Microlocal Analysis, D-Modules, and Alien Calculus | Differential Equations #7
Автор: jetbundle
Загружено: 2026-01-09
Просмотров: 157
In eps. 7, we realize that singularities are not "failures" of the function, but rather geometric objects living in the Phase Space (the Cotangent Bundle). By lifting our perspective from position space to phase space, we can resolve these singularities. We then algebrize this entire structure using D-Modules, turning differential equations into modules over a ring of operators. This culminates in the Riemann-Hilbert Correspondence, which reveals that the "solutions" to a differential equation are actually topological shapes (sheaves) disguised as analysis.
00:00 Intro + Cringe
04:46 Microlocal Analysis
09:51 D-Modules
18:46 Riemann-Hilbert Correspondance
21:17 Alien Calculus
26:29 Topological Quantum Field Theory
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