Welcome! I am a Professor in the School of Mathematics, Harbin Institute of Technology.
*I am now recruiting: postgraduate students and postdoctoral researchers.
My research takes place at the interface of the (formal) geometric theory of nonlinear 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 of 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 nonabelian Hodge theory.
If these topics interest you, or you would like to work with me, please contact: jlastname (at) hit.edu.cn.
Feel free to attend upcoming talks:
From Nonabelian Hodge Theory to Derived Kahler Geometry: YMSC Seminar on Complex Algebraic Geometry, Tsinghua University, May 8, 2026.
Differential Algebraic Stability Conditions: Department of Math, University of Kyoto (RIMS), February 20, 2026.
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
Previously: Before joining HIT I was a member of the Theory of Atoms research group 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).
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.