REU at Kent State University

Mailing address

Contact

Projects

Maps on matrices (Misha Chebotar) Description (in pdf) In many problems that appear in algebra and analysis it is required to describe maps satisfying certain properties. Matrix algebras serve as a perfect playground for testing such problems. This project is an instance of so-called Linear Preserver Problems, an active research area in matrix and operator theory.

Gersgorin-type Methods (Laura Smithies) Description This project will have strong components of both theory and application. Our focus will be techniques in eigenvalue estimation. We will begin with some introductory material and theoretical background development. We will discuss some of the many applications of eigenvalues in math and science, and look at some current research in eigenvalue estimation.

Lagrange Polynomials in Linear Algebra (Jenya Soprunova) Jordan normal form of a matrix is a very important tool in linear algebra. Unfortunately, there is no easy way to explain Jordan normal form and it's often skipped in introductory level linear algebra courses. We will follow a recent unpublished book by Askold and Irina Khovanskii to study how one can instead use interpolating Lagrange polynomial in such an important application as solving linear differential equations with constant coefficients. In the book the authors also apply this method to finding formulas for solving quadratic, cubic, and quartic polynomials, solving recurrence relations, finding the inverse of a matrix, as well as entire or meromorphic functions of a matrix. We will then try to apply this method in other problems where people traditionally use Jordan normal form.

Matrices and Tensors with Small Norm (Andrew Tonge) Description (in pdf)