Greg Knese's Home Page

I'm a Professor of Mathematics at Washington University in St. Louis.
I am Director of Graduate Studies in the Department of Mathematics since 2022.
I was previously at the University of Alabama (2010-2013) and UC Irvine (2007-2010).
You can email me at geknese shift2 wustl dot edu.
My office is 214 Cupples I
My CV
ORCID arXiv MathSciNet Google scholar

Research

I am interested in operator theory, complex analysis,
stable polynomials, and reproducing kernel Hilbert spaces
with applications to probability and theoretical computer science.

Editorial work

Handling editor for Bulletin of the London Math Society and Journal of the London Math Society

Grants/Awards

2025 WU Math Guido Weiss Teaching and Service Award.

NSF analysis grant 2023-2026 Stable Polynomials, Rational Singularities, and Operator Theory

NSF analysis grant 2019-2023 Operator theory and stable polynomials

NSF conference grant for IWOTA 2016

NSF analysis grant 2014-2018 Harmonic analysis and spaces of analytic functions in several variables

NSF analysis grant 2010-2014: Operator related function theory and algebraic varieties

Papers

References: amsrefs , bibtex
  1. Boundary local integrability of rational functions in two variables (2025) Accepted/to appear in Trans. Amer. Math. Soc.
  2. The Schur-Agler class in infinitely many variables 2025. To appear in Canadian Mathematical Bulletin. Open access link
  3. Hadamard multipliers of the Agler class Integr. Equ. Oper. Theory 97 , 12 (2025). doi Share-it link
    Reference 
    \bib{MR4905112}{article}{
   author={Knese, Greg},
   title={Hadamard multipliers of the Agler class},
   journal={Integral Equations Operator Theory},
   volume={97},
   date={2025},
   number={2},
   pages={Paper No. 12, 11},
   issn={0378-620X},
   review={\MR{4905112}},
   doi={10.1007/s00020-025-02799-6},
}

@article {MR4905112,
    AUTHOR = {Knese, Greg},
     TITLE = {Hadamard multipliers of the {A}gler class},
   JOURNAL = {Integral Equations Operator Theory},
  FJOURNAL = {Integral Equations and Operator Theory},
    VOLUME = {97},
      YEAR = {2025},
    NUMBER = {2},
     PAGES = {Paper No. 12, 11},
      ISSN = {0378-620X,1420-8989},
   MRCLASS = {47A13 (32A35 32A38 46L07)},
  MRNUMBER = {4905112},
       DOI = {10.1007/s00020-025-02799-6},
       URL = {https://doi.org/10.1007/s00020-025-02799-6},
}
  4. Testing von Neumann inequalities with nilpotent matrices Arkiv för Matematik, Vol. 63, Issue 2 (2025), pp. 311-324. DOI Journal link
    5. Reference 
    \bib{MR4989867}{article}{
   author={Knese, Greg},
   title={Testing von Neumann inequalities with nilpotent matrices},
   journal={Ark. Mat.},
   volume={63},
   date={2025},
   number={2},
   pages={311--324},
   issn={0004-2080},
   review={\MR{4989867}},
   doi={10.4310/arkiv.2025.v63.n2.a5},
}

@article {MR4989867,
    AUTHOR = {Knese, Greg},
     TITLE = {Testing von {N}eumann inequalities with nilpotent matrices},
   JOURNAL = {Ark. Mat.},
  FJOURNAL = {Arkiv f\"or Matematik},
    VOLUME = {63},
      YEAR = {2025},
    NUMBER = {2},
     PAGES = {311--324},
      ISSN = {0004-2080,1871-2487},
   MRCLASS = {99-06},
  MRNUMBER = {4989867},
       DOI = {10.4310/arkiv.2025.v63.n2.a5},
       URL = {https://doi-org.libproxy.washu.edu/10.4310/arkiv.2025.v63.n2.a5},
}
  5. Three radii associated to Schur functions on the polydisk Proc. Amer. Math. Soc. Series B 12 (2025) 48--63. Open access link
    Reference 
      \bib{MR4898520}{article}{
   author={Knese, Greg},
   title={Three radii associated to Schur functions on the polydisk},
   journal={Proc. Amer. Math. Soc. Ser. B},
   volume={12},
   date={2025},
   pages={48--63},
   review={\MR{4898520}},
   doi={10.1090/bproc/262},
}

