Job title:
Professor Emeritus
Research area:
Bio:
Year appointed: 1974
Year retired: 2014
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 Szegő 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 Birkhäuser 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.
Research interests:
Analysis, Probability, Integrable systems, Medical imaging