I would like to do a reading with some students about the numerical range and pseudospectra of operators. We will start by looking at matrices, and if time we will then see how what we have learned about matrices may apply to infinite-dimensional operators. By the end of this reading students will learn about the pseudospectrum and numerical range of matrices (finite-dimensional operators). These measurements are useful for approximating the spectrum, or set of eigenvalues, of matrices. If time permits, students may also begin to look into what these definitions mean for infinite-dimensional operators

• References: Lecture Notes on Spectra and Pseudospectra of Matrices and Operators by Arne Jensen
• Prerequisites: Linear Algebra. Analysis would be helpful, but not required.
• Meetings: Once per week from Oct 1 to Dec 15, 2022
• Type: Reading
• Size: 3-4 students

Instructor: Jeremy Upsal, Applied Mathematics, University of Washington