ryan tully-doyle   

office:  Maxcy 306

office hours:    TBD


research interests:    functional analysis, operator theory, several complex variables   [ cv ]

teaching: Numerical Analysis

resources:    Wolfram Alpha    ShareLaTeX    LaTeX symbols

conference slides:
AMS Sectional, University of Florida, Nov 2019: A Regal Approach to Loewner's Theorem in Commuting Variables
Fields Institute, Focus Session on Noncommutative Function Theory, June 2019: A Recent History of Loewner's Theorem
Department Seminar, 9/6/18: Is 1 + 2 + 3 + ... = -1/12 (50 minute version)
MAA NES Spring 2018:
Is 1 + 2 + 3 + ... = -1/12? (20 minute version)
IWOTA 2018: Escaping nontangential approach


Refereed journal articles

  1. Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions but those arising from conditional expectations do not (with J. E. Pascoe), to appear, Journal of Mathematical Analysis and Applications, 2019
  2. Representation of free Herglotz functions (with J. E. Pascoe and B. Passer), to appear, Indiana University Journal of Mathematics, 2018
  3. Free functions with symmetry (with J. E. Pascoe, D. Cushing), Mathematische Zeitschrift, 2017
  4. Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables (with J. E. Pascoe), Journal of Functional Analysis, 2017 273(1)
  5. Analytic functions on the bidisk at boundary singularities via Hilbert space methods, Operators and Matrices, 2017 11(1) 55-70
  6. Convex entire noncommutative functions are polynomials of degree two or less (with J.W. Helton, J. E. Pascoe, and V. Vinnikov), Integral Equations and Operator Theory , 2016 86(2) 151-163
  7. Nevanlinna Representations in Several Variables (with J. Agler, N.J. Young), Journal of Functional Analysis, 2016 270
  8. Boundary Behavior of Analytic Functions of Two Variables via Generalized Models (with J. Agler, N.J. Young), Indagationes Mathematicae 2012 23 995-1027
Papers in submission:
  1. The royal road to automatic noncommutative real analyticity, monotonicity, and convexity. (with J. E. Pascoe)
  2. Escaping non-tangentiality: towards a higher order Julia-Caratheodory theory based on amortized tangential approach. (with J. E. Pascoe and M. Sargent).
My mathematical brother: J. E. Pascoe

Linear algebra code examples: solving a system with mathematica

Other work:
Mathematical Cryptography (open textbook in progress, written in python/xml/ PreTeXt) current version: Spring 2019
Numerical Analysis (open textbook in progress, written in octave/xml/ PreTeXt) current version: Fall 2019