J. E. Pascoe's homepage

About me

Photo by Ivonne Vetter at MFO in 2013.

I am currently a fifth year graduate student in the Mathematics Department at the University of California, San Diego. My email is jpascoe@math.ucsd.edu. I am a student of Jim Agler.

Research

I work on several complex variables, operator theory, and several noncommuting variables. Some of my past work has dealt with:

Boundary behavior multivariable Pick funtions (sometimes called Nevanlinna functions.)
Operator monotone functions in several variables.
Invariant theory for free polynomials.
The Jacobian conjecture for free polynomials.

See my papers for details.

Papers

The inverse function theorem and the Jacobian conjecture for free analysis Math. Z. (2014)

Preprints

A detailed wedge-of-the-edge theorem
An inductive Julia-Caratheodory theorem
Note on Löwner's theorem on matrix monotone functions in several commuting variables of Agler, McCarthy and Young submitted
(With David Cushing and Ryan Tully-Doyle) Free functions with symmetry submitted
(With Ryan Tully-Doyle) Free Pick functions submitted
On the continuation of locally operator monotone functions submitted

Slides

Using operator theory to measure the asymptotic behavior of Pick functions in two variables at infinity Joint Math Meeting 2015: AMS Special Session on Multivariable operator theory
Free Functions with Symmetry Joint Math Meeting 2015: AMS Special Session on Noncommutative function theory
A wedge of the edge of the wedge ICMS 2014: Function theory in several complex variables in relation to modelling uncertainty
Hankel vector moment sequences Great Plains Operator Theory Symposium 2014
Matrix monotonicity in several noncommuting variables St. Louis AMS Sectional Meeting 2013
Injective free polynomials Hilbert Function Spaces 2013