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My research concerns mirror symmetry and logarithmic and toric geometry. My PhD at Cambridge, supervised by Mark Gross, studied the relationship between the Gross–Siebert toric-degeneration mirror construction and intrinsic mirror symmetry using punctured logarithmic Gromov–Witten invariants.
My preprint, Mirrors to toric degenerations via intrinsic mirror symmetry, develops this relationship for K3 surfaces and explores extensions towards higher dimensions.
Current research
I am developing two manuscripts extending questions from my PhD: one on log-smooth resolutions of toric degenerations in arbitrary dimension, and another on functoriality of the Gross–Siebert mirror construction. My broader research direction aims at the full extension of this mirror correspondence to higher dimensions.
I use AI-assisted exploration and computation in this work, coordinating parallel investigations, comparing approaches, checking the scope and dependencies of proposed proofs, and integrating results into coherent manuscripts.
Pure mathematics
2026. Mirrors to toric degenerations via intrinsic mirror symmetry, arXiv:2608.07381 [math.AG].
2019. Coulomb branch of a multiloop quiver gauge theory, Functional Analysis and its Applications 53, arXiv:1903.05822 [math.AG] (with M. Finkelberg).
In preparation
2026. Log-Smooth Resolutions of Special Toric Degenerations.
2026. The Zoo of K3 Degenerations and the Co-zoo of Gross–Siebert Mirrors.
Quantitative finance and applied mathematics
My work at Matlogica focused on mathematical and computational methods for pricing, risk and numerical optimisation.
2023. Automatic Adjoint Differentiation for special functions involving expectations, Journal of Computational Finance 27(2), arXiv:2204.05204 [q-fin.CP] (with J. Brito and A. Goloubentsev).
2022. Modifications to a classic BFGS library for use with SIMD-equipped hardware and an AAD library, arXiv preprint, arXiv:2209.14928 [q-fin.CP] (with A. Rodrigues).
2017. Permissible risk of operated facilities: Assessment methodology, Problems of Risk Analysis 14(4) (with I. N. Ivashchenko, K. I. Ivashchenko and L. V. Komelkov).
Expository work and translations
2018. Weil Conjectures Exposition, arXiv:1807.10812 [math.AG].
2018. Weil Conjectures I (English translation of Pierre Deligne’s La Conjecture de Weil I), arXiv:1807.10810 [math.AG].
Theses and essays
PhD dissertation, Cambridge, 2023: Mirrors to Toric Degenerations via Intrinsic Mirror Symmetry.
Part III essay, Cambridge, 2019: The Foundations of Logarithmic Geometry.
BSc thesis, HSE, 2019: Coulomb Branch of a Multiloop Quiver.
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