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SUMMARY:Jacob Kryczka
DTSTART:20250219T162000Z
DTEND:20250219T180000Z
DTSTAMP:20260423T010528Z
UID:GDEq/125
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDEq/125/">S
 ingularities and Bi-complexes for PDEs</a>\nby Jacob Kryczka as part of Ge
 ometry of differential equations seminar\n\n\nAbstract\nMany moduli spaces
  in geometry and physics\, like those appearing in symplectic topology\, q
 uantum gauge field theory (e.g. in homological mirror symmetry and Donalds
 on-Thomas theory) are constructed as parametrizing spaces of solutions to 
 non-linear partial differential equations modulo symmetries of the underly
 ing theory. These spaces are often non-smooth and possess multi non-equidi
 mensional components. Moreover\, when they may be written as intersections
  of higher dimensional components they typically exhibit singularities due
  to non-transverse intersections. To account for symmetries and provide a 
 suitable geometric model for non-transverse intersection loci\, one should
  enhance our mathematical tools to include higher and derived stacks. Seco
 ndary Calculus\, due to A. Vinogradov\, is a formal replacement for the di
 fferential calculus on the typically infinite dimensional space of solutio
 ns to a non-linear partial differential equation and is centered around th
 e study of the Variational Bi-complex of a system of equations. In my ta
 lk I will discuss a generalization in the setting of (relative) homotopica
 l algebraic geometry for possibly singular PDEs.\n\nThis is based on a ser
 ies of joint works with Artan Sheshmani and Shing-Tung Yau.\n
LOCATION:https://researchseminars.org/talk/GDEq/125/
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