Midwest Workshop on Schubert Calculus

Ohio State University, The, Columbus OH

Investigators

Abstract

This award provides travel and lodging support for participants in a Workshop on Schubert Calculus, to take place May 9-12, 2018, at the Ohio State University in Columbus, Ohio. The topic of the conference has its origins in 19th century enumerative geometry, when mathematicians computed numbers of geometric figures satisfying various conditions. The subject grew into a testing ground for Intersection Theory, which is now a cornerstone of modern mathematics. This workshop will bring together researchers and students coming from different backgrounds, to present various points of view on the subject of Schubert Calculus. A large part of Schubert Calculus concerns the cohomology rings of Grassmannians and flag manifolds, as well as their generalizations. The subject has deep connections to combinatorics, representation theory, and algebraic geometry, and the last 15 years have seen remarkable developments in the techniques of Schubert Calculus. A guiding problem is to find combinatorial formulas for the multiplication of Schubert classes in flag varieties; several new cases of this problem were solved. New research has extended our understanding of Schubert calculus to the infinite-dimensional affine (and Kac-Moody) flag varieties, simultaneously deepening the connection with representation theory. Major goals of this conference include sharing new results and introducing a new generation of students to the techniques, applications, and open problems in the field. More details about the workshop are available at https://people.math.osu.edu/anderson.2804/schub2018.html. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.