About me

I am a postdoctoral reseracher in the Real Algebraic Geometry group of Mario Kummer at TU Dresden. I did my PhD at the Max Planck Institute for Mathematics in the Sciences under the supervision of Bernd Sturmfels and Simon Telen. Before that, I was a student at Moscow State University, where my advisors were Gleb Pogudin and Yury Razmyslov. I am primarily interested in positive geometry, real algebraic geometry and their applications to physics. My other mathematical interests include differential algebra and algebraic combinatorics.

Here is my CV. You can also view my Google Scholar and ORCID pages.

My e-mail is pavlov@mis.mpg.de

Preprints

• Adjoints of Polytopes: Determinantal Representations and Smoothness (with Clemens Brüser and Mario Kummer), arXiv:2507.01672, 2025.
• Positive Polytopes with Few Facets in the Grassmannian (with Kristian Ranestad), arXiv:2503.01652, 2025.

Published articles

• Combinatorics of m=1 Grasstopes (with Yelena Mandelshtam and Elizabeth Pratt), Combinatorial Theory, 2025. Preprint
• Algebraic Geometry of Quantum Graphical Models (with Eliana Duarte and Maximilian Wiesmann), Advances in Applied Mathematics, 2025. Preprint
• From Feynman Diagrams to the Amplituhedron: A Gentle Review (with Shounak De, Marcus Spradlin and Anastasia Volovich), Special volume on Positive Geometry, Le Matematiche, 2025. Preprint
• Hyperplane Arrangements in the Grassmannian (with Elia Mazzucchelli and Kexin Wang), Special volume on Positive Geometry, Le Matematiche, 2025. Preprint
• On real and observable rational realizations of input-output equations (with Sebastian Falkensteiner and J. Rafael Sendra), Systems and Control Letters, 2025. Preprint
• Santaló Geometry of Convex Polytopes (with Simon Telen), SIAM Journal on Applied Algebra and Geometry, 2025. Preprint
• Gibbs Manifolds (with Bernd Sturmfels and Simon Telen), Information Geometry, 2024. Preprint
• Logarithmically Sparse Symmetric Matrices, Beiträge zur Algebra und Geometrie, 2024. Preprint
• On realizing differential-algebraic equations by rational dynamical systems (with Gleb Pogudin), ACM International Symposium on Symbolic and Algebraic Computation (ISSAC), 2022. Preprint
• From algebra to analysis: new proofs of theorems by Ritt and Seidenberg (with Gleb Pogudin and Yury Razmyslov), Proceedings of the American Mathematical Society, 2022. Preprint