Curriculum Vitae

Research Interests

  • Functional analysis, operator theory, operator analysis, free noncommutative analysis
  • Undergraduate mathematical programming, mathematical modeling

Appointments

  • 2020 - present: Assistant Professor, California Polytechnic State University, San Luis Obispo
  • 2017-2020: Assistant Professor, University of New Haven
  • 2019-2020: Assistant Dean, College of Arts and Sciences, University of New Haven
  • 2015-2017: Assistant Professor, Hampton University

Education

  • 2015* PhD Mathematics, University of California, San Diego *(medical leave, 2006-2012)
  • 2001 BS Mathematics, Cal Poly, San Luis Obispo

Publications

  1. Cauchy transforms of colored graphs in two variables (with L. Adlin, G. Thai, and S. Tiscareno). Lin. Alg. Appl. (2026)
  2. Induced Stinesping factorization and the Wittstock support theorem (with J. E. Pascoe). Results in Mathematics (2023)
  3. The royal road to automatic noncommutative real analyticity, monotonicity, and convexity (with J. E. Pascoe). Adv. Math. (2022)
  4. Iteration of low-degree rational inner skew-products on \(T^2\) (with A. Sola). Ann. Polon. Math.
  5. Monotonicty of the principal pivot transform (with J. E. Pascoe). Lin. Alg. Appl. (2022)
  6. Analytic continuation of concrete realizations and the McCarthy champagne conjecture. (with K. Bickel and J. E. Pascoe). Int. Math. Res. Not. (2022) arXiV
  7. Automatic real analyticity and a regal proof of a commutative multivariate Löwner theorem. (with J. E. Pascoe). Proc. Amer. Math. Soc. (2020) arXiV
  8. A controlled tangential Julia-Carathéodory theory via averaged Julia quotients. (with J. E. Pascoe and M. Sargent), Anal. PDE. arXiV
  9. Representation of free Herglotz functions (with J. E. Pascoe and B. Passer). Ind. Univ. J. Math (2019) arXiV
  10. Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions (with J. E. Pascoe). J. Math. Anal. App. (2019) arXiV
  11. Free functions with symmetry (with J. E. Pascoe, D. Cushing). Math. Z. (2017) arXiV
  12. Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables (with J. E. Pascoe). J. Func. Anal. (2017) arXiV
  13. Analytic functions on the bidisk at boundary singularities via Hilbert space methods. Oper. Matrices (2017) arXiV
  14. Convex entire noncommutative functions are polynomials of degree two or less (with J.W. Helton, J. E. Pascoe, and V. Vinnikov). Integral Equations Operator Theory 2016 arXiV
  15. Nevanlinna Representations in Several Variables (with J. Agler, N.J. Young). J. Func. Anal. (2016) arXiV
  16. Boundary Behavior of Analytic Functions of Two Variables via Generalized Models (with J. Agler, N.J. Young). Indag. Math. (2012) arXiV

Preprints

  1. Matrix convex verbatim enumeration functions are graphical (2026) arXiV
  2. Averaged mixed Julia-Fatou type theory with applications to spectral foliation. (with J. E. Pascoe). arXiV

Recent Slides

  1. Enumeration functions of formal languages, JMM 2026, Washington DX slides
  2. Noncommutative realizations and real analyticity, IWOTA 2021, Chapman University slides