Volumes of Sublevel Sets of Homogeneous Polynomials
summary
Computes volumes of sublevel sets {x: p(x) ≤ t} for homogeneous polynomials p by relating them to integrals and moment sequences; uses moments and convex optimization tools (e.g., semidefinite programming) to approximate or compute these volumes. Discusses how homogeneity simplifies the problem and enables practical volume computation via moment/SDP hierarchies.
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chapters (9)
- 0:00Introduction
- 3:00Sublevel set volumes
- 8:51Optimization problems
- 14:17Calculation methods
- 20:15Applications and examples
- 26:42Challenges and limits
- 31:13Mapping tools digression
- 35:00Conclusion
- 35:45Q&A
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