Research
"To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." -- Richard Feynman. (1918-1988), The Character of Physical Law
[Publications] [Undergraduate Research Sponsored] [Grants] [Conferences Organized] [Talks] [Journals Refereed For]

Publications

  1. On a problem of Halmos: unitary equivalence of a matrix to its transpose (with James E. Tener) (PDF) (ArXiV)
    (submitted)

  2. Unitary equivalence to a complex symmetric matrix: a modulus criterion (with Daniel Poore, Madeline Wyse)
    (in preparation)

  3. Truncated Toeplitz operators: spatial isomorphisms, unitary equivalence, and similarity (with Joseph Cima, William Ross, Warren Wogen) (PDF) (ArXiv)
    Indiana Univ. Math. J. (to appear).

  4. Complex symmetric partial isometries (with Warren Wogen) (PDF) (ArXiv)
    J. Funct. Analysis 257 (2009), 1251-1260.

  5. The norm of a truncated Toeplitz operator (with William Ross) (PDF) (ArXiv)
    CRM Proceedings (to appear).

  6. Unitary equivalence to a complex symmetric matrix: geometric criteria (with Levon Balayan) (PDF) (ArXiv)
    Operators and Matrices (to appear).

  7. A nonlinear extremal problem on the Hardy space (with William Ross) (PDF)
    Computation Methods and Function Theory 9 (2009), No. 2, 485--524.

  8. The norm and modulus of a Foguel operator (PDF) (ArXiv)
    Indiana Univ. Math. J. (to appear).

  9. Hermitian-symmetric inequalities in Hilbert space (PDF)
    Complex Analysis and Operator Theory (to appear).

  10. Some new classes of complex symmetric operators (with Warren Wogen) (PDF) (ArXiv)
    Trans. Amer. Math. Soc. (to appear).

  11. Aluthge transforms of complex symmetric operators (PDF)
    Integral Equations Operator Theory 60 (2008), 357-367.

  12. Means of unitaries, conjugations, and the Friedrichs operator (PDF)
    J. Math. Anal. Appl. 335 (2007), 941 - 947.

  13. Interpolation and complex symmetry (with Mihai Putinar) (PDF)
    Tohoku Math. J. 60 (2008), 423-440.

  14. Approximate antilinear eigenvalue problems and related inequalities (PDF)
    Proc. Amer. Math. Soc. 136 (2008), 171-179.

  15. The eigenstructure of complex symmetric operators (PDF)
    Operator Theory: Advances and Applications 179 (2008), 169-184.

  16. Variational principles for symmetric bilinear forms (with Jeffrey Danciger, Mihai Putinar) (PDF)
    Math. Nachr. 281 (2008), no. 6, 786--802.

  17. Conjugation and Clark operators (PDF)
    Contemp. Math. 393 (2006), 67-112.

  18. Norm estimates of complex symmetric operators applied to quantum systems (with Emil Prodan, Mihai Putinar) (PDF) (ArXiv)
    J. Phys. A: Math. Gen. 39, no. 2, (2006), 389-400.

  19. Complex symmetric operators and applications II (with Mihai Putinar) (PDF)
    Trans. Amer. Math. Soc. 359 (2007), 3913-3931.

  20. Inner matrices and Darlington synthesis (PDF)
    Methods. Funct. Anal. Topology. 11, no. 1, (2005), 37-47.

  21. The backward shift on Dirichlet-type spaces (PDF)
    Proc. Amer. Math. Soc. 133, no. 10, (2005), 3047-3056.

  22. Complex symmetric operators and applications (with Mihai Putinar) (PDF)
    Trans. Amer. Math. Soc. 358 (2006), 1285-1315.

  23. A *-closed subalgebra of the Smirnov class (PDF)
    Proc. Amer. Math. Soc. 133, no. 7, (2005), 2051-2059.

  24. Conjugation, the backward shift, and Toeplitz kernels (PDF)
    J. Operator Theory 54, no. 2, (2005), 239-250.

  25. Real outer functions (with Donald Sarason) (PDF)
    Indiana Univ. Math. J. 52, no. 6, (2003), 1397-1412.

Undergraduate Research Sponsored

Research Grants

Conferences Organized

Talks

  1. Hiddem symmetries in everyday operators (PDF)
    Mathematics Colloquium
    University of Richmond, (Sept. 28, 2009).

  2. Simultaneous Diophantine equations with side constraints: an elementary method (PDF)
    Claremont Colleges Algebra/Number Theory/Combinatorics Seminar
    Pomona College, (Apr. 7, 2009).

  3. Open questions about complex symmetric operators (PDF)
    Southeastern Analysis Meeting (SEAM 25)
    University of South Florida, (Mar. 21, 2009).

  4. Unitary equivalence to a complex symmetric matrix
    Claremont Colleges Analysis Seminar
    Pomona College, (Sep. 15, 2008).

  5. Unitary equivalence to a complex symmetric matrix (PDF)
    International Workshop on Operator Theory and Applications (IWOTA 2008)
    College of William and Mary, (July 22 - 26, 2008).

