Email: cbg@unicamp.br
1st Congress on Education, Outreach, and Innovation of CBG and Inauguration of the FabLab Rio Claro

Inaugural Workshop of the Brazilian Center for Geometry (CBG)

  • Home
  • Inaugural Workshop of the Brazilian Center for Geometry (CBG)
Event Image
00 Dias
00 Horas
00 Minutos
00 Segundos

Inaugural Workshop of the Brazilian Center for Geometry (CBG)

March 17–20, 2026

Location: IMECC Auditorium – UNICAMP, Campinas, SP, Brazil

The Inaugural Workshop of the Brazilian Center for Geometry (CBG) marks the official launch of CBG as a Research, Innovation, and Dissemination Center (CEPID) supported by FAPESP. The event is designed to foster integration among CBG participants and invited guests, including members of its International Advisory Board, with the goal of promoting the exchange of ideas within each vertical and across the verticals.

CBG brings together researchers in four thematic areas:

  • Differential Geometry (DG)

  • Algebraic Geometry (AG)

  • Applications of Geometry (ApliGeo)

  • Education, Outreach and Innovation (ED&I)

The program includes plenary lectures, vertical-specific seminars, discussions, and a poster session integrated with coffee breaks, as well as social activities.

FORMAT (DURATIONS)

  • Plenary Lectures (PL): 40 minutes + 10 minutes for questions

  • Thematic Session Seminars: 25 minutes + 5 minutes for questions

  • Vertical Discussions: 45 minutes

POSTERS
There will be poster sessions.

Interested participants should submit the title and abstract of their poster proposal via the registration form by March 1st.

DISCUSSIONS

The Discussion Sessions are intended to bring together researchers from the Verticals around themes of mutual interest and to foster dialogue in order to strengthen the integration of the CBG, with the initial objective of planning for 2026–2027.

Registration deadline: March 10.

Access the registration form

SPEAKERS — THEMATIC SESSIONS / SEMINARS

  • 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) — “Artin–Schreier Curves and the Number of Elements with Prescribed Norm and Trace”
  • Ivan Struchiner (IME – USP) — “Chern–Weil Classes of Cartan Connections”
  • Juliana Marta (Executive Manager of CBG) — “CBG: How To”
  • Leonardo Barichello (UNICAMP) — “Curricular Innovation for High School Mathematics in Brazil”
  • Marcelo Firer (UNICAMP) — “CBG and Mathematics Education in Basic Education”
  • Maurício Richartz (UFABC) — “Spacetime Geometry and Gravitational Phenomena at CBG”
  • Paolo Piccione (IME-USP) — “Conformal Curvatures”
  • Patrícia Schultz (EAIP-IMECC) — “CBG: How To”
  • Rúbia Barcelos Amaral (UNESP, Rio Claro) — “CBG Outreach Initiatives”
  • Sueli Irene Rodrigues Costa (UNICAMP) — “Geometry and Information”

Check the full program here

Contato

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

Event Information

Date

March 17–20, 2026

Venue

IMECC Auditorium – UNICAMP

Contact

workshop.cbg@ime.unicamp.br

Register here

Event Program

Preliminary Program (subject to change)

