+1}$ of a complete Riemannian manifold $M^n$ on which a compact, connected subgroup $G$ of $Iso(M^n)$ acts with maximal dimensional orbits of codimension one. We call $f$ a \emph{hypersurface of $G$-cohomogeneity one}. More precisely, we will review some results about Euclidean hypersurfaces and discuss a more recent work on such hypersurfaces in the hyperbolic space, where we provide a characterization if either $n \ge 3$ and $M^n$ is compact, or $n \ge 5$ and the connected components of the set where the sectional curvature is constant and equal to $-1$ are bounded.

Herivelto Martins Borges Filho (ICMC – USP)

Curvas de Artin-Schreier e o número de elementos com norma e traço prescritos

Estudamos o número $N_n(a,b)$ de elementos em extensões de corpos finitos com norma a e traço b prescritos, um problema clássico formulado por N. Katz e amplamente investigado nas últimas décadas. Estabelecemos uma relação explícita entre essa contagem e o número de pontos racionais em certas curvas de Artin–Schreier, obtendo estimativas que melhoram as previamente estabelecidas. Tais resultados têm aplicações na contagem de pontos em variedades tóricas de Calabi–Yau e na determinação do número de primo em certas progressões aritméticas de Fq[x].

Ivan Struchiner (IME – USP)

Chern-Weil Classes of Cartan Connections

In this talk, I will introduce a model-free approach to Cartan geometries that is useful for treating geometries which do not have a flat model (e.g., contact geometry). Any such Cartan geometry can then be used as a model for constructing Chern-Weil characteristic classes of other Cartan connections, generalizing the classical Chern-Weil theory for Cartan geometries based on a Klein model. The talk will be based on joint work with Luca Acornero and Mateus M. de Melo.

Leonardo Barichello (USP)

Inovação curricular para a matemática do Ensino Médio no Brasil

Nesta fala, abordarei como um dos projetos do eixo de Inovação do CBG visa oferecer respostas concretas para o desejo de renovação e inovação do currículo de matemática do Ensino Médio no Brasil. Além disso, pretendo abordar outros espaços para pedem por inovações semelhantes que podem ser lideradas por outros membros do centro em parceria com os pesquisadores desse eixo.

Marcelo Firer (UNICAMP)

O CBG e o ensino de matemática na Educação Básica

É amplamente conhecido e documentado o abismo existente entre o alto nível da pesquisa em matemática e o baixo nível do ensino dessa disciplina na Educação Básica oferecido à população em geral. O projeto CBG-Inovação visa desenvolver recursos voltados à melhoria do ensino de matemática, tendo como referência a população como um todo. Serão apresentadas a visão estratégica de atuação do CBG-Inovação, as iniciativas previstas e as parcerias que vêm sendo estabelecidas com órgãos públicos e organizações do terceiro setor.

Maurício Richartz (UFABC)

Spacetime Geometry and Gravitational Phenomena at the CBG

General Relativity has been a source of deep and inspiring problems in differential geometry for more than a century. The paradigm introduced by Einstein for gravitational phenomena remains solidly established on experimental bases and, at the same time, is still an open and fruitful field, with several opportunities for advances, particularly in problems involving black holes, strong gravitational fields, and gravitational waves. In this presentation, we discuss selected research lines associated with spacetime geometry and gravitational phenomena pursued within the Brazilian Center for Geometry (CBG). These include investigations of quasinormal modes, analyses of scattering and geodesic dynamics, studies of asymptotic symmetries of spacetime, and applications of Finslerian geometry to spacetime physics. Together, these efforts aim at a geometric classification of horizons, singularities, and gravitational analogs, contributing to a deeper understanding of spacetime structure.

Paolo Piccione (IME-USP)

Conformal Curvatures

In this talk, we will explore several notions of curvature, beginning with classical curves and surfaces in Euclidean space and advancing through the framework of Riemannian geometry. We will then shift our focus to conformal geometry, where the concept of curvature takes on new forms under angle-preserving transformations. The final part of the talk will highlight recent developments in Yamabe-type problems, discussing their geometric and analytical significance in the study of conformal curvatures.

Patrícia Schultz (EAIP-IMECC) e Juliana Marta (Gerente Executiva do CBG)

CBG: Como Funciona

Patrícia Schultz e Juliana Marta apresentarão o desenvolvimento do CBG desde suas fases iniciais até sua estrutura atual. Elas discutirão o caminho que o EAIP construiu para apoiar os pesquisadores do CBG durante a fase inicial do projeto, bem como como os pesquisadores podem agora aproveitar ao máximo o centro dentro dos processos já estabelecidos.

Participe e traga suas perguntas!

Rúbia Barcelos Amaral (UNESP, Rio Claro)

Ações de difusão do CBG

No âmbito da Difusão do Conhecimento, visamos criar espaços impactantes para a disseminação do conhecimento em geometria e matemática em todo o estado de São Paulo. Por meio da criação de Núcleos de Difusão do Conhecimento (NDC), esta iniciativa apoiará a divulgação científica e o engajamento comunitário. Esses núcleos servirão como polos para experiências educacionais imersivas em realidade aumentada e virtual, oferecendo recursos tecnológicos de ponta, como impressoras 3D e cortadoras a laser. Também oferecerão formação para professores, apoio a alunos do ensino médio e da graduação, e materiais para atividades de iniciação científica. Nessa mesa, vamos compartilhar planos do NDC para aprimorar o ensino e a aprendizagem da matemática, fomentar uma sociedade alfabetizada cientificamente e promover a educação continuada em geometria, desde a educação básica até os níveis avançados de pesquisa.

Sueli Irene Rodrigues Costa (UNICAMP)

Geometry and Information

In this talk it will be presented an introduction and some recent developments in two topics of geometry with applications in communications on which our research group have been working: Lattices and Information Geometry. Lattices are discrete additive subgroups of the n-dimensional Euclidean space and have been used in coding for reliability and security in transmissions through different channels. Currently, lattice-based cryptography is one of the main subareas of the so-called post-quantum Cryptography. Information Geometry is devoted to the study of statistical manifolds of probability distributions by considering different metrics and divergence measures and have been used in several applications related to data analysis. We will approach here particularly some statistical manifolds with the Fisher metric with applications to data clustering and machine learning.

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