About me
I am an Assistant Professor of Mathematics at Drexel University (Fall 2022-Present).
Previously, I was an Assistant Professor at the University of Florida from 2018-2022. I was a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow and William Chauvenet Postdoctoral Lecturer at Washington University in St. Louis (2015-2018).
I obtained my Ph.D. in Mathematics at the University of California, San Diego under Jim Agler in 2015. Prior to my Ph.D., I obtained an M.A. in Applied Math from UCSD in 2011, and my B.S. at the University of North Texas in 2010.
Email: jep362@drexel.edu
Research & Grants
Fields of Research Interest:
My research is predominantly in Hilbert space geometry and functional analysis.
Grants:
- "Local and algebraic phenomena in noncommutative function theory"
Binational Science Foundation Grant 2022235 (2024-present)
($172,899 USD, co-PI Eli Shamovich). This grant bridges the US and Israeli mathematical communities, funding deep structural investigations into the local behavior of noncommutative functions. - "Matrix Analysis for the 21st Century"
National Science Foundation Grant DMS-1953963 (2020-2023) and DMS-2319010 (2023-2024)
Supporting foundational research in multivariable operator theory, free probability, and the geometry of polynomials. - "The 38th Southeastern Analysis Meeting (SEAM)"
National Science Foundation Grant DMS-2154455 (2022-2023)
($33,400 USD, co-PIs Michael Jury and Scott McCullough). Facilitating the gathering and cross-pollination of regional and international analysts. - National Science Foundation Mathematical Sciences Postdoctoral Research Fellow
DMS-1606260 (2016-2019)
Postdoctoral support hosted at Washington University in St. Louis under the mentorship of John McCarthy.
I recommend reading about complete discrete Schoenberg-Delsarte theory if you desire joy.
Games, Strategy & Outreach
Mathematical thinking extends beyond the chalkboard. It thrives in systems of incomplete information, strategic resource management, and community cross-pollination. Below are links to games I have developed, as well as resources for my favorite card game, Bridge.
Original Games
- Wolfjack: A variation on honeymoon spades. (Developed with Geoffrey Hutinet Pascoe.)
- Airport Game: A variation on Uno. (Developed with Corey Stone.)
Bridge Resources
- Learn to Play Bridge: The ACBL's official interactive learning portal.
- Bridge Base Online (BBO): The premier platform for daily play and tournaments.
Community Outreach
Teaching Bridge is a powerful mechanism for combating cognitive decline and social isolation in older adults.
- PA Department of Aging - Volunteer Services: Connect with local Pennsylvania Area Agencies to teach specialty mind-stimulating games.
- AmeriCorps RSVP: A national network matching volunteers 55+ with community needs.
Global Nodes & Mathematical Cross-Pollination
Mathematics thrives as a complete graph, requiring constant flow between disparate physical and intellectual nodes. Below are the regions where I have spent significant time developing operator theory, alongside curated funding mechanisms and the key human collaborations that anchor these local graphs.
India
- Fulbright-Nehru Fellowships
- VAJRA Faculty Scheme
- Indo-US Science and Technology Forum
- CMI Banff satellite
Local Collaborators & Coauthors:
Tirthankar Bhattacharyya Chandan Pradhan Tapesh Yadav Sourav Pal Nitin Tomar Sujit S. Damase
Israel
Slovenia
Mathematics outside the world of forms
Mathematical progress is supported by a robust network. For each generation, new ideologies challenge our ability to constructively collaborate. Moreover massive amounts of mathematical talent goes underutilized due to the disregard and squabbles of the impure, as it were.
We wholeheartedly endorse the notion that no public-sector pure mathematicial contributions or collaborations should be rejected based upon the identity, deeds, (wicked or righteous) or beliefs (idiotic or profound) of the authors or the sponsors. Pure mathematics has no place in the often gangster world of politics and force, and vice versa. We strongly encourage mathematicians to cease such activities, to reject ideology, and to circumvent them by being the link between groups who have not reached a stage where they have the ability and will.
Mathematics saves lives.
We follow these axioms:
- To waste mathematical potential is morally wrong.
- Cultivation of pure mathematics is the fundamental human responsibility.
- Mathematics is not a tool.
- Every mathematician deserves to maximize their mathematical potential.
Prospective Graduate Students (PhD)
I am actively looking for motivated graduate students to join my research group at Drexel University. If you are interested in operator theory, noncommutative function theory, free probability, or related fields in analysis and algebra, I encourage you to apply to our PhD program.
- The Program: The Drexel Mathematics PhD program offers rigorous training and opportunities to engage in cutting-edge research in the heart of Philadelphia.
- Funding: Admitted PhD students are typically fully funded through Teaching Assistantships or Research Assistantships, which include a competitive stipend, full tuition remission, and a health insurance subsidy.
- How to Apply: You can find the formal application requirements, GRE/TOEFL details, and deadlines on the Drexel Graduate Admissions page.
- Contact Me: Before applying, I highly recommend reaching out to me via email (jep362@drexel.edu). Please include your CV and a brief description of your mathematical background and research interests so we can discuss potential alignment.