@article {MR4898520,
    AUTHOR = {Knese, Greg},
     TITLE = {Three radii associated to {S}chur functions on the polydisk},
   JOURNAL = {Proc. Amer. Math. Soc. Ser. B},
  FJOURNAL = {Proceedings of the American Mathematical Society. Series B},
    VOLUME = {12},
      YEAR = {2025},
     PAGES = {48--63},
      ISSN = {2330-1511},
   MRCLASS = {47A48 (32A35 32A38 47A13)},
  MRNUMBER = {4898520},
       DOI = {10.1090/bproc/262},
       URL = {https://doi.org/10.1090/bproc/262},
}
  6. Rational inner functions on the polydisk -- a survey, 2024. Living reference In: Alpay, D., Sabadini, I., Colombo, F. (eds) Operator Theory. Springer, Basel. doi
  7. (with K. Bickel, J.E.Pascoe, A.Sola) Stable polynomials and admissible numerators in product domains, (2025), Bull. London Math. Soc. 57: 377-394. doi
    Reference 
    \bib{MR4861887}{article}{
   author={Bickel, Kelly},
   author={Knese, Greg},
   author={Pascoe, James Eldred},
   author={Sola, Alan},
   title={Stable polynomials and admissible numerators in product domains},
   journal={Bull. Lond. Math. Soc.},
   volume={57},
   date={2025},
   number={2},
   pages={377--394},
   issn={0024-6093},
   review={\MR{4861887}},
   doi={10.1112/blms.13201},
}

@article {MR4861887,
    AUTHOR = {Bickel, Kelly and Knese, Greg and Pascoe, James Eldred and
              Sola, Alan},
     TITLE = {Stable polynomials and admissible numerators in product
              domains},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {57},
      YEAR = {2025},
    NUMBER = {2},
     PAGES = {377--394},
      ISSN = {0024-6093,1469-2120},
   MRCLASS = {32A08 (32A40 32B05)},
  MRNUMBER = {4861887},
       DOI = {10.1112/blms.13201},
       URL = {https://doi.org/10.1112/blms.13201},
}
  8. (with K. Bickel, J.E.Pascoe, A.Sola) Local theory of stable polynomials and bounded rational functions of several variables. Ann. Polon. Math. 133 (2024), no. 2, 95--169. Fulltext link
    Reference 
    \bib{MR4839351}{article}{
   author={Bickel, Kelly},
   author={Knese, Greg},
   author={Pascoe, James Eldred},
   author={Sola, Alan},
   title={Local theory of stable polynomials and bounded rational functions
   of several variables},
   journal={Ann. Polon. Math.},
   volume={133},
   date={2024},
   number={2},
   pages={95--169},
   issn={0066-2216},
   review={\MR{4839351}},
   doi={10.4064/ap240229-9-9},
}

@article {MR4839351,
    AUTHOR = {Bickel, Kelly and Knese, Greg and Pascoe, James Eldred and
              Sola, Alan},
     TITLE = {Local theory of stable polynomials and bounded rational
              functions of several variables},
   JOURNAL = {Ann. Polon. Math.},
  FJOURNAL = {Annales Polonici Mathematici},
    VOLUME = {133},
      YEAR = {2024},
    NUMBER = {2},
     PAGES = {95--169},
      ISSN = {0066-2216,1730-6272},
   MRCLASS = {32A40 (13H10 14H45)},
  MRNUMBER = {4839351},
       DOI = {10.4064/ap240229-9-9},
       URL = {https://doi.org/10.4064/ap240229-9-9},
}
  9. A simple proof of necessity in the McCullough-Quiggin theorem. Proc. Amer. Math. Soc. 148 (2020), no. 8, 3453-3456. Fulltext link
    Reference 
    \bib{MR4108851}{article}{
   author={Knese, Greg},
   title={A simple proof of necessity in the McCullough-Quiggin theorem},
   journal={Proc. Amer. Math. Soc.},
   volume={148},
   date={2020},
   number={8},
   pages={3453--3456},
   issn={0002-9939},
   review={\MR{4108851}},
   doi={10.1090/proc/15061},
}

