April 3, 2023
Allen Knutson to present annual Friends of Mathematics Lecture
Allen Knutson, professor of mathematics at Cornell University, will present a colloquium titled "Schubert Calculus and Puzzles" as part of the Mathematics Department Colloquium Lecture seriesat 2:30 p.m. April 4 in 102 Cardwell Hall.
The abstract for the lecture is: Two lines in the plane cross at one point; four lines in space cross how many other lines? The answer is two. Questions of this sort — with higher-dimensional subspaces in higher-dimensional ambient spaces — first studied systematically by Schubert in the 19th century, motivated Hilbert's 15th problem and from there the development of algebraic topology. At this point, it is easy to compute any one of these intersection numbers as an alternating sum, and the game has moved to computing them in manifestly positive ways.Knutson willtalk about the 21st-century developments, and in particular, how to solve many versions of these Schubert problems by counting "puzzles."
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