Journal Articles
- 1. J. E. Pascoe, Ryan Tully-Doyle. Matrix convex verbatim enumeration functions are graphical. J. Operator Theory.
- 2. J. E. Pascoe. The spectral constant for the quantum cross and asymptotics for annuli. Acta Sci. Math. (Szeged).
- 3. J. E. Pascoe. Noncommutative free universal mondromy, pluriharmonic conjugates and plurisubharmonicity. Trans. Amer. Math. Soc. (to appear).
- 4. J. E. Pascoe. The sequential compactness theorem in the strong operator topology modulo unitary conjugation. Oper. Theory 2025 (In Book).
- 5. Kelly Bickel, Greg Knese, J. E. Pascoe, Alan Sola. Stable polynomials and admissible numerators in product domains. Bull. Lond. Math. Soc. 57 (2) 377-394, 2025.
- 6. Kelly Bickel, Greg Knese, J. E. Pascoe, Alan Sola. Local theory of stable polynomials and bounded rational functions of several variables. Ann. Polon. Math. 133, 95-169, 2024.
- 7. J. E. Pascoe, Hugo Woerdeman. The degree one Laguerre-Pólya class and the shuffle-word-embedding conjecture. Canad. Math. Bull. 67 (3) 760-767, 2024.
- 8. Kelly Bickel, J. E. Pascoe, Meredith Sargent. Zero-free regions near a line. Math. Z. 305 (2023).
- 9. Scott McCullough, J. E. Pascoe. Geometric Dilations and Operator Annuli. J. Funct. Anal. 285 (2023) issue 7.
- 10. J. E. Pascoe. Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem. Tohoku Math. J. 75 (2023) no. 4.
- 11. Kelly Bickel, J. E. Pascoe, Ryan Tully-Doyle. Analytic continuation of concrete realizations and the McCarthy Champagne conjecture. Int. Math. Res. Not. IMRN 2023, no. 9, 7845-7882.
- 12. J. E. Pascoe, Ryan Tully-Doyle. Induced Stinespring factorization and the Wittstock support theorem. Results Math. 78 (2023), no. 4, Paper No. 135.
- 13. J. E. Pascoe, Ryan Tully-Doyle. The royal road to automatic noncommutative real analyticity, monotonicity, and convexity. Adv. Math. 407 (2022), Paper No. 108548.
- 14. Michael Jury, Igor Klep, Mark Mancuso, Scott McCullough, J. E. Pascoe. Noncommutative partially convex rational functions. Rev. Mat. Iberoam. 38 (2022), no. 3, 731-759.
- 15. Kelly Bickel, J. E. Pascoe, Alan Sola. Singularities of rational inner functions in higher dimensions. Amer. J. Math. 144 (2022), no. 4, 1115-1157.
- 16. J. E. Pascoe, Tapesh Yadav. Macroscale behavior of random lower triangular matrices. Anal. Math. Phys. 12 (2022), no. 1, Paper No. 12, 11 pp.
- 17. J. E. Pascoe, Ryan Tully-Doyle. Monotonicity of the principal pivot transform. Linear Algebra Appl. 643 (2022), 161-165.
- 18. J. E. Pascoe. The outer spectral radius and dynamics of completely positive maps. Israel J. Math. 244 (2021), no. 2, 945-969.
- 19. J. E. Pascoe, Meredith Sargent, Ryan Tully-Doyle. A controlled tangential Julia-Carathéodory theory via averaged Julia quotients. Anal. PDE 14 (2021), no. 6, 1773-1795.
- 20. Igor Klep, J. E. Pascoe, Jurij Volčič. Positive univariate trace polynomials. J. Algebra 579 (2021), 303-317.
- 21. Michael Jury, Igor Klep, Mark Mancuso, Scott McCullough, J. E. Pascoe. Noncommutative partial convexity via Γ-convexity. J. Geom. Anal. 31 (2021), no. 3, 3137-3160.
- 22. J. E. Pascoe, Ryan Tully-Doyle. Automatic real analyticity and a regal proof of a commutative multivariate Löwner theorem. Proc. Amer. Math. Soc., 149 (2021), 2019-2024.
- 23. J. E. Pascoe. Trace minmax functions and the radical Laguerre Pólya class. Res. Math. Sci. 8 (2021), no. 1, 9.
- 24. Kelly Bickel, J. E. Pascoe, Alan Sola. Level curve portaits of rational inner functions. Ann. Sc. Norm. Super. Pisa Cl. Sci., (2020) PP. 449-494 | Vol. XXI.
- 25. Meric Augat, Michael Jury, J. E. Pascoe. Effective noncommuative Nevanlinna-Pick interpolation on the row ball and applications. J. Math. Anal. Appl. 492 (2020), no. 2, 124457, 21 pp.
- 26. Igor Klep, J. E. Pascoe, Gregor Podlogar and Jurij Volčič. Noncommutative rational functions invariant under the action of a finite solvable group. J. Math. Anal. Appl. 490 (2020), no. 2, 124341, 17 pp.
- 27. J. E. Pascoe. An entire free holomorphic function which is unbounded on the row ball. J. Operator Theory, 84 (2020), no. 2, 365-367.
