SIMIS Seminar on Derived and Noncommutative Geometry：Moduli Stacks of Solutions to Non-linear PDES and their related Singularities

Speaker: Jacob Kryczka (BIMSA)

Abstract: Many moduli spaces in geometry and physics, like those appearing in symplectic topology, quantum gauge field theory and in relation to homological mirror symmetry, are constructed as parametrizing spaces of solutions to nonlinear differential operators modulo symmetries of the underlying theory.

These spaces are often not smooth, with multi non-equidimensional components, and in cases where they are given as intersections of higher dimensional components they exhibit singularities due to non-transverse intersections.

This suggests that one should treat such spaces within the framework of higher and derived differential/algebraic geometry.

In this talk I will explain some PDE theoretic notions in these contexts and discuss necessary ingredients for posing parameterized global generalized Cauchy problems.

Time: 16:00-19:00 (with tea break), Wednesday, Sept. 18, 2024

Location: Room 1410, Block A, No. 657 Songhu Road, Yangpu District, Shanghai