@article {MR4108851,
    AUTHOR = {Knese, Greg},
     TITLE = {A simple proof of necessity in the {M}c{C}ullough-{Q}uiggin
              theorem},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {148},
      YEAR = {2020},
    NUMBER = {8},
     PAGES = {3453--3456},
      ISSN = {0002-9939,1088-6826},
   MRCLASS = {46E22 (47A57)},
  MRNUMBER = {4108851},
MRREVIEWER = {Daniel\ Pascuas},
       DOI = {10.1090/proc/15061},
       URL = {https://doi.org/10.1090/proc/15061},
}
  10. Kummert’s approach to realization on the bidisk. Indiana Univ. Math. J. 70 (2021), no. 6, 2369-2403. Fulltext link
    Reference 
    \bib{MR4359913}{article}{
   author={Knese, Greg},
   title={Kummert's approach to realization on the bidisk},
   journal={Indiana Univ. Math. J.},
   volume={70},
   date={2021},
   number={6},
   pages={2369--2403},
   issn={0022-2518},
   review={\MR{4359913}},
   doi={10.1512/iumj.2021.70.8738},
}

@article {MR4359913,
    AUTHOR = {Knese, Greg},
     TITLE = {Kummert's approach to realization on the bidisk},
   JOURNAL = {Indiana Univ. Math. J.},
  FJOURNAL = {Indiana University Mathematics Journal},
    VOLUME = {70},
      YEAR = {2021},
    NUMBER = {6},
     PAGES = {2369--2403},
      ISSN = {0022-2518,1943-5258},
   MRCLASS = {47A48 (32A08 32H02 47A57)},
  MRNUMBER = {4359913},
MRREVIEWER = {Galina\ S.\ Borisova},
       DOI = {10.1512/iumj.2021.70.8738},
       URL = {https://doi.org/10.1512/iumj.2021.70.8738},
}
  11. (with E.D. Knese, Keel, Bennert, Moiseev, Grokhovskaya, Dodonov) An [O III] search for extended emission around AGN with H I mapping: a distant cloud ionized by Mkn 1 . Monthly Notices of the Royal Astronomical Society, Volume 496, Issue 2, August 2020, pages 1035-1050.
    Note This is an astronomy paper with a spherical version of the Buffon needle problem in the appendix. Available here
  12. Global bounds on stable polynomials , Complex Anal. Oper. Theory 13 (2019), no. 4, 1895-1915. DOI
    Reference 
    
\bib{MR3957021}{article}{
   author={Knese, Greg},
   title={Global bounds on stable polynomials},
   journal={Complex Anal. Oper. Theory},
   volume={13},
   date={2019},
   number={4},
   pages={1895--1915},
   issn={1661-8254},
   review={\MR{3957021}},
   doi={10.1007/s11785-018-0873-7},
}

