Applied math seminar, Jeremy Upsal, Department of Applied Mathematics, U. of Washington
Event Type:
Seminar
Speaker:
Applied math seminar, Jeremy Upsal, Department of Applied Mathematics, U. of Washington
Event Date:
Monday, November 8, 2021 -
3:30pm to 4:30pm
Location:
Zoom Meeting
Audience:
General PublicFaculty/StaffStudentsAlumni/Friends
Sponsor/s:
Pavel Lushnikov
Event Description:
Title: Establishing and using a nonlinear Gershgorin theorem for operator matrices to solve ODEs with parameter dependence
Abstract: The connection between linear-algebra and differential equations is one that we learn about early on in our undergraduate education. One connection that is not commonly made/taught is the connection between an ODE with parameter dependence and the corresponding spectral (or eigenvalue) problem. Indeed, these ODEs can often be difficult to solve and are often skipped in introductory classes on differential equations. In this talk I will introduce and utilize this connection to garner information about ODEs through the use of linear-algebra and operator-theory theorems, particularly theorems related to the famous linear algebra Gershgorin Disk Theorem. After demonstrating the efficacy of known theorems, I will demonstrate a problem coming from the theory of integrable PDE theory for which no known (to me) theorems apply. This problem is related to the stability of solutions of the sine-Gordon equation. I will then establish a new theorem, a Gershgorin-type theorem for operator-valued nonlinear eigenvalue problems, which can be used to overcome this road block.
Bio: Dr. Jeremy Upsal grew up in Santa Fe, New Mexico, so he is very excited to be giving a talk at UNM. After graduating from high school in Santa Fe, Jeremy earned his BS in Applied Math from the University of Colorado at Boulder. In 2014, Jeremy began his PhD studies in Applied Math at the University of Washington. Jeremy graduated from the University of Washington in 2020 under the advice of Bernard Deconinck. Jeremy’s thesis and primary work is on the stability of stationary solutions of integrable PDEs.
