Wrap Session part 2

on YouTube ↗01h 10m

" summary

Argues that Newton degenerations of symbolic determinants coming from quiver semi‑invariants sit inside the orbit closure of the determinant, and constructs those symbolic determinants (CV_Q,α,β) from quivers so their Newton faces produce explicit orbit‑closure points. Conjectures: the Newton degenerations lie in VP exactly for tame/finite quivers and fail for wild quivers, with wildness causing exponential circuit blowup. Relies on perfect matching polytope / Edmonds‑style membership being in P; proves that when those combinatorial memberships hold, each face yields a small circuit. Open problems: generalize Edmonds to tame quivers and settle membership/NNL complexity.

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" chapters (15)

1. 0:00Quiver theory and orbit closures
2. 0:30Newton degenerations and determinant orbits
3. 7:58Semi-invariants of wild quivers
4. 15:08Tame versus finite type quivers
5. 17:39Edmonds' theorem and matchings
6. 24:04Newton polytopes and VP conjecture
7. 28:44Complexity class implications
8. 31:10Open problems on polynomials
9. 37:45Orbit closures of symmetric polynomials
10. 43:21Lower bound methods framework
11. 49:52Border rank versus maximum rank
12. 56:03KP and P classes
13. 57:54Polynomials on low-dimensional subspaces
14. 1:03:46Explicit constructions and questions
15. 1:07:40Closing remarks