@article {MR3957021,
    AUTHOR = {Knese, Greg},
     TITLE = {Global bounds on stable polynomials},
   JOURNAL = {Complex Anal. Oper. Theory},
  FJOURNAL = {Complex Analysis and Operator Theory},
    VOLUME = {13},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {1895--1915},
      ISSN = {1661-8254,1661-8262},
   MRCLASS = {32A60 (30C15 30D15 32A15)},
  MRNUMBER = {3957021},
MRREVIEWER = {Anna\ M.\ Vishnyakova},
       DOI = {10.1007/s11785-018-0873-7},
       URL = {https://doi.org/10.1007/s11785-018-0873-7},
}
  13. Extreme points and saturated polynomials. Illinois J. Math. 63 (2019), no. 1, 47-74.
    Reference 
      \bib{MR3959867}{article}{
   author={Knese, Greg},
   title={Extreme points and saturated polynomials},
   journal={Illinois J. Math.},
   volume={63},
   date={2019},
   number={1},
   pages={47--74},
   issn={0019-2082},
   review={\MR{3959867}},
   doi={10.1215/00192082-7600059},
}

@article {MR3959867,
    AUTHOR = {Knese, Greg},
     TITLE = {Extreme points and saturated polynomials},
   JOURNAL = {Illinois J. Math.},
  FJOURNAL = {Illinois Journal of Mathematics},
    VOLUME = {63},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {47--74},
      ISSN = {0019-2082,1945-6581},
   MRCLASS = {32A10 (46A55 47A57)},
  MRNUMBER = {3959867},
MRREVIEWER = {Daniel\ M.\ Pellegrino},
       DOI = {10.1215/00192082-7600059},
       URL = {https://doi.org/10.1215/00192082-7600059},
}
  14. (with Kosinski, Ransford, and Sola) Cyclic polynomials in anisotropic Dirichlet spaces. J. Anal. Math. 138 (2019), no. 1, 23-47.
    Reference 
     \bib{MR3996031}{article}{
   author={Knese, Greg},
   author={Kosi\'nski, \L ukasz},
   author={Ransford, Thomas J.},
   author={Sola, Alan A.},
   title={Cyclic polynomials in anisotropic Dirichlet spaces},
   journal={J. Anal. Math.},
   volume={138},
   date={2019},
   number={1},
   pages={23--47},
   issn={0021-7670},
   review={\MR{3996031}},
   doi={10.1007/s11854-019-0014-x},
}

@article {MR3996031,
    AUTHOR = {Knese, Greg and Kosi\'nski, \L ukasz and Ransford, Thomas J.
              and Sola, Alan A.},
     TITLE = {Cyclic polynomials in anisotropic {D}irichlet spaces},
   JOURNAL = {J. Anal. Math.},
  FJOURNAL = {Journal d'Analyse Math\'ematique},
    VOLUME = {138},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {23--47},
      ISSN = {0021-7670,1565-8538},
   MRCLASS = {47A16 (32A99)},
  MRNUMBER = {3996031},
MRREVIEWER = {Yu-Xia\ Liang},
       DOI = {10.1007/s11854-019-0014-x},
       URL = {https://doi.org/10.1007/s11854-019-0014-x},
}
  15. The von Neumann inequality for 3x3 matrices , Bull. Lond. Math. Soc. 48 (2016), no. 1, 53-57.
    Reference 
      \bib{MR3455747}{article}{
   author={Knese, Greg},
   title={The von Neumann inequality for $3\times 3$ matrices},
   journal={Bull. Lond. Math. Soc.},
   volume={48},
   date={2016},
   number={1},
   pages={53--57},
   issn={0024-6093},
   review={\MR{3455747}},
   doi={10.1112/blms/bdv087},
}

@article {MR3455747,
    AUTHOR = {Knese, Greg},
     TITLE = {The von {N}eumann inequality for {$3\times 3$} matrices},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {48},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {53--57},
      ISSN = {0024-6093,1469-2120},
   MRCLASS = {32E30 (30E05 47A63)},
  MRNUMBER = {3455747},
MRREVIEWER = {\L ukasz\ Kosi\'nski},
       DOI = {10.1112/blms/bdv087},
       URL = {https://doi.org/10.1112/blms/bdv087},
}
  16. Integrability and regularity of rational functions , Proc. Lond. Math. Soc. (3) 111 (2015), no. 6, 1261-1306.
    Reference 
    \bib{MR3447794}{article}{
   author={Knese, Greg},
   title={Integrability and regularity of rational functions},
   journal={Proc. Lond. Math. Soc. (3)},
   volume={111},
   date={2015},
   number={6},
   pages={1261--1306},
   issn={0024-6115},
   review={\MR{3447794}},
   doi={10.1112/plms/pdv061},
}

