Newton-Okounkov Bodies
- Event Type
- Seminar/Symposium
- Sponsor
- Algebra, Geometry, Combinatorics Seminar
- Location
- 3217 Everitt
- Date
- Sep 14, 2023 3:00 pm
- Speaker
- Ian Cavey (UIUC)
- Contact
- Alexander Yong
- ayong@illinois.edu
- Views
- 68
Newton-Okounkov Bodies are convex sets in Euclidean space that encode (asymptotic) information about sections of line bundles on algebraic varieties. This construction depends on a non-canonical choice of valuation on the function field of the variety. For example, Gelfand-Tsetlin polytopes and Feigin–Fourier–Littelmann–Vinberg polytopes can both be realized as Newton-Okounkov bodies of the same line bundles on flag varieties for different choices of valuations. In this talk, I will explain the construction of Newton-Okounkov bodies, their basic properties, and what kinds of problems they are useful for.