Interpolation for Polynomials in Two Variables

Explore the intricacies of polynomial interpolation in two variables through this comprehensive 53-minute conference talk delivered by Rick Miranda, President of Colorado State University, at the WIMSA Inaugural Conference 2022. Delve into a wide range of topics, including general setup, naive dimension counts, the Picard Group, and the Intersection Form. Examine virtual and expected dimensions, Segre's Conjecture, and the SGHH Conjecture. Investigate Nagata's Conjecture, effective classes, and the Interesting Cones. Learn about the Cone Theorem, extremal rays, and the Nefness Lemma. Discover good and wonderful rays, the A-Conjecture, and examples of good rays. Gain insights into the outline of the proof and additional supporting evidence in this in-depth exploration of advanced mathematical concepts.

Intro
General setup
Naive dimension counts
The Picard Group
The Intersection Form
Virtual and Expected Dimension
Segre's Conjecture
SGHH Conjecture
Nagata's Conjecture
Effective classes
The Interesting Cones
The Cone Theorem
Cones, Extremal Rays
The Nefness Lemma
Good and Wonderful Rays
The A-Conjecture
Examples of Good Rays
Outline of the proof
A bit more evidence