F. Alberto Grünbaum

Professor Emeritus
Primary Research Area: 
Applied Mathematics
Additional Research Areas: 
Mathematical Analysis
Research Interests: 
Analysis, Probability, Integrable systems, Medical imaging
Contact Information
905 Evans Hall
grunbaum [at] math [dot] berkeley [dot] edu
+1 (510) 642-5348
Year Appointed: 
Selected Publications: 
  1. Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio; Bispectrality
    and time-band limiting: matrix-valued polynomials.
    Int. Math. Res. Not. IMRN 2020, no. 13, 4016–4036.
  2. Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L. Quantum Markov
    chains: recurrence, Schur functions and splitting rules. Ann. Henri
    Poincaré 21 (2020), no. 1, 189–239. 81P47 (81S22)
  3. Casper, W. Riley; Grünbaum, F. Alberto; Yakimov, M.; Zurrián, I,
    Reflective prolate-spheroidal operators and the KP/KdV equations.
    PNAS September 10, 2019 116 (37) 18310-18315.
  4.  Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun
    operator and band-time limiting. Comm. Math. Phys. 364 (2018), no. 3,
  5.  Grünbaum, F. Alberto; de la Iglesia, Manuel D. Stochastic LU
    factorizations, Darboux transformations and urn models. J. Appl. Probab.
    55 (2018), no. 3, 862–886. 60J10 (33C45 42C05)
  6. Grünbaum, F. A.; Velázquez, L. A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Adv. Math. 326 (2018), 352–464
  7. Cedzich,C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.;
    Werner, A. H.;Werner, R. F. The topological classification of
    one-dimensional symmetric quantum walks. Ann. Henri Poincaré 19 (2018),
    no. 2,
  8. Grünbaum, Francisco Alberto; Velázquez, Luis The
    CMV bispectral problem. Int. Math. Res. Not. IMRN 2017, no. 19,
  9. Castro, M.; Grünbaum,
    F. A. Time-and-band limiting for matrix orthogonal polynomials of Jacobi
    type.     Random Matrices Theory Appl. 6   (2017), no.4, 1740001, 12
  10. Grünbaum, F. A.; Pacharoni,
    I.; Zurrián, I. Time and band limiting for matrix valued functions: an
    integral and a commuting differential  operator. Inverse Problems 33
    (2017), no. 2, 025005, 14 pp. 
  11. Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Tridiagonalization
    and the Heun equation. J. Math. Phys. 58 (2017), no. 3, 031703,  12 pp. 
  12. Cedzich, C.; Grünbaum, F. A.;
    Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. Bulk-edge       
    correspondence of one-dimensional quantum walks. J. Phys. A 49 (2016),
    no. 21, 21LT01, 12 pp. 81Q35   
  13. Cedzich,C.; Grünbaum,  F. A.; Velázquez, L.; Werner, A. H.; Werner, R.
    F. A quantum dynamical approach to matrix Khrushchev's formulas. Comm.
    Pure Appl. Math. 69 (2016), no. 5, 909–957.
  14. Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián,
    Ignacio Nahuel Time and band limiting for matrix valued functions, an
    example. SIGMA Symmetry Integrability Geom. Methods Appl. 11 (2015),
    Paper 044, 14 pp. 42C10  
  15. Grünbaum, F. Alberto
    Some noncommutative matrix algebras arising in the bispectral problem.
    SIGMA Symmetry Integrability Geom. Methods Appl. 10 (2014), Paper 078, 9
  16. J. Bourgain, F.A. Grünbaum, L. Velázquez and J. Wilkening; Quantum recurrence of a subspace and operator valued Schur functions, (on line already)  in Comm. Math. Phys. (2014)  arXiv: 1302.7286 v1.
  17. F.A. Grünbaum, L. Velázquez, A. Werner and R. Werner; Recurrence for discrete time unitary evolutions, Comm. Math. Phys. (320) 2013
  18. F.A. Grünbaum, L. Velázquez, The quantum walk of F. Riesz,
    Foundations of computational mathematics, Budapest 2011, 93-112, London
    Math. Soc. Lecture Note Ser. 403, Cambridge Univ. Press, Cambridge,
  19. M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, Matrix valued Szegő polynomials and quantum random walks, Comm. Pure Appl. Math. 63 (2010) 464-507
  20. Grünbaum, F. Alberto (2010). An urn model associated with Jacobi polynomials. Commun. Appl. Math. Comput. Sci. 5 55-63. [MR] [GS?]
  21. Grünbaum, F. Alberto (2009). Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. In Modern analysis and applications. The Mark Krein Centenary Conference. Vol. 1: Operator theory and related topics Oper. Theory Adv. Appl. 190 267-277 Birkhäuser Verlag Basel. [link] [MR] [GS?
  22. Grünbaum, F. Alberto (2008). Random walks and orthogonal polynomials: some challenges. In Probability, geometry and integrable systems Math. Sci. Res. Inst. Publ. 55 241-260 Cambridge Univ. Press Cambridge. [MR] [GS?]
  23. Grünbaum, F. Alberto and de la Iglesia, Manuel D. (2008). Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. SIAM J. Matrix Anal. Appl. 30 No.2, 741-761.