Mathematics · Artificial intelligence · Education

Research connecting
knowledge
and opportunity.

I am Krerley Oliveira, Full Professor of Mathematics at UFAL, Brazil. My work spans dynamical systems and ergodic theory, applied artificial intelligence, and the development of young talent.

Timeline 1995 — 2025

From olympiads to research and developing talent.

  1. Recognition

    OBM bronze medal

    A bronze medal at the Brazilian Mathematical Olympiad, an early milestone in my mathematical journey.

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  2. Education

    Master’s degree at IMPA

    Completion of my master’s degree in Mathematics at the Institute for Pure and Applied Mathematics.

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  3. Olympiads

    OIMU bronze medal

    Bronze medal at the 2nd Ibero-American University Mathematics Olympiad, representing Brazil.

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  4. Olympiads

    OIMU silver medal

    Silver medal at the 3rd Ibero-American University Mathematics Olympiad.

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  5. Education

    PhD at IMPA

    PhD in Mathematics, specialising in Dynamical Systems and establishing my research focus in ergodic theory.

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  6. Project

    UFAL and the Alagoas Olympiad

    Joined UFAL and helped establish the Alagoas Mathematics Olympiad, supporting the discovery and development of young talent.

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  7. Researcher development

    Graduate Mathematics programme

    Helped establish UFAL’s graduate programme, recognised by the Ministry of Education in 2004, and served as its coordinator.

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  8. Mathematics education

    First OBMEP in Alagoas

    State coordination of the first Brazilian Mathematical Olympiad for Public Schools, expanding access to training and competitions.

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  9. Publication

    Maximal entropy measures

    Paper with Marcelo Viana on the existence and uniqueness of maximising measures for classes of local diffeomorphisms.

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  10. Recognition

    Brazilian Academy of Sciences

    Elected an Affiliate Member of the ABC, joining the first generation of its Young Academy.

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  11. Researcher development

    Mathematics PhD programme at UFAL

    Helped establish and coordinate the doctoral programme, expanding researcher training in Alagoas.

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  12. Researcher development

    First Brazilian School on Dynamical Systems

    Coordinated the project supporting the school at UFAL, bringing together students and researchers from Brazil and abroad.

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  13. Book and recognition

    Jabuti Prize finalist

    Iniciação à Matemática, coauthored with Adán J. Corcho Fernández and published in 2010, shortlisted in the Exact Sciences category.

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  14. Publication

    Nonuniform specification

    Publication of Every expanding measure has the nonuniform specification property in Proceedings of the American Mathematical Society, volume 140, pages 1309–1320.

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  15. Publication

    Foundations of Ergodic Theory

    Cambridge University Press published the textbook I coauthored with Marcelo Viana on the foundations of ergodic theory.

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  16. Team recognition

    Grand Prix Scientifique Louis D.

    Member of the research team associated with the prize awarded to Marcelo Viana and François Labourie in France.

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  17. Olympiads

    Brazilian team leader at the IMO

    Led Brazil’s team at the International Mathematical Olympiad, held that year in Rio de Janeiro.

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  18. Project

    Establishment of LED/UFAL

    Launch of the laboratory I coordinate, conducting applied research in natural language processing, computer vision and data science.

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  19. Recognition

    Banco do Nordeste distinction

    Regional Development distinction in the Academic category, recognising my research and its contribution to the region.

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  20. Project

    Data science during the pandemic

    Led a Serrapilheira-supported project for clinical monitoring and data integration across municipal health networks.

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  21. Project

    Public procurement oversight

    Guided a team in an MPPB challenge applying mathematical methods to identify potential overpricing.

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  22. Recognition

    Cidadão Benemérito de Maceió

    Honorary title awarded by Maceió’s City Council in recognition of service to the city.

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  23. Publication and project

    Machine learning for justice

    Online publication of our paper on classifying petitions from Alagoas courts, subsequently included in the 2025 volume of Artificial Intelligence and Law.

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  24. Project

    NES begins teaching

    Launch of Novo Ensino Suplementar’s teaching activities: advanced mathematics, computing and data science for high school students.

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  25. International education

    Teaching at SigmaCamp

    Faculty participation in the international mathematics and science immersion programme for young students.

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  26. Project

    Launch of PETI–OBM

    General coordination of the international training programme’s launch, with scholarships, tutoring and support for lower-income students.

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  27. Programme recognition

    USP Social Impact Award

    NES receives second place in the Quality Education category, recognising the collective work of developing young talent.

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Research areas

Two fields, a mathematical foundation.

Selected books and papers introducing the central themes of my research and applications developed in collaboration.

All publications on Google Scholar
01

Dynamical Systems and Ergodic Theory

Mathematical research · Books and papers

I study the long-term behaviour of dynamical systems, focusing on invariant measures, entropy and non-uniformly hyperbolic dynamics.

Selected publications

  1. Foundations of Ergodic Theory

    A textbook on the foundations of ergodic theory, coauthored with Marcelo Viana.

    Cambridge University Press · 2016

  2. Equilibrium states for non-uniformly expanding maps

    Construction of equilibrium states for open classes of non-uniformly expanding maps, studying uniqueness and ergodic properties.

    Krerley Oliveira · Ergodic Theory and Dynamical Systems · 2003

  3. Equilibrium states for hyperbolic potentials via inducing schemes

    Existence of finitely many ergodic equilibrium states for hyperbolic potentials in systems that may have critical sets.

    José F. Alves, Krerley Oliveira, Eduardo Santana · Nonlinearity · 2024

Google Scholar
02

Applied Machine Learning

Applied research · LED/UFAL coordination

With the LED/UFAL team, I develop natural language processing, computer vision and predictive modelling methods for public institutions and companies.

Selected publications

  1. Automating petition classification in Brazil’s legal system: a two-step deep learning approach

    Classification of court petitions through the identification of relevant text segments.

    Coauthored · Artificial Intelligence and Law · 2025

  2. Sequence Labeling in Product Descriptions on Invoices: Comparing LLM-based settings with a CRF baseline

    Comparison of models for extracting information from product descriptions on invoices.

    With E. Darrazão and L. C. Gomes Jr. · JBCS · 2025

  3. Automated analysis of feline posture using deep learning and geometric modeling

    Neural networks and geometry for automatically describing cat posture in images and video.

    Coauthored · Frontiers in Veterinary Science · 2026

Google Scholar

Projects I coordinate

Research addressing concrete problems.

Four fields of collaboration at LED/UFAL. I coordinate teams bringing together researchers, students and institutional partners.

Data Science and Statistics Laboratory · UFAL
01

Human health

WHO / PAHO · Hapvida

I coordinate data science and AI projects for clinical research and health service planning, working with care teams and researchers.

Work and developments

  1. Clinical data and post-Covid · WHO / PAHO

    AI for structuring clinical information and identifying post-Covid cases, with Florianópolis’s health network and the WHO Global Clinical Platform initiative.

    Research collaboration · Rede Colaborativa Brasil

  2. Emergency care demand forecasting · Hapvida

    Development of models to forecast patient demand and support medical staffing and care capacity planning.

    Research and development · Challenge presented in 2026

Explore LED’s work
02

Animal health

CEVA Santé Animale · France

I coordinate a computer vision collaboration to study animal behaviour and welfare. Our work with CEVA combines deep learning and geometric modelling of feline posture.

Work and developments

  1. Automatic posture recognition

    Development of compact neural networks to classify posture and identify side views in images.

    Development reported in the paper · 2026

  2. Head, back and tail descriptors

    Integration of pose estimation and geometry to produce interpretable descriptors for behaviour and welfare research.

    Development reported in the same study · 2026

Collaboration paper
03

Justice

Alagoas Court of Justice · TJ/AL

I coordinate projects applying natural language processing to the organisation and analysis of legal documents, developed collectively by the LED/UFAL team.

Work and developments

  1. Hércules

    A system supporting case analysis. UFAL reports that it assisted with more than 40,000 cases in the first half of 2023.

    System developed by LED/UFAL

  2. Automated petition classification

    A two-stage method, informed by expert annotations, to identify relevant information and classify petitions from Alagoas courts.

    Coauthored paper · Artificial Intelligence and Law

Partnership and results
04

Tax and public spending oversight

Piauí State Finance Department · SEFAZ/PI · MPPB

I coordinate work on tax documents and public procurement. The research turns textual descriptions into comparable information to support oversight and spending controls.

Work and developments

  1. Information extraction from invoices

    Feature engineering and evaluation on medicine invoices from Piauí to identify elements within product descriptions.

