Robert Buckingham

http://homepages.uc.edu/~buckinrt

Ph.D.: Duke University 2005 (Mathematics)

M.A.: Duke University 2001 (Mathematics)

S.B.: MIT 2000 (Mathematics)

S.B.: MIT 2000 (Physics)

Asymptotic behavior and universality of stochastic processes, random matrices, and nonlinear wave equations.

2014 -To Present Associate Professor, University of Cincinnati,

2009 -2014 Assistant Professor, University of Cincinnati,

2008 -2009 Postdoctoral Fellow (Theme Year on Probabilistic Methods in Mathematical Physics), Centre de Recherches Mathematiques, Universite de Montreal

2005 -2008 Postdoctoral Assistant Professor, University of Michigan, Ann Arbor

Grant: #DMS-1615718 Investigators:Buckingham, Robert 08-01-2016 -07-31-2019 National Science Foundation New Directions in the Asymptotics of Nonlinear Waves Role:PI $208,916.00 Active Level:Federal

Grant: #DMS-1441641 Investigators:Buckingham, Robert; Peligrad, Magda; Wang, Yizao; Yen, Ju-Yi 07-01-2014 -06-30-2015 National Science Foundation Cincinnati Symposium on Probability Theory and Applications 2014 Role:PI

Grant: #DMS-1312458 Investigators:Buckingham, Robert 08-2013 -07-2016 National Science Foundation Nonlinear Wave Dynamics: Emergent Methods and Phenomena Role:PI

Grant: #Award No. 245775 Investigators:Buckingham, Robert 09-2012 -08-2013 Simons Foundation Universality in Stochastic Processes and Differential Equations Role:PI

Grant: #DMS-1832863 Investigators:Buckingham, Robert 09-01-2018 -08-31-2019 National Science Foundation Cincinnati Symposium on Probability Theory and Applications 2018 Role:PI $20,000.00 Awarded Level:Federal

Grant: #DMS-2108019 Investigators:Buckingham, Robert 08-01-2021 -07-31-2024 National Science Foundation Frontiers in Dispersive Wave Equations Role:PI 203816.00 Active Level:Federal

Grant: #DMS-2413604 Investigators:Buckingham, Robert; Guo, Xiaoqin; Peligrad, Magda; Wang, Yizao; Yen, Ju-Yi 05-01-2024 -04-30-2025 National Science Foundation Conference: Cincinnati Symposium on Probability 2024 Role:Collaborator 48620.00 Active Level:Federal

Peer Reviewed Publications

Large-order asymptotics for multiple-pole solitons of the focusing non- linear Schrödinger equation (with D. Bilman), J. Nonlinear Sci. doi:10.1007/s00332-019-09542-7 (2019).

Nonintersecting Brownian bridges on the unit circle with drift (with K. Liechty), J. Funct. Anal. 276 (2019), 1717–1772.

Large-degree asymptotics of rational Painlevé-IV functions associated to generalized Hermite polynomials, Int. Math. Rev. Not. IMRN rny172 (2018).

The k-tacnode process (with K. Liechty), Probab. Theory Related Fields doi:10.1007/s00440-018-0885-2 (2018).

Large Deformations of the Tracy–Widom Distribution I: Non-oscillatory Asymptotics (with T. Bothner), Commun. Math. Physics 359 (2018), 223-263.

Semiclassical soliton ensembles for the three-wave resonant interaction equations (with R. Jenkins and P. Miller), Commun. Math. Phys. 354 (2017), 1015-1100.

Large-degree asymptotics of rational Painleve-II functions:  noncritical behaviour (with P. Miller), Nonlinearity 28 (2015), 1539-1596.

Large-degree asymptotics of rational Painleve-II functions:  noncritical behaviour (with P. Miller), Nonlinearity 27 (2014), 2489-2577.

The sine-Gordon equation in the semiclassical limit:  Dynamics of fluxon condensates (with P. Miller),  Mem. Amer. Math. Soc.  225, number 1059 (2013), 1-136.

Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes (with M. Bertola, S. Y. Lee, and V. Pierce), J. Stat. Phys. 153 (2013), 654-697.

Spectra of random Hermitian matrices with a small-rank external source: the critical and near critical regimes (with M. Bertola, S. Y. Lee, and V. Pierce), J. Stat. Phys. 146 (2012), 475-518.

Semiclassical spectral confinement for the sine-Gordon equation.  Math.Comput. Simulation 82 (2012):  1030-1037

The sine-Gordon equation in the semiclassical limit:  critical behavior near a separatrix (with P. Miller),  J. Anal. Math. 118 (2012):  397-492.

Total Integrals of Painleve II solutions (with J. Baik, J. DiFranco, and A. Its), Nonlinearity 22 (2009), 1021-1061.

Asymptotics of Tracy-Widom distributions and the total integral of a Painleve II function (with J. Baik and J. DiFranco), Commun. Math. Phys. 280 (2008), 463-497.

Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation (with P. Miller), Physica D  237 (2008), 2296-2341.

Long-time asymptotics of the nonlinear Schrodinger equation shock problem (with S. Venakides), Commun. Pure Appl. Math.  60 (2007), 1349-1414.

Volume determination for bulk materials in bunkers (with S. Ahmed, P. Gremaud, C. Hauck, C. Kuster, M. Prodanovic, T. Royal, and V. Silantyev), Internat. J. Numer. Methods Engr.  61 (2004), 2239-2249.

Thin film traveling waves and the Navier slip condition (with M. Shearer and A. Bertozzi), SIAM J. Appl. Math.  63  (2003),  722-744.

Fluid Polygons (with J. Bush), Gallery of Fluid Motion, Phys. Fluids 13 (2001), S10.

Peer Reviewed Conference/Workshop Proceedings

The semiclassical focusing nonlinear Schrodinger equation (with A. Tovbis, S. Venakides, and X. Zhou), Proceedings of Recent Advances in Nonlinear Partial Differential Equations and Applications:  a Workshop in Honor of Peter Lax and Louis Niremberg, AMS Proceedings of Symposia in Applied Mathematics 65 (2007), 47-80.