@article {MR3447794,
    AUTHOR = {Knese, Greg},
     TITLE = {Integrability and regularity of rational functions},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {111},
      YEAR = {2015},
    NUMBER = {6},
     PAGES = {1261--1306},
      ISSN = {0024-6115,1460-244X},
   MRCLASS = {32A20 (26C15 30C15 30D40 32A40 47A57)},
  MRNUMBER = {3447794},
MRREVIEWER = {Angelica\ Malaspina},
       DOI = {10.1112/plms/pdv061},
       URL = {https://doi.org/10.1112/plms/pdv061},
}
  17. (with Beneteau, Kosinski, Liaw, Seco, and Sola) Cyclic polynomials in two variables , Trans. Amer. Math. Soc. 368 (2016), no. 12, 8737-8754.
    Reference 
    \bib{MR3551587}{article}{
   author={B\'en\'eteau, Catherine},
   author={Knese, Greg},
   author={Kosi\'nski, \L ukasz},
   author={Liaw, Constanze},
   author={Seco, Daniel},
   author={Sola, Alan},
   title={Cyclic polynomials in two variables},
   journal={Trans. Amer. Math. Soc.},
   volume={368},
   date={2016},
   number={12},
   pages={8737--8754},
   issn={0002-9947},
   review={\MR{3551587}},
   doi={10.1090/tran6689},
}

@article {MR3551587,
    AUTHOR = {B\'en\'eteau, Catherine and Knese, Greg and Kosi\'nski, \L
              ukasz and Liaw, Constanze and Seco, Daniel and Sola, Alan},
     TITLE = {Cyclic polynomials in two variables},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {368},
      YEAR = {2016},
    NUMBER = {12},
     PAGES = {8737--8754},
      ISSN = {0002-9947,1088-6850},
   MRCLASS = {32A37 (47A13)},
  MRNUMBER = {3551587},
MRREVIEWER = {Joan\ F\`abrega},
       DOI = {10.1090/tran6689},
       URL = {https://doi.org/10.1090/tran6689},
}
  18. (with K. Bickel) Canonical Agler decompositions and transfer function realizations , Trans. Amer. Math. Soc. 368 (2016), no. 9, 6293-6324.
    Reference 
     \bib{MR3461035}{article}{
   author={Bickel, Kelly},
   author={Knese, Greg},
   title={Canonical Agler decompositions and transfer function realizations},
   journal={Trans. Amer. Math. Soc.},
   volume={368},
   date={2016},
   number={9},
   pages={6293--6324},
   issn={0002-9947},
   review={\MR{3461035}},
   doi={10.1090/tran/6542},
}

@article {MR3461035,
    AUTHOR = {Bickel, Kelly and Knese, Greg},
     TITLE = {Canonical {A}gler decompositions and transfer function
              realizations},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {368},
      YEAR = {2016},
    NUMBER = {9},
     PAGES = {6293--6324},
      ISSN = {0002-9947,1088-6850},
   MRCLASS = {47B32 (46E22 47A40 47A57 93B15 93B36 93C35)},
  MRNUMBER = {3461035},
MRREVIEWER = {Takanori\ Yamamoto},
       DOI = {10.1090/tran/6542},
       URL = {https://doi.org/10.1090/tran/6542},
}
  19. Determinantal representations of semi-hyperbolic polynomials , Michigan Math. J. 65 (2016), no. 3, 473-487.
    Reference 
     \bib{MR3542761}{article}{
   author={Knese, Greg},
   title={Determinantal representations of semihyperbolic polynomials},
   journal={Michigan Math. J.},
   volume={65},
   date={2016},
   number={3},
   pages={473--487},
   issn={0026-2285},
   review={\MR{3542761}},
   doi={10.1307/mmj/1472066143},
}

