Welcome! I am currently a member of the Theory of Atoms research group of Prof. Ludmil Katzarkov at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Before that I was a post-doc in the Algebraic Geometry group at BIMSA (Beijing Institute of Mathematical Sciences and Applications). My mentors were Prof. A Sheshmani and Prof. S.-T. Yau.
I am working at the interface of the (formal) geometric theory of non-linear partial differential equations and derived algebraic and analytic geometry. I am interested in applying tools from higher homotopy theory and derived geometry to study moduli spaces of solutions to non-linear PDEs with the aim to better understand their singularities. I am seeking applications to enumerative algebraic geometry, categorified DT-theory and homological mirror symmetry. More recently I am studying questions related to stability from the differential-algebraic perspective, with a view towards answering questions in birational geometry.
Please feel free to contact me: jlastname (at) math.bas.bg, or attend upcoming talks:
Differential Algebraic Stability Conditions, The 10th International Congress of Chinese Mathematicians (ICCM, 2025) January 04, 2026, Shanghai, China.
(An invitation to...) Differential Algebraic Stability Conditions: Harbin Institute of Technology (HIT), December 28, 2025.
Differential Algebraic Stability Conditions: BIMSA Second Post-doc Workshop, December 23, 2025.
Differential-algebraic stability conditions and Birational Geometry (HSE-BIMSA Conference in Geometry and Physics), November 10-14 2025, Moscow, Russia
Homotopy Methods in the Geometric Theory of PDEs (Celebrating the Consortium IMSAC and Geometry at Large, Sofia and Burgas, Bulgaria), August 5-9 (Abstracts) and 11-14, 2025 (Conference Poster)
Singularities and Bi-complexes for PDEs (J. Krasil'shchik's Geometry of Differential Equation Seminar), February 19, 2025
Non-linear PDEs and Secondary Calculus via Derived Algebraic Geometry (BIMSA Algebraic Geometry Seminar), December 12, 2024
D-ideal sheaves, D-Hilbert scheme, and enumerative geometry of Nonlinear PDE (HSE-BIMSA Conference in Algebraic Geometry and Mathematical Physics), November 5-9, 2024, Moscow, Russia
Moduli Stacks of Solutions to Non-linear PDES and their related Singularities (SIMIS Seminar on Derived and Non-commutative Geometry), 16:00-19:00, Sept. 16, 2024, Shanghai, China
Derived Geometry and Non-linear PDEs (Physics LATAM Seminar), August 07,09, 2024
I am also interested in the following broad topics:
Homotopy theory, algebraic (co)operads, properads and up-to-homotopy algebraic structures
Shifted Poisson/Symplectic structures and derived algebraic geometry; how they naturally appear in classical field theories.
Categorification
My Curriculum Vitae.
More detailed information is available here.
I am interested in the search for a conceptual and axiomatic framework for studying ubiquitous structures in mathematics and physics in a unified way.
From the viewpoint of jet-spaces and Diffieties.
More generally, I am interesting in homotopy coherent mathematics.
More than anything else, I am interested in the amalgamation of all the above topics and their potential use in studying various problems in theoretical physics, in particular, quantum field theory.
My office is A3-4-209, stop by anytime for discussions!