- Multi-Variable Operator Theory
- Hardy Space Over the Bidisk
- Model Theory for Contractions
- Commutators of Operator Pairs
- Joint spectra
- Hardy and Bergman spaces over other domains

- Several Complex Variables
- Topology
- Hyperplane arrangements
- Complement of hypersurfaces

# Complete List of Publications

- 1, "A cross-section from inner function to invariant subspaces", Int. Equ. and Oper. Theory 28(1997), no. 2, 238--244.
- 2, "Quotient Hardy modules" with R. G. Douglas, Houston J. Math. 24 (1998), no. 3, 507--517.
- 3, "BCL index and Fredholm tuples", Proc. Amer. Math. Soc. 127 (1999), no. 8, 2385--2393.
- 4, "Berger-Shaw theorem in the Hardy space over the bidisk", J. Oper. Theory (1999), vol. 42, no. 2, 379--404.
- 5, "Operator theory in the Hardy space over the bidisk(I)", (with R. G. Douglas) Int. Equ. and Oper. Theory, 38(2000), no. 2, 207--221.
- 6, "Operator theory in the Hardy space over the bidisk(II)", Int. Equ. and Oper. Theory, 42 (2002) 99-124. .
- 7, "Operator theory in the Hardy space over the bidisk(III)", J. of Funct. Analy., 186, 521-545 (2001) .
- 8, "A trace formula for isometric pairs", Proc. A.M.S.131 (2003), No.2, 533-541 .
- 9, "Beurling's phenomenon in two variables", Integr. Equ. Oper. Theory, 48 (2004), No.3, 411-423.
- 10, "On Two variable Jordan block", Acta Sci. Math. (Szeged), 69 (2003), No.3-4, 739-754.
- 11, "The core function for the Hardy modules on the torus", (with K. Guo), Indiana Univ. Math. J, 53(2004), No.1, 205-222.
- 12, "Strictly contractive compression on the torus", (with K. Izuchi), Acta. Sci. Math. (Szeged), 70(2004), No.1-2, 147-165.
- 13, "The root operator on Bergman shift invariant subspaces", (with K. Zhu), Illinois J. Math., 47 (2003), No.4, 1227-1242.
- 14, "Hilbert-Schmidt submodules and issues of unitary equivalence", J. Oper. Theory 53 (2005), No.1, 169-184.
- 15, "The core operator and congruent submodules", J. Funct. Anal. 228 (2005), no. 2, 469–489.
- 16, "On two variable Jordan block. II", Integral Equations Operator Theory 56 (2006), no. 3, 431–449.
- 17, "Inner sequence based invariant subspaces in $H^2(D^2)$" (with M. Seto), Proc. Amer. Math. Soc. 135 (2007), no. 8, 2519–2526
- 18, "Functional spectrum of contractions", J. Funct. Anal. 250 (2007), no. 1, 68–85.
- 19, "N_f-type quotient modules on the torus" (with K. Izuchi), New York J. Math. 14 (2008), 431–457.
- 20, "A note on classification of submodules in $H^2(D^2)$", Proc. Amer. Math. Soc. 137 (2009), no. 8, 2655–2659.
- 21, "Projective spectrum in Banach algebras", J. Topol. Anal. 1 (2009), no. 3, 289–306.
- 22, "On the spectrum of operator-valued entire functions" (with J. Bannon), preprint.
- 23, "Analyticity of joint spectrum via determinant" (with M. Stessin and K. Zhu), preprint.

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