- 28. J. E. Pascoe. Committee spaces and the random column-row property. Complex Anal. Oper. Theory 14 Paper No. 13. (2020).
- 29. J. E. Pascoe, Benjamin Passer, Ryan Tully-Doyle. Representation of free Herglotz functions. Indiana Univ. Math. J. 68 No. 4 (2019), 1199-1215.
- 30. J. E. Pascoe. The wedge-of-the-edge theorem: edge-of-the-wedge type phenomenon within the common real boundary. Canad. Math. Bull. 62 (2019), no. 2, 417-427.
- 31. J. E. Pascoe. An elementary method to compute the algebra generated by some given matrices. Linear Algebra Appl. 571 (2019), 132-142.
- 32. J. E. Pascoe. Note on Löwner's theorem on matrix monotone functions in several commuting variables of Agler, McCarthy and Young. Monatsh. Math. 189 no. 2 (2019), 377-381.
- 33. J. E. Pascoe, Ryan Tully-Doyle. Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions. J. Math. Anal. Appl. 472 (2) 2019. 1487-1498.
- 34. J. E. Pascoe. An inductive Julia-Carathéodory theorem for Pick functions in two variables. Proc. Edinb. Math. Soc., (2) 61 (2018), no. 3. 647-660.
- 35. David Cushing, J. E. Pascoe, Ryan Tully-Doyle. Free functions with symmetry. Math. Z., 289 (2018), no. 3-4, 837-857.
- 36. 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).
- 37. J. E. Pascoe. The noncommutative Löwner theorem for matrix monotone functions over operator systems. Linear Algebra Appl. 541 (2018) 54-59.
- 38. J. E. Pascoe. Positivstellensätze for noncommutative rational expressions. Proc. Amer. Math. Soc., 146 (2018) 933-937.
- 39. John E. McCarthy, J. E. Pascoe. A non-commutative Julia Inequality. Math. Ann., 370 (1-2) 423-446, 2018.
- 40. 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.
- 41. J. E. Pascoe, Ryan Tully-Doyle. Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables. J. Funct. Anal., 273 (1) 283-328 (2017).
- 42. John McCarthy, J. E. Pascoe. The Julia-Carathéodory theorem on the bidisk revisited. Acta Sci. Math. (Szeged), 83:1-2, 165-175, 2017.
- 43. Igor Klep, J. E. Pascoe, Jurij Volčič. Regular and positive noncommutative rational functions. J. Lond. Math. Soc., 95 (2) 613-632, 2017.
- 44. J. William Helton, J. E. Pascoe, Ryan Tully-Doyle, Victor Vinnikov. Convex entire noncommutative functions are polynomials of degree two or less. Integral Equations Operator Theory, 86 (2), 151-163, 2016.
- 45. J. E. Pascoe. The inverse function theorem and the Jacobian conjecture for free analysis. Math. Z., 278 (3-4) 987-994, 2014.
Preprints
- Sujit Sakharam Damase, J. E. Pascoe. On positive definite thresholding of correlation matrices. preprint.
- Greg Knese, J. E. Pascoe, Alan Sola. Stable polynomials and bounded rational functions in the unit ball. preprint.
- Sujit Sakharam Damase, J. E. Pascoe. Complete discrete Schoenberg-Delsarte theory for homogeneous spaces. preprint.
- Sourav Pal, J. E. Pascoe, Nitin Tomar. Spectral constants for the quantum annulus. preprint.
- Geoffrey Hutinet, J. E. Pascoe. Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit. preprint.
- Michael Coopman, Austin Jacobs, H. B. Pascoe, J. E. Pascoe. The geometry of inconvenience and perverse equilibria in trade networks. preprint.
- J. E. Pascoe. Germination phenomena. preprint.
- J. E. Pascoe, Ryan Tully-Doyle. Averaged mixed Julia-Fatou type theory with applications to spectral foliation. preprint.
- J. E. Pascoe. Free noncommutative principal divisors and commutativity of the tracial fundamental group. preprint.
- J. E. Pascoe. Noncommutative Schur-type products and their Schoenberg theorem. in revision.
Coauthors & Collaborators
A mathematical career is defined by its human edges. The links below utilize a dynamic routing protocol (bypassing the inevitable decay of static URLs) to resolve directly to each mathematician's current active homepage.
Meric Augat
Tirthankar Bhattacharyya
Kelly Bickel
David Cushing
Sujit S. Damase
Cynthia Flores
J. William Helton
Geoffrey Hutinet
Michael Jury
Matthew Kennedy
Igor Klep
Greg Knese
Scott McCullough
Sourav Pal
Benjamin Passer
Gregor Podlogar
Chandan Pradhan
Eli Shamovich
Alan Sola
Nitin Tomar
Ryan Tully-Doyle
Victor Vinnikov
Jurij Volčič
Hugo Woerdeman
Links
- Oberwolfach Photo Collection
- WolframAlpha
- Online Encyclopedia of Integer Sequences
- How to learn how to program.
- Reviews of integer sequences
- My genealogy
- My mathematical brother
Photo by Ivonne Vetter at MFO in 2013.
