I am an assistant professor with tenure in the Algebra, Geometry, and Number Theory group in the Mathematical Institute of Leiden University.

Before this, I held postdoc positions in Leibniz University Hannover, Max Planck Institute for Mathematics in Bonn, and Max Planck Institute for Mathematics in the Sciences in Leipzig. I completed my PhD in Mathematics at Humboldt University of Berlin with a short stay at University of Amsterdam.

For my full CV: Click here.

Contact me at: emre (at) sertoz (dot) com

Research Interests

Arithmetic of the periods of algebraic varieties. Heights and transcendence.
Computation of periods and Picard rank of surfaces in projective space (try PeriodSuite).
Moduli spaces in algebraic geometry, in particular moduli spaces of curves with various embellishments.
Projective geometry with an emphasis on enumerative problems.
Numerical and computational algebraic geometry.

Selected papers (the list of all my papers is here)

• Heights on curves and limits of Hodge structures, with S. Bloch and R. de Jong.
  • Journal of the London Mathematical Society, 108: 340-361, 2023 (DOI).
  • Here is my Oberwolfach talk explaining the result.
• Separation of periods of quartic surfaces, with P. Lairez,
      Algebra & Number Theory, 17(10), 1753–1778, 2023 (DOI).
• A numerical transcendental method in algebraic geometry, with P. Lairez,
      SIAM Journal on Applied Algebra and Geometry, 3(4), 559–584, 2019 (DOI).
• Prym varieties of genus four curves, with N. Bruin,
      Transactions of the American Mathematical Society 373 (2020) 149-183 (DOI).
• Computing periods of hypersurfaces,
      Mathematics of Computation, 88, 2987–3022, 2019 (DOI), software: PeriodSuite.

PhD Students

1. Sanskar Agrawal (Leiden University and Max Planck Institute SWS), co-supervised with Joël Ouaknine. 2025-
2. Stef Nomden (Leiden University and Max Planck Institute SWS), co-supervised with Joël Ouaknine. 2025-

Master’s students

1. Rafael Mohr (Leipzig University / Max Planck Institute for Mathematics in the Sciences), 2019–2020
2. Samuele Pollaci (University of Bonn / Max Planck Institute for Mathematics), 2021–2022.
   • Outcome article accepted to the 2023 International Conference on Machine Learning.
3. Kamillo Ferry (Leibniz University Hannover), 2022.
   • Thesis counted towards a double master’s degree, one in pure math and one in computer science.
4. Hidde Bakker (Leiden University and Delft University), 2025-

Undergraduate students

1. Lance Bakker, 2025 Spring. The arithmetic of solutions to linear differential equations with polynomial coefficients.
2. Casper Madlener, 2025 Spring. A new classification of semi-linear F[X,Y]/(XY)-modules.
3. Vitto van Leeuwen, 2025/2026 (Ongoing).
4. Daniël van Westreenen, 2025/2026 (Ongoing).

Organizational activities

1. Organising the Lorentz workshop “Recurrence, transcendence, and Diophantine approximation,” with Valérie Berthé, Peter Koymans, Lola Thompson. July 14-18, 2025.
2. Reading seminar on Arithmetic deformation to the normal cone. Joint with Robin de Jong. Fall 2024.
3. Reading seminar on Limit Mixed Hodge Structures. Joint with Zhelun Chen. Spring 2024.
4. Reading seminar on Mixed Hodge Structures. Joint with Zhelun Chen. Fall 2023.
5. Co-organising “Computational Geometry” workshop at the Banff International Research Station (Alberta, Canada) in 2024. Joint with Alexander Kasprzyk, Alessio Corti, Elana Kalashnikov, Marta Panizzut.
6. Organised the session Algebraic geometry through numerical computation in the International Congress on Mathematical Software 2020, joint with Taylor Brysiewicz, 13-17 July 2020, Braunschweig/Germany.
7. I am one of the editors for the Cubic Surfaces special issue in Le Matematiche, with Marta Panizzut and Kristian Ranestad, 2020.
8. Cubic surfaces wiki and the corresponding event in Oslo, 13 May 2019.
9. Non-Linear Algebra Seminar, joint with Max Pfeffer, from December 2018 to May 2019, Leipzig/Germany.
10. Minisymposium on Riemann Surfaces, 9-13 July 2019, Bern/Switzerland.
11. Numerical Computing in Algebraic Geometry, 13-17 August 2018, Leipzig/Germany.