Irrational Toric Varieties and the Secondary Polytope

Explore the fascinating world of irrational toric varieties in this illuminating lecture by Frank Sottile from Texas A&M University. Delve into the two flavors of classical toric varieties and their applications in mathematics, focusing on the positive real part as the main object of study. Discover Birch's 1963 findings on the homeomorphism between irrational toric varieties and the convex hull of set A. Examine recent developments in the theory of irrational toric varieties associated with arbitrary fans in R^n, including their structure as R^n-equivariant cell complexes. Explore the intriguing parallel between classical theory and irrational projective toric varieties, particularly the homeomorphism between Hausdorff limits and the secondary polytope. Gain insights into this collaborative work with Garcia-Puente, Zhu, Postinghel, Villamizar, and Pir, as Sottile sketches the compelling story of irrational toric varieties in this hour-long presentation from the University of Miami.