Professor Emeritus

Research 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

http://math.berkeley.edu/~grunbaum/

Year Appointed:
1974

Retired:
2014


Publications Selected Publications:
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.
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)
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.
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun
operator and band-time limiting. Comm. Math. Phys. 364 (2018), no. 3,
1041–1068.
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)
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
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,
325–383.
Grünbaum, Francisco Alberto; Velázquez, Luis The
CMV bispectral problem. Int. Math. Res. Not. IMRN 2017, no. 19,
5833–5860.
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
pp.
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.
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Tridiagonalization
and the Heun equation. J. Math. Phys. 58 (2017), no. 3, 031703, 12 pp.
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
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.
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
Grünbaum, F. Alberto
Some noncommutative matrix algebras arising in the bispectral problem.
SIGMA Symmetry Integrability Geom. Methods Appl. 10 (2014), Paper 078, 9
pp.
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.
F.A. Grünbaum, L. Velázquez, A. Werner and R. Werner; Recurrence for discrete time unitary evolutions, Comm. Math. Phys. (320) 2013
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,
2013.
M.J. Cantero, F.A. Grünbaum, L. Moral, L. Velázquez, Matrix valued Szeg? polynomials and quantum random walks, Comm. Pure Appl. Math. 63 (2010) 464-507
Grünbaum, F. Alberto (2010). An urn model associated with Jacobi polynomials. Commun. Appl. Math. Comput. Sci. 5 55-63. [MR] [GS?]
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 Birkh?user Verlag Basel. [link] [MR] [GS?
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?]
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.