# Robert Buckingham

## Professor

## Professor and Graduate Program Director

### French Hall

5506

A&S Mathematical Sciences - 0025

## Professional Summary

## Education

Ph.D.: Duke University 2005 (Mathematics)

M.A.: Duke University 2001 (Mathematics)

S.B.: MIT 2000 (Mathematics)

S.B.: MIT 2000 (Physics)

## Research and Practice Interests

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

## Positions and Work Experience

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

## Research Support

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

## Abbreviated Publications

### 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.