Selected publications

(with Bill Helton, Igor Klep and Jurij Volcic) Noncommutative polynomials describing convex sets, to appear in Foundations of Computational Mathematics.

(with Mike Jury, Igor Klep, Mark Mancuso and James Pascoe) Noncommutative partial convexity via \(\Gamma\)-Convexity, to appear in the Journal of Geometric Analysis.

(with Bill Helton, Igor Klep and Jurij Volcic) Bianalytic free maps between spectrahedra and spectraballs, Journal of Functional Analysis, 279 (2020), 108472, 61pp.

(with Igor Klep, Kelim \v Civic and Alja\v z Zalar) There are many more positive maps than completely positive maps, International Mathematics Research Notices 2019 (2019), no. 11, 3313–3375,

(with Bill Helton, Igor Klep and Markus Schweighofer) Dilations, linear matrix inequalities, the matrix cube problem and beta distributions, Memoirs of the American Mathematical Society (2019), no. 1232, vi+106 pp.

(with Meric Augat, Bill Helton and Igor Klep) Bianalytic maps between free spectrahedra, Mathematische Annalen, 371 (2018), no. 1-2, 883–959.

(with Harry Dym and Bill Helton) Non-commutative polynomials with convex level slices, Indiana University Mathematics Journal 66 (2017), no. 6, 2071–2135.

(with Bill Helton and Igor Klep) The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra, Journal of the European Mathematical Society (JEMS), 19 (2017) 1845-1897.

(with Meric Augat and Sriram Balasubramanian) Compact sets in the free topology, Linear Algebra and its Applications 506 (2016), 6-9.

(with Bill Helton and Igor Klep) Matrix convex hulls of free semialgebraic sets, Transactions of the American Mathematical Society 368 (2016), no. 5, 3105–3139.

(with Jakob Cimpric, Bill Helton and Chris Nelson) Real Nullstellensatz and ∗-ideals in ∗-algebras. Electron. J. Linear Algebra 30 (2015), 19–50.

(with Bill Helton) Free convex sets defined by rational expressions have LMI representations. J. Convex Anal. 21 (2014), no. 2, 425–448.

(with Sriram Balasubramanian) Quasi-convex free polynomials. Proc. Amer. Math. Soc. 142 (2014), no. 8, 2581–2591.

(with Jakob Cimprič, Bill Helton, Igor Klep, and Chris Nelson) On real one-sided ideals in a free algebra. J. Pure Appl. Algebra 218 (2014), no. 2, 269–284.

(with Jakob Cimprič, Bill Helton, and Chris Nelson) A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: algorithms. Proc. Lond. Math. Soc. (3) 106 (2013), no. 5, 1060–1086.

(with Bill Helton and Igor Klep) The matricial relaxation of a linear matrix inequality. Math. Program. 138 (2013), no. 1-2, Ser. A, 401–445.

(with Bill Helton) Every convex free basic semi-algebraic set has an LMI representation. Ann. of Math. (2) 176 (2012), no. 2, 979–1013.

(with Bill Helton and Igor Klep) The convex Positivstellensatz in a free algebra. Adv. Math. 231 (2012), no. 1, 516–534.

(with Saida Sultanic) Agler-commutant lifting on an annulus. Integral Equations Operator Theory 72 (2012), no. 4, 449–482.

(with Greg Knese and Michael Jury) Nevanlinna-Pick interpolation on distinguished varieties in the bidisk. J. Funct. Anal. 262 (2012), no. 9,3812–3838.

(with Tavan Trent) The Douglas property for multiplier algebras of operators. J. Math. Anal. Appl. 389 (2012), no. 1, 130–137.

(with Bill Helton and Igor Klep) Proper analytic free maps. J. Funct. Anal. 260 (2011), no. 5, 1476–1490.

(with Damon Hay, Bill Helton and Adrian Lim) Non-commutative partial matrix convexity. Indiana Univ. Math. J. 57 (2008), no. 6, 2815–2842.

(with Bill Helton and Mihai Putinar) Strong majorization in a free ∗-algebra. Math. Z. 255 (2007), no. 3, 579–596.

(with Mihai Putinar) Noncommutative sums of squares. Pacific J. Math. 218 (2005), no. 1, 167–171.

(with Michael Dritschel) The failure of rational dilation on a triply connected domain. J. Amer. Math. Soc. 18 (2005), no. 4, 873–918.

(with Michael Dritschel) Boundary representations for families of representations of operator algebras and spaces. J. Operator Theory 53(2005), no. 1, 159–167.

(with Vern Paulsen) C∗-envelopes and interpolation theory. Indiana Univ. Math. J. 51 (2002), no. 2, 479–505.

(with Stefan Richter) Bergman-type reproducing kernels, contractive divisors, and dilations. J. Funct. Anal. 190 (2002), no. 2, 447–480.

Isometric representations of some quotients of H∞ of an annulus. Integral Equations Operator Theory 39 (2001), no. 3, 335–362.

Factorization of operator-valued polynomials in several non-commuting variables. Linear Algebra Appl. 326 (2001), no. 1-3, 193–203.

(with Tavan Trent) Invariant subspaces and Nevanlinna-Pick kernels. J. Funct. Anal. 178 (2000), no. 1, 226–249.

Commutant lifting on a two holed domain. Integral Equations Operator Theory 35 (1999), no. 1, 65–84.

(with Robert Clancy) Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel. Proc. Amer. Math. Soc. 126 (1998), no. 11,3299–3305.

The trisecant identity and operator theory. Integral Equations Operator Theory 25 (1996), no. 1, 104–127.

Nevanlinna-Pick type interpolation in a dual algebra. J. Funct. Anal. 135 (1996), no. 1, 93–131.

Minimal separators of 2-chordal graphs. Linear Algebra Appl. 184 (1993), 187–199.