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## James Eldred Pascoe

Assistant Professor

### Research

Functional Analysis, matrix inequalities, moment problems, several complex variables, noncommutative function theory, multivariable operator theory, real algebraic geometry, random matrix theory and free probability.

### Background

University of Florida, Assistant Professor, 2018-Present

Washington University in St. Louis, National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship 2016-2018 (Mentor: John McCarthy)

Washington University in St. Louis, William Chauvenet Postdoctoral Lecturer 2015-2018 (Mentor: John McCarthy)

University of California, San Diego, PhD, Mathematics 2015 (Advisor: Jim Agler)

University of California, San Diego, MA, Applied Mathematics 2011

University of North Texas, Denton, BS, Mathematics 2010

### For graduate students

If you are a UF graduate student and you want to work with me, send me an email. We have weekly lab meetings, tentatively at 2PM on Fridays. Moreover, you should internalize Mark Thomforde’s guide to being a graduate student. If you are not yet a UF graduate student, send me an email, and apply.

### Current group members

- James Eldred Pascoe
- Tapesh Yadav (2nd Year graduate student)
- Austin Jacobs (3rd Year graduate student)

### Diversity is Strength

The University of Florida maintains a strong commitment to making our campus a welcoming place for all people, especially marginalized groups and traditional outsiders.

### Contact Information

Email: pascoej@ufl.edu

Office Hours: 5 MWF

### 2302syllabus

### Selected Works

[1] Kelly Bickel, J. E. Pascoe, Ryan Tully-Doyle Analytic continuation of concrete realizations and the McCarthy Champagne conjecture. preprint.

[2] J. E. Pascoe Noncommutative free universal mondromy, pluriharmonic conjugates and plurisubharmonicity.* preprint.*

[3] Kelly Bickel, J. E. Pascoe, Alan Sola. Singularities of rational inner functions in higher dimensions. *American Journal of Mathematics*. to appear. (2020)

[4] J. E. Pascoe, Meredith Sargent, Ryan Tully-Doyle. A controlled tangential Julia-Carathéodory theory via averaged Julia quotients. *Analysis and PDE*. to appear. (2020)

[5] Kelly Bickel, J. E. Pascoe, Alan Sola. Derivatives of rational inner functions: geometry of singularities and integrability at the boundary.* Proc. Lond. Math. Soc.* , 116 (2) 281-329 (2018).

[6] John E. McCarthy, J. E. Pascoe. A non-commutative Julia Inequality. *Mathematische Annalen*. , 370 (1-2) 423-446, 2018.

[7] J. E. Pascoe, Ryan Tully-Doyle. Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables. *Journal of Functional Analysis*, 273 (1) 283-328 (2017)

[8] J. E. Pascoe. A wedge-of-the-edge theorem: analytic continuation of multivariable Pick functions in and around the boundary. *Bull. Lond. Math. Soc.*, 49 (5) 916-945, 2017

[9] J. E. Pascoe. The inverse function theorem and the Jacobian conjecture for free analysis.* Math. Z*., 278 (3-4) 987-994, 2014.

For a full list, see my cv.