Beijing Institute of Mathematical Sciences and Applications

Kenji Fukaya , Lynn Heller , Sebastian Heller , Kotaro Kawai , Enric Sole Farre

Artan Sheshmani

Tuesday, April 7, 2026 2:30 PM - 4:30 PM

A3-4-301

Zoom 293 812 9202 (BIMSA)

We report on recent series of joint works with Jacob Kryczka and Shing-Tung Yau on construction of derived moduli spaces of solutions to nonlinear PDE. We construct a parameterizing space of ideal sheaves of involutive and formally integrable non-linear partial differential equations in the algebraic-geometric setting. We elaborate on the construction of a D-geometric analog of Grothendieck's Quot (resp. Hilbert) functor and prove that its is represented by a D-scheme which is suitably of finite type. A natural derived enhancement of the so-called D-Quot (resp. D-Hilbert) moduli functor is constructed and its representability by a differentially graded D-manifold with corresponding finiteness properties is studied. If time permits, we further elaborate on how this technology leads to construction of derived Donaldson-Uhlenbeck-Yau (DUY) correspondences, which is a series of joint works in progess.

Artan Sheshmani is a Professor of pure Mathematics, specialized in Algebraic geometry, Enumerative and Derived Geometry, and Mathematics of String Theory. He joined BIMSA as a Professor in September 2023. Prior to BIMSA he was a senior personnel at Simons Collaboration Program on Homological Mirror Symmetry at Harvard University Center for Mathematical Sciences and Applications (CMSA) for 7 years, during a portion of which he was jointly an Associate Professor of Mathematics at Institut for Mathematik (formerly the Center for Quantum Geometry of Moduli Spaces) at Aarhus University in Denmark (2016-2022). He is working on geometry of moduli spaces of sheaves and curves from enumerative geometry point of view as well as studying their structural properties from derived geometry and geometric representation theory point of view.