@article {MR3542761,
    AUTHOR = {Knese, Greg},
     TITLE = {Determinantal representations of semihyperbolic polynomials},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {65},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {473--487},
      ISSN = {0026-2285,1945-2365},
   MRCLASS = {14P10 (15A15 47A57 90C22 90C25)},
  MRNUMBER = {3542761},
MRREVIEWER = {Alja\v z\ Zalar},
       DOI = {10.1307/mmj/1472066143},
       URL = {https://doi.org/10.1307/mmj/1472066143},
}
  20. (with J. McCarthy and K. Moen) Unions of Lebesgue spaces and A_1 majorants , Pacific J. Math. 280 (2016), no. 2, 411-432.
    Reference 
      \bib{MR3453978}{article}{
   author={Knese, Greg},
   author={McCarthy, John E.},
   author={Moen, Kabe},
   title={Unions of Lebesgue spaces and $A_1$ majorants},
   journal={Pacific J. Math.},
   volume={280},
   date={2016},
   number={2},
   pages={411--432},
   issn={0030-8730},
   review={\MR{3453978}},
   doi={10.2140/pjm.2016.280.411},
}

@article {MR3453978,
    AUTHOR = {Knese, Greg and McCarthy, John E. and Moen, Kabe},
     TITLE = {Unions of {L}ebesgue spaces and {$A_1$} majorants},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {280},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {411--432},
      ISSN = {0030-8730,1945-5844},
   MRCLASS = {42B25 (30H10 30H15 42B35 46E30)},
  MRNUMBER = {3453978},
MRREVIEWER = {Vivien\ G.\ Miller},
       DOI = {10.2140/pjm.2016.280.411},
       URL = {https://doi.org/10.2140/pjm.2016.280.411},
}
  21. (with J. Geronimo and P. Iliev) Polynomials with no zeros on a face of the bidisk , J. Funct. Anal. 270 (2016), no. 9, 3505-3558.
    Reference 
      \bib{MR3475462}{article}{
   author={Geronimo, Jeffrey S.},
   author={Iliev, Plamen},
   author={Knese, Greg},
   title={Polynomials with no zeros on a face of the bidisk},
   journal={J. Funct. Anal.},
   volume={270},
   date={2016},
   number={9},
   pages={3505--3558},
   issn={0022-1236},
   review={\MR{3475462}},
   doi={10.1016/j.jfa.2016.02.002},
}

