Erik Paemurru

About Me

As of August 2025, I am working in the Theory of Atoms research group of Prof. Ludmil Katzarkov at Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, Sofia, Bulgaria. I received my PhD in December 2020 from Loughborough University, UK, my advisor was Prof. Hamid Abban.

My research interests include birational geometry of singular Fano varieties, especially nonrationality problems and Sarkisov links. Fano varieties are central in geometry, generalising the sphere to higher dimensions. Fano varieties also have close connections to physics, as the anticanonical sections of Fano varieties provide the main construction of Calabi–Yau manifolds used in string theory. In a recent work, inspired by ideas from mirror symmetry, the nonrationality of very general cubic fourfolds was proved using the theory of atoms. While in Sofia, I plan to study the theory of atoms, its applications to nonrationality questions and its connections to noncommutative spectra. I am also interested in computer algebra and I am one of the developers of the OSCAR computer algebra system.

Below are the previous academic positions I have held:

• postdoc at Saarland University, Germany, mentor Prof. Simon Brandhorst (2023–2025),
• joint position between ICMS–Sofia, Bulgaria and the University of Miami, USA, mentor Prof. Ludmil Katzarkov (2022–2023),
• postdoc at University of Basel, Switzerland, mentor Prof. Jérémy Blanc (2020–2021),
• Early Career Research Fellow at Imperial College London, UK, mentor Prof. Paolo Cascini.

Contact

Email: algebraicgeometry [at] runbox [dot] com

Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 8
Sofia 1113, Bulgaria

Publications

1. Blowups of smooth Fano hypersurfaces, their birational geometry and divisorial stability (joint with L. Campo, T. Guerreiro), to appear in New York Journal of Mathematics, arXiv:2311.11386
2. Log canonical thresholds of high multiplicity reduced plane curves (joint with N. Viswanathan), to appear in Glasgow Mathematical Journal, arXiv:2311.00963
3. Counting divisorial contractions with centre a cAₙ-singularity, Publications of the Research Institute for Mathematical Sciences, Kyoto University 60 (2024), no. 4, 699–721, doi:10.4171/prims/60-4-2
4. Birational geometry of sextic double solids with a compound Aₙ singularity, Nagoya Mathematical Journal (2024), 1–52, doi:10.1017/nmj.2024.17
5. 2n²-inequality for cA₁ points and applications to birational rigidity (joint with I. Krylov, T. Okada, J. Park), Compositio Mathematica 160 (2024), no. 7, 1551–1595, doi:10.1112/S0010437X24007164
6. Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron, Annali dell’ Università di Ferrara 70 (2024), 1069–1082, doi:10.1007/s11565-024-00524-6
7. Del Pezzo Surfaces in Weighted Projective Spaces, Proceedings of the Edinburgh Mathematical Society 61(2) (2018), doi:10.1017/S0013091517000335

Preprints

1. Very ample sheaves on weighted projective spaces and weighted blowups (joint with S. Muller), arXiv preprint 2025, arXiv:2510.03036
2. Local inequalities for cAₖ singularities (joint with I. Krylov, T. Okada), arXiv preprint 2025, arXiv:2508.21676

Invited talks and presentations

Teaching