Welcome to the home page of the Mathematics Graduate Student Organization (MGSO) at Texas A&M University in College Station. The purpose of this organization is to encourage communication among students, faculty, and staff, and contribute to a rich social life in the department through cultural and scientific dialogue. We would also like to provide an environment where students in the mathematics department can practice their presentation skills as well as view the techniques of others. It is our goal to be a source of support and information for all graduate students.
The main activity of the MGSO is the Graduate Student Seminar. This seminar is for grad students, (largely) by grad students: Volunteer to give a talk!
Seminar: Fall 2014, Thursdays, Blocker 506A, 4:00-4:50 PM
Speaker: Prof. Colleen Robles
Title: Flag varieties, Schubert subvarieties, and a canonical system of differential equations.
Time / Date: 4:00 - 5:00 , October 30
Flag varieties (aka flag manifolds) are ubiquitous. Examples include the grassmannians Gr(k,n) of k-dimensional subspaces in complex n-space. Schubert subvarieties play an indispensable role in the geometry, representation theory and combinatorics associated with flag varieties. I will discuss an instance of this phenomenon in which the Schubert subvarieties tell us a great deal about a differential system on the flag variety.
Each flag variety is a homogeneous manifold G/P. The differential system we will consider may be characterized as the unique, minimal, bracket-generating G-homogeneous distribution on G/P. (All these words mean that the system is a very natural object of study. For example, this system is the differential constraint governing variations of Hodge structure.)
I will introduce flag varieties, their Schubert subvarieties and this canonical system; discuss several illuminating examples; and indicate how the Schubert varieties help us understand the solutions of the system.