    Coauthored paper · ERBD · 2023

  2. Language models for product descriptions

    Comparison of language-model and CRF approaches for structuring the textual content of invoices.

    Coauthored paper · JBCS · 2025

  3. Public procurement overpricing analysis · MPPB

    Team guidance in a mathematical solutions challenge to compare products and support the identification of potential overpricing.

    Collaborative project · Workshop · 2021

Institutional partnerships

Mathematics and industry

Mathematical solutions workshops

I organize and participate in workshops that bring together researchers, students, companies and public institutions to formulate problems, test models and develop solutions collaboratively.

USP · São Carlos

Co-organizer · June 15–19, 2026

12th Workshop on Mathematical Solutions for Industrial Problems, organized with Tiago Pereira. Teams from different institutions worked on challenges presented by Hapvida, Stone and the Alagoas State Court of Accounts (TCE-AL).

FGV · Rio de Janeiro

Organizer of two editions

The Mathematics in Industry Workshop at FGV's School of Applied Mathematics. A week of teamwork on problems proposed by companies, with mathematical modelling and faculty guidance. In 2026, I was a member of the responsible faculty team.

IMPA · Centro Pi / CeMEAI

Technical and scientific committee · 2021 · online

7th Workshop on Mathematical Solutions for Industrial Problems. I served on the technical and scientific committee of an edition addressing challenges from companies and public institutions, including the Public Prosecutor's Office of Paraíba.

UFAL · Maceió

Co-organizer · 2019

Workshop on Mathematical Solutions for the Productive Sector, held in Maceió. Organized with Thales Vieira and Adriano Barbosa, connecting researchers with challenges from the productive sector in Alagoas.

Selected participation · IMPA, 2020

Language, images and practical problems

At the Mathematics and Industry Workshop, I presented applications of natural language processing and image analysis in justice, tourism, the environment and retail, including the analysis of oil spills along the Alagoas coast.

Education and researcher development

From developing talent to research.

Research supervision, the development of graduate programmes and mathematics education initiatives for young people.

Graduate education and research

Training researchers

My work includes supervising master’s, doctoral and undergraduate research, as well as postdoctoral researchers. Four completed PhD theses are documented in my Lattes CV, last updated in 2024.

Building graduate mathematics at UFAL

I helped establish the graduate Mathematics programme in 2004 and the PhD programme in 2010, and coordinated both.

Supervision and scientific collaboration

Postdoctoral supervision of Jérôme Rousseau (2010) and Xueting Tian (2011), with research in dynamical systems and ergodic theory.

01

NES

Novo Ensino Suplementar · Coordination

An advanced programme in mathematics, computing and data science for talented young students, combining long-term guidance with exposure to research.

Initiatives and highlights

  1. Sustained academic training

    Establishment of a supplementary learning pathway for high school students, with teaching activities beginning in 2023.

    Education programme

  2. Research on industrial problems

    Student participation and joint organisation of the 2026 workshop with USP, connecting education with problems from companies and institutions.

    NES / UFAL and CeMEAI / USP cooperation

  3. USP Social Impact Award

    The programme received second place in the Quality Education category in 2025.

    Institutional recognition · 2025

Explore NES
02

PETI

Special International Training Programme · OBM · General coordination

Intensive training for high-achieving mathematics students from lower-income families, preparing them for national and international olympiads.

Initiatives and highlights

  1. Mathematical olympiad training

    A programme in algebra, combinatorics, geometry and number theory, taught by specialist instructors.

    Intensive training · AOBM

  2. Scholarships, tutoring and student support

    Academic guidance, psychological support and technological assistance included in the programme’s launch in 2025.

    Programme launch and participation support · 2025

Explore PETI–OBM
03

SigmaCamp

Ambassador in Brazil · Programme development and teaching

I work on SigmaCamp’s expansion in Brazil and connect students with immersive mathematics and science experiences alongside an international community of researchers.

Initiatives and highlights

  1. Expansion in Brazil · ETAPA SigmaCamp

    Development of opportunities for scientific immersion in Brazil, including the Brazilian edition held with Sistema Etapa.

    Mathematics and science immersion

  2. Sigma Challenge

    Engaging students in interdisciplinary challenges and opportunities to attend scientific programmes in Brazil and abroad.

