CV

General Information

Name Lucas M. Moschen
Languages Portuguese, English, studying French
E-mail lucas.moschen22@imperial.ac.uk
Description My research interests lie at the intersection of mathematical modelling, control theory, and numerical analysis for differential equations. I am currently focused on developing optimal control methods for mean-field PDEs, such as the McKean-Vlasov and Fokker-Planck equations, with applications to large-scale stochastic systems like opinion dynamics. My previous work has explored optimal control problems in constrained systems, including epidemic models and stochastic population dynamics, with methods spanning probability, optimisation, and reinforcement learning.

Education

  • 2024 - current
    Ph.D. in Mathematics
    Imperial College London, London (UK)
    • Supervisors Grigorios Pavliotis and Dante Kalise
    • Research Focus Optimal control of mean-field PDEs (McKean-Vlasov and Fokker-Planck), with emphasis on theoretical analysis and numerical stabilization techniques.
  • 2023 - 2024
    MSc in Mathematics of Modelling
    Sorbonne University, Laboratoire Jacques-Louis Lions - Paris (France)
    • Supervisors Camille Coron and Luis Almeida
    • Memoire "Modeling and Control of Mosquito Populations, From Stochastic Processes to Reinforcement Learning"
    • Research Focus Analysis and control of stochastic models for mosquito populations.
  • 2022 - 2023
    MSc in Mathematical Modelling
    Fundação Getulio Vargas, School of Applied Mathematics - Rio de Janeiro (Brazil)
    • Supervisor María Soledad Aronna
    • Master's Thesis "Optimal vaccination strategies for epidemics in metropolitan areas"
    • Research Focus Optimal control of constrained affine systems, applied to epidemic dynamics in networks of cities.
  • 2018 - 2021
    BSc in Applied Mathematics
    Fundação Getulio Vargas, School of Applied Mathematics - Rio de Janeiro (Brazil)
    • Supervisor Luiz Max Carvalho
    • Bachelor Dissertation "Prevalence estimation and binary regression methods for respondent-driven sampling with outcome uncertainty"
    • Research Focus Bayesian methods for prevalence estimation under partial graph observation.

Research Experience

  • 2024 - present
    Optimal Control and Mean-Field Games
    Imperial College London
    • Developing numerical stabilization methods for optimal control of McKean-Vlasov and Fokker-Planck PDEs.
    • Supervised by Grigorios Pavliotis and Dante Kalise.
    • Publications in progress (see Publications section).
  • 2023 - 2024
    Control and Stochastic Modeling in Biology
    Sorbonne University
    • Developed models for mosquito population control using reinforcement learning.
    • Supervised by Luis Almeida and Camille Coron.
  • 2022 - 2023
    Optimal Control in Epidemiology
    FGV
    • Investigated optimal vaccination strategies in networks of cities.
    • Supervised by Maria Soledad Aronna
    • Resulted in two publications and conference talks.
  • 2022 - 2023
    Statistical Inference and Bayesian Methods
    Fundação Getulio Vargas (FGV)
    • Developed parameter inference and diagnostics for bivariate beta distributions.
    • Co-authored a paper under submission (with Luiz Max Carvalho).
  • 2014 - 2021
    Early Research & Scientific Initiation
    Fundação Getulio Vargas & IMPA
    • Undergraduate research on optimal control in biological models (supervised by Maria Soledad Aronna).
    • Junior Scientific Initiation at IMPA (2014-2017).
    • Co-authored early papers on optimal control and epidemiology.

Teaching Experience

  • 2024 - present
    Graduate Teaching Assistant
    Imperial College London
    • BSc level
      • Analysis I (2024), Linear Algebra and Groups (2024)
  • 2019 - 2023
    Teaching Assistant
    Fundação Getulio Vargas, School of Applied Mathematics
    • MSc level
      • Partial Differential Equations and Applications (2023), Probability (2023), Functional Analysis (2022), Statistical Inference (2022), Bayesian Statistics (2022)
    • BSc level
      • Partial Differential Equations (2021, 2022), Curves and Surfaces (2021, 2022), Introduction to Numerical Analysis (2021), Statistical Inference (2020), Ordinary Differential Equations (2020), Linear Algebra (2019)
  • 2019
    Volunteer Algebra Teacher
    Project Elos Educação - Rio de Janeiro (Brazil)
    • Prepared students for high school entrance exams.

