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: Spring 2016, Thursdays, Blocker 506A, 4:00-4:50 PM

Next Talk

Speaker:   Cameron Farnsworth

Title:   Symmetric border rank of the determinant and Young flattenings

Time / Date:   4:00 - 5:00 , April 14

Abstract

In the late 1700's Edward Waring posed a question regarding writing natural numbers as sums of ${\scriptstyle d}$-th powers of natural numbers. Since the formulation of this problem many variants have been devised. In particular, any homogeneous complex degree ${\scriptstyle d}$ polynomial may be written as a linear combination of ${\scriptstyle d}$-th powers of linear forms. The symmetric rank or Waring rank of a homogeneous degree ${\scriptstyle d}$ polynomial ${\scriptstyle P}$ is the minimum number of terms needed to write a polynomial this way. The polynomial Waring problem asks for an explicit polynomial ${\scriptstyle P}$, what is its symmetric rank?

In this talk, we define a geometric variant of symmetric rank called symmetric border rank that allows us to work with the tools of algebraic geometry. We use the method of Young flattenings defined by Landsberg and Ottaviani to prove new lower bounds for the symmetric border rank of the polynomial ${\scriptstyle \det_n}$ obtained from the determinant of an ${\scriptstyle n\times n}$ matrix of indeterminates.