  6. Rationals, irrationals, and quotients of primes (PDF)
    Pomona College Mathematics Talent Search Honors Day
    Pomona College, (Apr. 26, 2008).

  7. Inner matrix functions and Darlington synthesis
    Claremont Colleges Analysis Seminar
    Pomona College, (Apr. 21, 2008).

  8. New classes of complex symmetric operators (PDF)
    Southeastern Analysis Meeting (SEAM 24)
    Vanderbilt University, (Mar. 5-9, 2008).

  9. The backward shift on Dirichlet-type spaces
    Claremont Colleges Analysis Seminar
    Claremont McKenna College, (Sep. 13, 2007).

  10. Real Smirnov functions and applications (PDF)
    Distinguished Visiting Professor Program Colloquium
    Bucknell University, (Aug. 30, 2007).

  11. Complex symmetric operators: an overview (PDF)
    Distinguished Visiting Professor Program Colloquium
    Bucknell University, (Aug. 28, 2007).

  12. Remarks on complex symmetric operators (PDF)
    Southeastern Analysis Meeting (SEAM 23)
    University of Richmond, (Mar. 10, 2007).

  13. An adjoint of Beurling's theorem
    Claremont Colleges Analysis Seminar
    Pomona College, (Mar. 5, 2007).

  14. Real complex functions (PDF)
    Claremont Colleges Mathematics Colloquium
    Claremont McKenna College, (Feb. 14, 2007).

  15. Complex symmetric operators: matrices, operators, functions (PDF)
    Southern California Functional Analysis Seminar
    Claremont McKenna College, (Oct. 28, 2006).

  16. Southeastern Analysis Meeting (SEAM 22)
    University of Florida, (Mar. 4, 2006).

  17. Mathematics Colloquium
    Vassar College, (Feb. 14, 2006).

  18. Mathematics Colloquium
    University of Arkansas, (Feb. 10, 2006).

  19. Complex Analysis Seminar
    University of Arkansas, (Feb. 9, 2006).

  20. Mathematics Colloquium
    University of Hawaii, (Feb. 3, 2006).

  21. Mathematics Colloquium
    Pomona College, (Jan. 27, 2006).

  22. Mathematics Colloquium
    North Dakota State University, (Jan. 20, 2006).

  23. Mathematics Colloquium
    Texas A & M University, (Dec. 6, 2005).

  24. Complex Analysis Seminar
    University of Washington, (Oct. 18, 2005).

  25. Recent Advances in Operator-Related Function Theory
    El Escorial (Spain), (Oct. 7, 2005).

  26. Mathematics Colloquium
    California State University, Channel Islands, (Sep. 16, 2005).

  27. International Workshop on Operator Theory and Applications (IWOTA 2005)
    University of Connecticut, (July 24, 2005).

  28. Mathematics Colloquium
    California Polytechnic State University, San Luis Obispo, (Apr. 29, 2005).

  29. Operator Theory Seminar (two lectures)
    University of Virginia, (Apr. 11-12, 2005).

  30. Southeastern Analysis Meeting (SEAM 21)
    Washington and Lee University, (Apr. 8-9, 2005).

  31. Mathematics Colloquium
    Virginia Polytechnic Institute and State University, (Apr. 6, 2005).

  32. Functional Analysis Seminar
    U.C. Santa Barbara, (Nov. 3, 2004).

  33. Functional Analysis Seminar (two lectures)
    U.C. Santa Barbara, (Sep. 29, 2004; Oct. 6, 2004).

  34. Berkeley Analysis Seminar
    U.C. Berkeley, (Sep. 7, 2004).

  35. Recent Advances in Operator-Related Function Theory
    Trinity College, Dublin (Ireland), (Aug. 4, 2004).

  36. Functional Analysis Seminar
    U.C. Santa Barbara, (May 13, 2004).

  37. Lund University Mathematics Colloquium
    Lund University, Lund (Sweden), (Apr. 28, 2004).

  38. Lund University Analysis Seminar
    Lund University, Lund (Sweden), (Apr. 27, 2004).

  39. Tennessee Analysis Seminar (two lectures)
    University of Tennessee, Knoxville, (Mar. 22, 2004; Mar. 29, 2004).

  40. Southeastern Analysis Meeting (SEAM 20)
    University of Alabama, Tuscaloosa, (Mar. 26-27, 2004).

  41. Functional Analysis Seminar
    University of California, San Diego, (Mar. 10, 2004).

  42. Claremont Colleges Mathematics Colloquium
    Harvey Mudd College, (Feb. 25, 2004).

  43. AMS Special Session: Linear Operators on Function Spaces
    University of North Carolina, Chapel Hill, (Oct. 24, 2003).

  44. Functional Analysis Seminar
    U.C. Santa Barbara, (2003).

  45. Berkeley Analysis Seminar
    U.C. Berkeley, (2003).

Journals Refereed For