WP Table Builder
TUESDAY (17/03)
  • 14:00–15:00 Opening Ceremony
  • 15:00–15:30 Coffee break
  • 15:30–16:00 Seminar – Ethan Cotterill
  • 16:00–16:30 Seminar – Ivan Struchiner
  • 16:30–17:00 Seminar – Herivelto Martins Borges Filho
  • 17:15–18:00 Discussion (GA + GD) - room 253
THURSDAY (19/03)
  • 09:00–10:00 Plenary Lecture – Ugo Bruzzo
  • 10:00–10:30 Coffee break + Poster Session
  • 10:30–11:00 Seminar – Rúbia Amaral
  • 11:00–11:30 Seminar – Marcelo Firer
  • 11:30–12:00 Seminar – Leonardo Barichello
  • 12:00–14:00 Lunch
  • 14:00–15:00 Plenary Lecture – Zsolt Lavicza
  • 15:00–15:30 Coffee break + Poster Session
  • 15:30–16:00 Seminar – Carlile Lavor
  • 16:00–16:30 Seminar – Carolina Araujo
  • 16:30–17:00 Seminar – Sueli Irene Rodrigues Costa
  • 17:15–18:00 Discussion (AG + GA) - room 253
  • 18:30–22:00 Cocktail Reception CPV
WEDNESDAY (18/03)
  • 09:00–10:00 Plenary Lecture – Bobby Acharya
  • 10:00–10:30 Coffee break + Poster Session
  • 10:30–11:30 Plenary Lecture – Jorge Lauret
  • 11:30–12:00 Seminar – Patrícia Schultz e Juliana Marta
  • 12:00–14:00 Lunch
  • 14:00–15:00 Plenary Lecture – Oscar García-Prada
  • 15:00–15:30 Coffee break + Poster Session
  • 15:30–16:00 Seminar – Dahisy Lima
  • 16:00–16:30 Seminar – Maurício Richartz
  • 16:30–17:00 Seminar – Fernando Manfio
  • 17:15–18:00 Discussion (GD + AG) - room 253
FRIDAY (20/03)
  • 09:00–10:00 Plenary Lecture – Alicia Dickenstein (Online)
  • 10:00–10:30 Coffee break
  • 10:30–11:30 Discussion (ED&I) - room 253
  • 11:30–14:00 Lunch
  • 14:00–15:00 Closing Lecture: Paolo Piccione (Online)
  • 15:00–15:30 Closing Session
  • 17:00–20:00 Happy hour

Plenary Lecture

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)

Thematic Sessions

The following speakers have been confirmed.

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)

Artin–Schreier Curves and the Number of Elements with Prescribed Norm and Trace

We study the number $N_n(a,b)$ of elements in extensions of finite fields with prescribed norm $a$ and trace $b$, a classical problem formulated by Nicholas Katz and widely investigated in recent decades. We establish an explicit relationship between this counting problem and the number of rational points on certain Artin–Schreier curves, obtaining estimates that improve upon previously known bounds. These results have applications to point counting on Calabi–Yau toric varieties and to determining the number of prime polynomials in certain arithmetic progressions in 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)

Curricular Innovation for High School Mathematics in Brazil

In this talk, I will address how one of the projects within the CBG’s Innovation axis seeks to provide concrete responses to the demand for renewal and innovation in the high school mathematics curriculum in Brazil. In addition, I intend to discuss other areas that call for similar innovations, which may be led by other members of the Center in partnership with the researchers of this axis.

Marcelo Firer (UNICAMP)

The CBG and the Teaching of Mathematics in Basic Education

It is widely known and well documented that there is a significant gap between the high level of research in mathematics and the low quality of mathematics education offered to the general population in Basic Education. The CBG-Innovation project aims to develop resources focused on improving the teaching of mathematics, taking the population as a whole as its reference. The strategic vision guiding CBG-Innovation, the planned initiatives, and the partnerships that have been established with public agencies and third-sector organizations will be presented.

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) and Juliana Marta (CBG Executive Manager)

CBG: How To

Patrícia Schultz and Juliana Marta will present the development of CBG from its early stages to its current structure. They will discuss the path EAIP built to support CBG researchers during the initial phase of the project, and how researchers can now make the best use of the center within the processes that are already established.

Join us and bring your questions!

Rúbia Barcelos Amaral (UNESP, Rio Claro)

CBG Outreach Actions

Within the scope of Knowledge Dissemination, we aim to create impactful spaces for spreading knowledge in geometry and mathematics throughout the state of São Paulo. Through the establishment of Knowledge Dissemination Centers (NDCs), this initiative will support science communication and community engagement. These centers will serve as hubs for immersive educational experiences in augmented and virtual reality, offering cutting-edge technological resources such as 3D printers and laser cutters. They will also provide teacher training, support for high school and undergraduate students, and materials for undergraduate research activities. In this session, we will share the NDC plans to enhance the teaching and learning of mathematics, foster a scientifically literate society, and promote continuing education in geometry, from basic education to advanced research levels.

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.

Photos of the Event

Click on the images to enlarge them.