My most recent papers are:
 A geometric characterization of the symmetrized bidisc, J. Math. Anal. Applic., 473 (2019) 13771413, joint with J. Agler and Z. A. Lykova.
 Noncommutative manifolds, the free square root and symmetric functions in
two noncommuting variables, Trans. London Math. Soc. 5 (2018) 132183, open access, joint with J. Agler and J. McCarthy.
 Characterizations of some domains via Caratheodory extremals, joint with J. Agler and Z. A. Lykova, to appear in J. Geom. Anal. (2019).
 Analytic interpolation into the tetrablock and a $\mu$synthesis problem,
joint with Z. A. Lykova and Amos Ajibo, to appear in Operator Theory: Advances and Applications, Birkhauser, Basel, 2019.
 Caratheodory extremal functions on the symmetrized bidisc, joint with J. Agler
and Z. A. Lykova, in: Bart H., ter Horst S., Ran A., Woerdeman H. (eds) Operator Theory, Analysis and the State Space Approach, Operator Theory: Advances and Applications, 271 (2018) 121, Birkhäuser, Cham.
 Algebraic and geometric aspects of rational $\Gamma$inner
functions
Advances in Math 328 (2018) 133159, open access, joint with Jim Agler and Z. A. Lykova.
 Realization of functions on the symmetrized bidisc, J. Math. Anal.
Applic. 453 (2017) 227240, open access, joint with J. Agler and Z. A. Lykova.
 A rich structure related to the construction of
analytic matrix functions,
J. Functional Analysis, 272 (2017) 17041754, open access, joint with D. C. Brown and Z. A. Lykova.
 Geodesics, retracts, and the normpreserving extension property in the
symmetrized bidisc, Memoirs of the American Mathematical Society, 258, no. 1242, joint with Jim Agler and Z. A. Lykova.
 Finite Blaschke products and the construction of rational
$\Gamma$inner functions , J. Math. Analysis and Applications, 447 (2017), open access, joint with
Jim Agler and Z. A. Lykova.

Nevanlinna representations in several variables, J. Functional Analysis, 270 (2016) 30003046, open access,
joint with Jim Agler and Ryan TullyDoyle.
 Review of Foundations of free noncommutative function theory , by Dmitry S.
KaliuzhnyiVerbovetskyi and Victor Vinnikov, in Bull. London Math. Soc. 47 (2015) 10361039.
 The complex geometry of a domain related to musynthesis, March 2014, joint with Jim Agler and Z. A. Lykova.
 3extremal holomorphic maps and the symmetrised bidisc, July 2013, joint with Jim Agler and Z. A. Lykova.
 Symmetric functions of two noncommuting variables, July 2013,
joint with Jim Agler.
 A case of musynthesis as a quadratic semidefinite program, December 2012, joint with Jim Agler
and Z. A. Lykova.
 Correction to `A Schwarz Lemma for a domain related to musynthesis',
February 2013, joint with A. Abouhajar and M. C. White.
 Extremal holomorphic maps and the symmetrised bidisc, October 2011, joint with Jim Agler and Z. A. Lykova.
 Boundary behavior of analytic functions of two variables via
generalized models, March 2012,
joint with Jim Agler and Ryan TullyDoyle;
 On the representation of holomorphic functions on polyhedra,
November 2011, joint with Jim Agler and John McCarthy;
 Some analysable instances of musynthesis, March 2011;
 The boundary CaratheodoryFejer problem, November 2010,
joint with Jim Agler and Z. A. Lykova;
 Operator monotone functions and Loewner functions of several variables,
September 2010, joint with J. Agler and J. E. McCarthy;

PseudoTaylor expansions and the CaratheodoryFejer problem, January 2011, joint with Jim Agler and
Z. A. Lykova.
Click here
for abstracts and bibliographic details
of recent publications (1999present).
Preprints of papers which have not yet appeared are on the eprint archive.
Here is my full publication list as a pdf file.