Honors and Awards

  • 2023
    • Best poster presentation for the work on COVID-19 mathematical modelling at the Latin American Congress on Industrial and Applied Mathematics;
    • Best poster presentation for the work on COVID-19 mathematical modelling at the IX Congreso de Matemática Aplicada, Computacional e Industrial;
  • 2022
    • Scientific Initiation Award SBMAC (3rd place) for my Bachelor's Dissertation
  • 2021
    • Academic Excellence with the highest final grade in the BSc course.
  • 2013 - 2017
    • Two gold, one silver and two bronze medals in the Brazilian Mathematical Olympiad of Public Schools;

Social Engagement

  • 2024 - present
    Academic & Professional Societies
    • SBMAC Jovem Member, Brazilian Society of Computational and Applied Mathematics - Supporting content dissemination on social media.
    • SIAM Student Chapter Member - Organizing academic events and outreach activities.
    • Department Representative at Imperial College London.
  • 2023
    Academic Representation & Conference Organization
    • Member of the Local Committee for the Latin American Congress on Industrial and Applied Mathematics (LACIAM 2023).
    • Representative of graduate students on the School of Applied Mathematics (FGV) Board.
  • 2018 - 2019
    Community & Student Leadership
    • Vice-President of the Student Association, School of Applied Mathematics, FGV.
    • Volunteer at the Elos Educação project, Rio de Janeiro, Brazil (2019) - Providing educational support for students.

Conferences

  • 2024
    • Summer School on Collective Behavior and Pattern Formation (Paris, France) - Organized by CIRM, with all costs covered; poster presentation.
    • XLIII National Congress of Applied and Computational Mathematics (Porto de Galinhas, Brazil) - Poster presentation.
  • 2023
    • PGMODays 2023 (Palaiseau, France) - Oral presentation "Optimal Vaccination Strategies in Metropolitan Areas", organized by Hadamard Foundation.
    • 10th Heidelberg Laureate Forum (Heidelberg, Germany) - Participant, funded by Klaus Tschira Stiftung.
    • 34th Brazilian Mathematics Colloquium (Rio de Janeiro, Brazil) - Poster presentation "Optimal Vaccination Strategies in Interconnected Metropolitan Areas", organized by IMPA.
    • IX Congreso de Matemática Aplicada, Computacional e Industrial (Santa Fé, Argentina) - Poster presentation "Mathematical Modeling of COVID-19 and Analysis of Rio de Janeiro's Outbreak in 2020", organized by ASAMACI.
    • Latin American Congress on Industrial and Applied Mathematics (Rio de Janeiro, Brazil) - Poster presentation "Mathematical Modeling of COVID-19 and Analysis of Rio de Janeiro's Outbreak in 2020", organized by FGV EMAp and SBMAC.
  • 2022
    • V Mathematical Colloquium of the Southern Region (online) - Poster presentation "Parameter Estimation of a Bivariate Beta Distribution".
  • 2021
    • XL National Congress of Applied and Computational Mathematics (online) - Participant, organized by SBMAC.
    • XXXIII Brazilian Mathematics Colloquium (online) - Participant, organized by IMPA.
  • 2020
    • II Fluminense Meeting of Women in Biomathematics (online) - Poster presentation "A Model for COVID-19 with Isolation, Quarantine, and Testing".
  • 2019
    • XXXII Brazilian Mathematics Colloquium (Rio de Janeiro, Brazil) - Participant, organized by IMPA.
  • 2018
    • III Brazilian Congress of Young Researchers in Pure and Applied Mathematics and Statistics (Curitiba, Brazil) - Participant, organized by Federal University of Paraná.

Relevant Knowledge

  • Programming languages
    • Programming skills in Python, R, Julia, C++, Matlab and JavaScript
  • Additional programming skills
    • Programming tools Git, Visual Studio Code and Project Jupyter