Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Grassmannians

Seminar | February 6 | 5-6 p.m. | 939 Evans Hall

 Charles Wang, UC Berkeley

 Department of Mathematics

Grassmannians serve as a useful parameter space for objects satisfying some geometric conditions. For example, we may ask given four general lines in $\mathbf {P^3}$, how many lines meet all four? We will answer this question by studying the Chow rings of $\mathbf { G}(1,3)$, the space of lines in 3-space. Afterwards, we will introduce the Schubert Calculus, which answer more general questions of this form, and describe a combinatorial approach to understanding these questions.