Enis Kaya

About me:

I am pleased to announce that I'll join Bilkent University as an assistant professor in September 2025. For now, I'm a postdoctoral researcher at the KU Leuven; my mentors are Johannes Nicaise and Arne Smeets. Before that I was a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences in Leipzig; my mentors were Bernd Sturmfels and Daniele Agostini. I did my PhD at the University of Groningen under the supervision of J. Steffen Müller.

My main research interest is in algorithmic arithmetic geometry. I am particularly interested in theoretical and algorithmic aspects of p-adic integration theories and p-adic height pairings on curves and abelian varieties, mostly in the case of bad reduction, and their applications to problems with an arithmetic flavor such as finding rational points on curves of genus at least two. Needless to say, I'm a member of the society of p-adicts! I also like topics in tropical geometry and classical algebraic geometry. 

People working in and near p-adic integration theories really care about "wide open spaces", so do The Chicks.

Publications and preprints:

1. Rational curves on del Pezzo surfaces (with Stephen McKean, Sam Streeter and H. Uppal), in preparation.

2. Algorithms for p-adic heights on hyperelliptic curves of arbitrary reduction (with Francesca Bianchi and J. Steffen Müller), Res. Number Theory 11 (2025), no. 1, Paper No. 31, ANTS XVI, abstract,; journal, arXiv, code.

3. Coleman-Gross heights and p-adic Néron functions on Jacobians of genus 2 curves (with Francesca Bianchi and J. Steffen Müller), submitted, abstract; arXiv.

4. Jumps of Jacobians via orthogonal canonical forms (with Michaël Maex and Art Waeterschoot), Proc. Amer. Math. Soc. 153 (2025), no. 3, 947–961, abstract; journal, arXiv.

5. Computation of admissible Arakelov-Green functions on metrized graphs (with Ruben Merlijn van Dijk), to appear in Involve, a Journal of Mathematics, abstract; journal, arXiv, code.

6. Sampling from p-adic algebraic manifolds (with Yassine El Maazouz), to appear in SIAM Journal on Applied Algebra and Geometry, abstract; arXiv, code.

7. Tropical invariants for binary quintics and reduction types of Picard curves (with Yassine El Maazouz and Paul Alexander Helminck), Glasg. Math. J. 66 (2024), no.1, 65-87, abstract; journal, arXiv, code.

8. Lines on p-adic and real cubic surfaces (with Rida Ait El Manssour, Yassine El Maazouz and Kemal Rose), Abh. Math. Semin. Univ. Hambg. (2023), no. 93, 149-162, abstract; journal, arXiv, code.

9. Explicit Vologodsky integration for hyperelliptic curves, Math. Comp. 91 (2022), no. 337, 2367-2396, abstract; journal, arXiv, code.

10. p-adic integration on bad reduction hyperelliptic curves (with Eric Katz), Int. Math. Res. Not. IMRN (2022), no. 8, 6038-6106, abstract; journal, arXiv, code.

Theses:

1. p-adic integration on hyperelliptic curves of bad reduction: algorithms and applications, PhD Thesis, Stellingen (2021), University of Groningen, abstract.

2. On extended Selmer groups for Coleman deformations, MSc Thesis (2017), Koç University.

3. Kronecker's jugendtraum, BSc Thesis II (2015), Mimar Sinan University.

4. Calculating the class number in imaginary quadratic fields, BSc Thesis I (2015), Mimar Sinan University.

Some presentations:

1. p-adic integration theories on curves, Combinatorial Synergies in Geometry and Number Theory, IMPA, March 27, 2025, video.

2. p-adic integrals & heights on curves, and their computation, UCD Algebra and Number Theory Seminar, November 21, 2024.

3. Rational curves on del Pezzo surfaces, ODTÜ-BİLKENT Algebraic Geometry Seminar, November 1, 2024.

4. Algorithms for p-adic heights on hyperelliptic curves of arbitrary reduction, ANTS XVI, MIT, July 18, 2024.

5. A journey into the world of p-adic heights, Math Seminar, Sabancı University, December 20, 2023.

6. Computing admissible Arakelov-Green functions on metrized graphs, WGT-Workshop on Graph Theory and Its Applications-XI, Boğaziçi University, November 10, 2023.

7. Computing Schneider p-adic heights on hyperelliptic Mumford curves, The Autumn Session of the GVL-APP, Université de Lille, December 12, 2022.

8. Mumford curves, Mini-Workshop on Curves and Riemann Surfaces, MPI MiS, November 25, 2021.

9. Explicit p-adic heights for hyperelliptic curves, Number Theory Seminar, Boston University, November 22, 2021.

10. Explicit Vologodsky integration for hyperelliptic Curves, DIAMANT Symposium Autumn 2020, November 26, 2020.

11. Explicit Vologodsky integration for hyperelliptic curves, NTAG Seminar, Simon Fraser University, November 5, 2020, video.

12. On Selmer groups and factoring p-adic L-functions, Seminari de Teoria de Nombres de Barcelona 2017, Universitat de Barcelona, January 24, 2017.

Some expository notes:

1. Tropikal varyetelerin yapı teoremi (Büşra Sert ile), Matematik Dünyası - 118 (2023).

2. Tropikal cebirsel geometrinin temel teoremi (Büşra Sert ile), Matematik Dünyası - 116 (2023).

3. Tropikal geometri nedir? (Şekil 1.3.2), Sabancı Üniversitesi IEEE Matematik Topluluğu, 24 Aralık 2021, video.

4. Sonlu cisimler üzerinde polinomlar (Ayhan Dil ile), Matematik Dünyası - 106 (2018), özetçe.

5. Contractions and canonical models, notes for the Topics in Algebraic Geometry seminar at the University of Leiden, Spring 2018.

6. Cantor-Schröder-Berstein teoremi, 2011.

7. Matematikte temel fikirler: kanıt ve yapı, 2011, kitabın kapağı ve hikayesi.

Some links: 

• Leuven Seminar on Number Theory and Algebraic Geometry.

• Leuven COSIC (Computer Security and Industrial Cryptography group) Seminar.

• Leuven Student Seminars in Mathematics.

• Belgian-Dutch Algebraic Geometry Seminar.

• Leipzig seminar on Algebra, Algebraic Geometry and Algebraic Topology.

• Groningen algebra research seminar.

• TGiF (Tropical Geometry in Frankfurt).

• Intercity number theory seminar.

• DIAMANT (Discrete, Interactive and Algorithmic Mathematics, Algebra and Number Theory).

• The Turkish Mathematical Society Distinguished Colloquium Series, videos are here.

• UCGEN (Uluslararası Cebirsel GEometri Neşesi).

• IMBM (İstanbul Matematiksel Bilimler Merkezi) Number Theory Seminars.

• Ankara-Istanbul Algebraic Geometry & Number Theory Meetings.

• ODTÜ-BİLKENT Algebraic Geometry Seminar.

• Gökova Geometry / Topology Conferences.

• Matematik Dayanışma Platformu.

• DRP Turkey.

• Matematiğin Peşinde: matematikle ilgili, matematiği öğrenmeyi de paylaşmayı da seven bir topluluk.

• MΣΣT a Mathematician: a collection of  video interviews with mathematicians.