Rouquier Dimension Equals Krull Dimension for Toric Varieties

Explore the relationship between Rouquier dimension and Krull dimension in toric varieties through this 57-minute lecture by David Favero from the University of Alberta. Delve into the generalization of projective dimension through Rouquier dimension in triangulated categories and examine Orlov's conjecture, which posits the equality of Rouquier dimension in a variety's derived category to its Krull dimension. Learn about the recent proof of this conjecture for toric varieties, achieved through homological mirror symmetry, as presented in joint work with Jesse Huang. Gain insights into how this result can be interpreted as a multi-graded version of Hilbert's syzygy theorem, advancing our understanding of algebraic geometry and category theory.