I worked on the Gross-Siebert program in mirror symmetry, developing the relationship between classical mirror symmetry constructions (Batyrev-Borisov, toric degenerations) and a general construction using punctured logarithmic Gromov-Witten invariants. My PhD dissertation establishes the correspondence in the cases of elliptic curves and K3 surfaces, and gives a detailed sketch with partial results in all dimensions. Several papers based on the dissertation will be released soon.
I am also passionate about research in quantitative finance, which I performed while working at MatLogica.
Publications:
Preprints expanding on the PhD dissertation (in preparation).
Coulomb branch of a multiloop quiver gauge theory, Functional Analysis and its Applications 53 (2019), arXiv:1903.05822 [math.AG] (with M.Finkelberg, based on my bachelor thesis).
Papers in Quantitative Finance & Applied Mathematics:
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).
Modifications to a classic BFGS library for use with SIMD-equipped hardware and an AAD library, ArXiv e-prints (2022), arXiv:2209.14928 [q-fin.CP] (with A.Rodrigues).
Permissible risk of operated facilities: Assessment methodology, Problems of risk analysis (2017), see here (with I.N. Ivashchenko, K.I.Ivashchenko, and L.V. Komelkov).
Expository papers and translations:
Weil Conjectures Exposition, ArXiv e-prints (2018), arXiv:1807.10812 [math.AG].
Weil Conjectures I (translation of La Conjecture de Weil I by Pierre Deligne), ArXiv e-prints (2018), arXiv:1807.10810 [math.AG].
Bachelor thesis: Coulomb Branch of a Multiloop Quiver
Part III Essay: The Foundations of Logarithmic Geometry
PhD dissertation: Mirrors to Toric Degenerations via Intrinsic Mirror Symmetry