@article {MR3475462,
    AUTHOR = {Geronimo, Jeffrey S. and Iliev, Plamen and Knese, Greg},
     TITLE = {Polynomials with no zeros on a face of the bidisk},
   JOURNAL = {J. Funct. Anal.},
  FJOURNAL = {Journal of Functional Analysis},
    VOLUME = {270},
      YEAR = {2016},
    NUMBER = {9},
     PAGES = {3505--3558},
      ISSN = {0022-1236,1096-0783},
   MRCLASS = {47A57 (30E05 42C05)},
  MRNUMBER = {3475462},
MRREVIEWER = {Sergey\ M.\ Zagorodnyuk},
       DOI = {10.1016/j.jfa.2016.02.002},
       URL = {https://doi.org/10.1016/j.jfa.2016.02.002},
}
  22. (with P.M. Gauthier) Zero-free polynomial approximation on a chain of Jordan domains , Ann. Sci. Math. Qu\'ebec 36 (2012), no.1, 107-112.
  23. (with K. Bickel) Inner functions on the bidisk and associated Hilbert spaces , J. Funct. Anal. 265 (2013), no. 11, 2753-2790.
  24. Uchiyama's lemma and the John-Nirenberg inequality , Bull. Lond. Math. Soc. 45 (2013), no. 4, 683-692.
  25. (with J. Geronimo and P. Iliev) Orthogonality relations for bivariate Bernstein-Szego measures , Recent advances in orthogonal polynomials, special functions, and their applications, 119-131, Contemp. Math., 578, Amer. Math. Soc., Providence, RI, 2012. Also here
  26. Schur-Agler class rational inner functions on the tridisk , Proc. Amer. Math. Soc., 139(2011), 4063-4072. Also here .
  27. A refined Agler decomposition and geometric applications , Indiana Univ. Math. J. 60 (2011), 1831-1842. Also here
  28. (with M. Jury and S. McCullough) Nevanlinna-Pick interpolation on distinguished varieties in the bidisk , 2012, J. Functional Analysis, 262(9), 3812-3838.
  29. Stable symmetric polynomials and the Schur-Agler class , Illinois J. Math. 55 (2011), no. 4, 1603-1620 (2013).
  30. Rational inner functions in the Schur-Agler class of the polydisk , 2011, Publ. Mat., 55(2), 343-357.
  31. Kernel decompositions for Schur functions on the polydisk, 2011, Complex Analysis and Operator Theory, 5(4), 1093-1111. See also here
  32. Polynomials with no zeros on the bidisk, , Analysis and PDE, Vol. 3 (2010) No. 2, 109-149. See also here.
  33. Polynomials defining distinguished varieties, 2010, Trans. Math. Amer. Soc., 362(11), 5635-5655.
  34. (with M.Jury and S.McCullough) Agler interpolation families of kernels, 14 pages,
    Operators and Matrices, Vol. 3 (2009) No. 4, 571-587.
  35. (with J. Agler and J. McCarthy) Algebraic pairs of isometries, 2012, J. Operator Theory, 67(1), 215-236. Also here .
  36. Bernstein-Szegõ measures on the two dimensional torus, Indiana Univ. Math. J. 57 No. 3 (2008), 1353-1376. Also here .
  37. Function theory on the Neil parabola, Michigan Math. J., Vol. 55, Issue 1 (2007), 139-154.
  38. A Schwarz lemma on the polydisk, Proc. Amer. Math. Soc., 135 (2007), 2759-2768.

Teaching

Introduction to Analysis. Fall 2025.
Honors Mathematics II. Spring 2025.
Honors Mathematics I. Fall 2024.
Foundations for Higher Mathematics. Spring 2024.
Analytic combinatorics. Fall 2023.
Graduate Topics course: analysis of Dirichlet series. Spring 2023.
Introduction to Combinatorics, Fall 2022.
(Graduate topics course) Analytic combinatorics. Spring 2022.
Mathematical geodesy, Fall 2021.
Analytic Combinatorics, Spring 2021.
Complex Analysis II, Spring 2021.
Complex Analysis I, Fall 2020.
Differential Equations, Fall 2019.
Topics course on Reproducing kernel Hilbert space, Spring 2019
Partial Differential Equations, Math 415, Fall 2018
Analytic Combinatorics, Math 470, Fall 2018
Function theory on the polydisk, Math 522, Spring 2018
Measure Theory and Functional Analysis II Math 5052 Spring 2018
Measure Theory and Functional Analysis I Math 5051 Fall 2017
Measure Theory and Functional Analysis II Math 5052 Spring 2017
Geometry I Math 5041 Fall 2016
Calculus of Several Variables Math 318 Spring 2016
Complex Analysis II Math 5022 Spring 2016
Complex Analysis I Math 5021 Fall 2015
Measure theory and functional analysis II Math 5052 Spring 2015
Measure theory and functional analysis I Math 5051 Fall 2014
Matrix Algebra Math 309 Fall 2013
Older teaching

Other things

McCarthy Fest 2024
IWOTA 2016
Operator theory and the singular value decomposition Oberwolfach snapshot. pdf
My Youtube channel
IWOTA youtube channel
Slides and audio for the presentation "Rational inner functions on the bidisk" presented at the Fields institute.
LaTeX style file , metafont file , and user's guide to a font/notation I created for two of the above papers.
My math genealogy