The PIMS Postdoctoral Fellow Seminar: Meredith Sargent

I will give a very broad overview discussing various uses and generalizations of the shift operator (and its adjoint). In the classical case we consider the Hardy space of analytic functions on the complex disk with square summable Taylor coefficients. The shift operator is simply multiplication by z and this "shifts" the coefficients of the function. The backward shift does the opposite, and in the case of the Hardy space, it's actually the adjoint of the shift. (This doesn't happen in every function space!) There are many classical results about subspaces that are invariant under the shift or its adjoint and connecting these to functions and operators. I'll discuss some of the generalizations of the shift operators and some of my recent and current projects and how they connect to the classical theory.

Speaker biography: Meredith Sargent received her PhD from Washington University in St. Louis in 2018. Her thesis work was about Dirichlet series (generalizations of the Riemann zeta function), their integrals on vertical lines, and how these connect to integrals on the infinite polytorus. She then worked as a Visiting Assistant Professor at the University of Arkansas from 2018-2021 where she focused on optimal polynomial approximants in several variable contexts. Since Fall 2021, she has been a PIMS postdoctoral fellow at the University of Manitoba working with Robert T. W. Martin on problems about analytic functions of non commuting variables. She also organizes the Manitoba eXperimental Mathematics Laboratory, modeled on the program at the University of Washington for undergraduate research and is supervising students this semester.

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This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.