6 papers
Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
Jacob Kryczka, Yuuji Tanaka, Shing-Tung Yau
Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory,…
Tyurin Degenerations, Derived Lagrangians and Categorification of DT Invariants
Jacob Kryczka, Artan Sheshmani
We consider the moduli space of rigidified perfect complexes with support on a general complete intersection Calabi-Yau threefold and its Tyurin degeneration $X\rightsquigarrow…
The -Geometric Hilbert Scheme -- Part I: Involutivity and Stability
Jacob Kryczka, Artan Sheshmani
We construct a moduli space of formally integrable and involutive ideal sheaves arising from systems of partial differential equations (PDEs) in the algebro-geometric setting, by i…
The -Geometric Hilbert Scheme -- Part II: Hilbert and Quot DG-Schemes
Jacob Kryczka, Artan Sheshmani
This is the second in a series of two papers developing a moduli-theoretic framework for differential ideal sheaves associated with formally integrable, involutive systems of algeb…
Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism
Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau
This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement…
Derived Moduli Spaces of Nonlinear PDEs: Singular Propagations
Jacob Kryczka, Artan Sheshmani, Shing-Tung Yau
We construct a sheaf theoretic and derived geometric machinery to study nonlinear partial differential equations and their singular supports. We establish a notion of derived micro…