graduate student seminar - Michael Glasner and Noam Kolodner

Mon, 24/05/202116:00-18:00
Manchester faculty room

The first talk 16:00-17:00 will be by Michael Glasner.

Title: Ladder OperatorsAbstract: Since its discovery quantum mechanics has been the inspiration for many mathematical theories. We will study one such example, namely the stationary Schrodinger equation for the harmonic oscillator. We will attempt to solve this equation and in the process discover a rich algebraic structure that describes the spectral properties of some differential operators. This will allow us to solve this differential equation in a very non-standard way, obtaining results which are interesting in their own right such as the orthogonal basis of Gauss Hermite functions for L_2(R). If time permits we will also discuss Irreducible representations of the Lie algebra SU(2) where similar algebraic structures play a central role.

The second talk 17:00-18:00 will be by Noam Kolodner.

TitlePlucker coordinates
AbstractIn this lecture I am going to talk about a classic subject from algebraic geometry called the plucker coordinates. I am going to address this subject as if it were an advanced subject in linear algebra.

Let n,m be natural numbers such that m is greater or equal to n. Let M be an n*m matrix with rank n. Calculate all the m choose n , n by n minors of M. In the lecture I will answer the following questions: What information can we learn about the original matrix M by the collection of n by n minors? How do we reconstruct this information about the original matrix? If we consider M to be a system of linear equations what information can we gather about the space of solutions? Given a collection of m choose n numbers can one determine whether or not this collection arises as a set of n by n minors of a n*m matrix?
All these questions have vary nice and somewhat surprising answers. The proofs include some beautiful tricks using determinants.