Twisted foldings and double moment graphs

Schubert calculus is a well-established area of modern geometry that studies configurations and intersections of linear subspaces. Since its invention more than a century ago, it became one of the fundamental tools in different areas of mathematics, physics and computer science that deal with solving various types of linear equations. A typical question which is addressed by the methods of Schubert calculus can be stated as: How many parameters one needs to describe general solutions to a given system of linear equations satisfying some linear boundary conditions. The proposed project is dedicated to developing new formulas and algorithms that help to establish new relations between linear systems associated to different configurations of the so called root vectors.

In simple words, we look at certain configuration of vectors that are stable under reflections (the root system). To each such configuration we assign a system of linear equations (global sections of structure sheaf on the moment graph). Folding this configuration of vectors into a smaller one (performing the twisted folding) we obtain smaller system of linear equations. Solving the latter, one recovers most of the solutions of the original (large) system. TO BE CON’T

Faculty Supervisor:

Kirill Zaynullin

Student:

Partner:

Università degli Studi di Roma Tor Vergata

Discipline:

Mathematics

Sector:

Education

University:

University of Ottawa

Program: