Research

I am working 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. At the moment I am mostly engaged with writing up a thesis that will include the cases of elliptic curves and K3 surfaces, and a detailed sketch with partial results in all dimensions. Several papers based on the thesis will be released in due time. More broadly, I am interested in logarithmic geometry with an emphasis on logarithmic Gromov-Witten theory.

I am also passionate about research in the applications of mathematics to quantitative finance, performing this research as part of my work at MatLogica.

Publications:

• 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).

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

Papers in Applied Mathematics:

• 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).

• Automatic Adjoint Differentiation for special functions involving expectations, ArXiv e-prints (2022), arXiv:2204.05204 [q-fin.CP] (with J.Brito and A.Goloubentsev).

• 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).