    Access and talent discovery

  3. Teaching at SigmaCamp and SigmaNext

    Courses and lectures introducing young students to advanced mathematics alongside researchers from different institutions.

    Faculty · SigmaNext 2026

Explore SigmaCamp
04

NUTI – AMA

Intensive Training Centre · Co-coordination with Davi Lima

A partnership with the Association of Municipalities of Alagoas to expand municipal public-school students’ access to advanced mathematics training.

Initiatives and highlights

  1. Olympiad preparation

    Problem-solving training for students in grades 6–9, building on the Institute of Mathematics’ olympiad preparation work.

    Mathematics education · Municipal schools

  2. Expanding access with AMA

    Launch of the partnership in 2025, selecting students from municipalities across Alagoas and providing scholarships to support their participation.

    Institutional partnership · 2025

Explore NUTI – AMA

About

Research and the people it reaches.

I earned my master's degree and PhD at IMPA and joined UFAL in 2003. My work combines research, graduate supervision and the coordination of education and artificial intelligence projects. I was an Affiliate Member of the Brazilian Academy of Sciences.

International experience

Research and teaching abroad.

Year-long visits to Penn State and Université Paris-Sud, alongside courses, seminars and academic collaborations at institutions abroad.

Pennsylvania · United States1 year

Penn State University

Visiting professor · Postdoctoral research · 2007 — 2008

A year of research and university teaching, as part of my work in dynamical systems and ergodic theory.

Orsay · France1 year

Université Paris-Sud

Visiting Senior Research Fellow · 2015 — 2016

A year of research in Orsay as a Visiting Senior Research Fellow, working in dynamical systems and ergodic theory.

Courses and lectures abroad

Connecticut · United States · 2023 · 2024 · 2025 · 2026

SigmaCamp · SigmaNext

Teaching at SigmaCamp and SigmaNext

Visits to the United States to take part in immersive science programmes and mathematics education for young students.

  • 2026 — The Mathematics Behind Card Shuffling: a SigmaNext minicourse exploring the mathematics of card tricks and shuffling through groups, combinatorics, graphs and probability.

Lahore · Pakistan · 2020 · 2024 · 2026

IMM · Lahore University of Management Sciences

Teaching in the International Mathematics Master

International faculty member in the master’s programme hosted by LUMS.

  • 2020 — Numerical Linear Algebra.
  • 2024 — Numerical Linear Algebra and Analysis, including methods for eigenvalues and eigenvectors.
  • 2026 — Differential Geometry, including a module on hyperbolic geometry.

Trieste · Italy · 2012 · 2015

Abdus Salam ICTP

Schools and conferences in dynamical systems

Courses and research presentations at the International Centre for Theoretical Physics.

  • 2012 — Course on Markov partitions for surface diffeomorphisms, with Omri Sarig.
  • 2015 — Lecture on equilibrium states for partially hyperbolic maps.

Abu Dhabi · United Arab Emirates · 2024

Khalifa University

Mathematics and applied AI abroad

A Mathematics Seminar lecture sharing LED/UFAL’s experience with natural language processing and computer vision.

  • Projects in healthcare, justice, retail and animal health, alongside discussions of potential academic cooperation.

Utrecht · Netherlands · 2016

Utrecht University

Equilibrium states and iterated systems

A lecture at the Utrecht Stochastics Seminar on 18 May, exploring uniqueness of equilibrium states.

  • Results for iterated function systems and partially hyperbolic horseshoes.

Further academic visits and activities

Beyond work

Triathlon and community initiatives

I compete in amateur triathlon and take part in social initiatives and sports organisation in Maceió.

Explore this side of my life

Social initiatives and sports organisation

My involvement in sport also includes community organisation, training infrastructure and access to sporting activities in Maceió.

  • Creation of an athletic association in Maceió.
  • Involvement in organising Challenge Maceió.
  • Participation in the creation of the Álvaro Vasconcelos Training Space.
  • Philanthropic initiatives, including a swimming school in Benedito Bentes for low-income students from public schools.

Contact and collaboration

Research, partnerships and new opportunities.

krerley@mat.ufal.br

Get in touch about mathematical research, applied AI projects, talks or support for programmes developing young talent.

Institute of Mathematics · UFAL · Maceió, Brazil
krerley@mat.ufal.br