Curriculum Vitae
Education:
- Ph.D University of Arizona, Applied Mathematics, December 1994. Thesis Title: Macroscopic Lattice Dynamics. Thesis Committee: N. M. Ercolani, C. D. Levermore, A. C. Scott
- M.S. University of Arizona, Applied Mathematics, December 1991.
- National Science Foundation Graduate Fellow, University of Arizona, 1991-1993.
- B.S. (Summa Cum Laude) Southern Methodist University, Mathematical Sciences, May 1989.
- B.S. (Summa Cum Laude) Southern Methodist University, Computer Science, May 1989.
Professional History:
- September 2007-Present: Professor, Department of Mathematics, University of Michigan.
- September 2006-December 2006: University Fellow, Statistical and Applied Mathematical Sciences Institute (SAMSI), and Visiting Associate Professor, Department of Mathematics, University of North Carolina, Chapel Hill.
- September 2003-August 2007: Associate Professor, Department of Mathematics, University of Michigan.
- August 2000-August 2003: Assistant Professor, Department of Mathematics, University of Michigan.
- June 1998-August 2000: Logan Fellow, Department of Mathematics and Statistics, Monash University, Clayton, Victoria, Australia.
- September 1997-June 1998: Member, School of Mathematics, Institute for Advanced Study, Princeton, New Jersey.
- January 1995-September 1997: Postdoctoral Fellow, Optical Sciences Centre, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australia.
Main Research Interests:
- Multiscale phenomena in nonlinear systems of mathematical physics, including random matrix theory and singular limits of dispersive waves. Modulation theory of nonlinear multiphase waves. Modulational stability and resonance.
- Integrable nonlinear systems. Soliton theory and methods of algebraic geometry.
- Complex analysis. Riemann-Hilbert problems and applications to integrable systems theory, random matrix theory, and approximation theory.
- Exactly solvable linear wave equations. Applications to optical waveguide theory.
Awards and Funding Received:
- 2012: National Science Foundation Research Grant. Funded project title: Frontiers in Asymptotic Analysis for Integrable Nonlinear Waves. $315,000. Grant number DMS-1206131.
- 2008: National Science Foundation Research Grant. Funded project title: Asymptotic Problems in Nonlinear Waves and Beyond. $300,000. Grant number DMS-0807653.
- 2004: National Science Foundation FRG Grant. Funded project title: Asymptotic Questions in Integrable Nonlinear Wave Theory. $314,837. Grant number DMS-0354373.
- 2002: Alfred P. Sloan Foundation Research Fellowship.
- 2001: National Science Foundation Research Grant. Funded project title: The Semiclassical Limit of the Focusing Nonlinear Schrödinger Equation. $102,002. Grant number DMS-0103909.
- 2001: Rackham Fellowship, University of Michigan. Funded project title: The Semiclassical Limit of the Focusing Nonlinear Schrödinger Equation.
- 1997: Logan Fellowship, Monash University. Funded project title: Spontaneous Oscillations in Weakly Dispersive Discrete Integrable Systems: Prediction of Onset and Characterization.
- 1995: Institute of Advanced Studies/Australian Universities' Research Collaboration Scheme. Funded project title: Integrable Numerical Schemes.
- 1990: National Science Foundation Graduate Fellowship.
Important Presentations:
- Invited Lecture, 69th Midwest Partial Differential Equations Seminar, University of Illinois, Chicago, Illinois, April 2012.
- Semiplenary Lecture, Workshop on Asymptotics and High Oscillation, Foundations of Computational Mathematics, Budapest, Hungary, July 2011.
- Invited Lecture, 61st Midwest Partial Differential Equations Seminar, The Ohio State University, Columbus, Ohio, November 2008.
- Semiplenary Lecture, Workshop on Asymptotic Analysis, Foundations of Computational Mathematics, City University of Hong Kong, Hong Kong, China, June 2008.
- Keynote Address, 4th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, Georgia, April 2005.
- Invited Lecture, 26th Midwest Probability Colloquium, Tutorial Program on Random Matrix Theory, Northwestern University, Evanston, Illinois, October 2004.
- Plenary Address, SIAM Dynamical Systems, Snowbird, Utah, May 2003.
Teaching and Mentorship Experience:
Undergraduate Teaching:
- 2011: Lecturer in Undergraduate Summer School "Introduction to Mathematical Physics and Quantization", May 23-28, 2011, Notre Dame University.
- 2004-2006: Course coordinator for University of Michigan Math 216 (Introduction to Differential Equations), a large, multisection course.
- 2002: Research Experience for Undergraduates (REU) mentorship. Project title (joint with T. Blass): The sine-Gordon equation and its applications to long Josephson junctions.
- 2000-Present: University of Michigan Math 185 (Honors Calculus and Analytical Geometry I), Math 216 (Introduction to Differential Equations), Math 255 (Applied Honors Calculus III: Multivariate Calculus), and Math 256 (Applied Honors Calculus IV: Differential Equations).
- 1993-1994: Teaching Assistant, Department of Mathematics, University of Arizona.
Graduate Teaching and Mentorship:
- 2008-Present: Director, graduate program in Applied and Interdisciplinary Mathematics (AIM).
- 2011-Present: PhD supervision of Alfredo Wetzel, a student in Applied and Interdisciplinary Mathematics (AIM).
- 2007-2010: PhD supervision of Zhengjie Xu, a student in Applied and Interdisciplinary Mathematics (AIM). Thesis title: "Asymptotic Analysis and Numerical Analysis of the Benjamin-Ono Equation".
- 2012-Present: Dissertation committee of C. Zhang (Electrical Engineering). 2010-Present: Dissertation committee of Z. Liu (Mathematics). 2010-2012: Dissertation committee of M. Masarik (AIM). 2009-2012: Dissertation committee of D. Rooney (AIM) and S. Flores (AIM). 2011: Dissertation committee of N. Totz (Mathematics). 2010-2011: Dissertation committee of M. Ma (Electrical Engineering). 2009-2010: Dissertation committee of T. Wu (Electrical Engineering) and Brian Jennings (AIM). 2008-2010: Dissertation committee of T. Ohsawa (AIM). 2008: Dissertation committee of R. Hegde (Electrical Engineering). 2005-2008: Dissertation committee of A. Tabatabaeenejad (Electrical Engineering). 2003: Dissertation committee of R. Walker (Mathematics). 2002: Dissertation committee of E. Kirr (Mathematics) and V. Perlin (Electrical Engineering).
- 2006: Textbook authorship. Applied Asymptotic Analysis, Graduate Studies in Mathematics, Volume 75, AMS publications, Providence. (467 pages)
- 2009: Tutorial lecturer in the Graduate Summer Workshop on Random Matrix Theory, MSRI, July 2009. 2006: Co-teaching of a graduate course in Random Matrix Theory held at the Statistical and Applied Mathematical Sciences Institute (SAMSI) in Fall 2006.
- 2000-Present: University of Michigan Math 501 (Applied and Interdisciplinary Mathematics Student Seminar), Math 556 (Methods of Applied Mathematics I: Applied Functional Analysis), Math 557 (Methods of Applied Mathematics II: Asymptotic Methods), Math 558 (Applied Nonlinear Dynamics), Math 651 (Integrable Systems, Nonlinear Waves, and Soliton Theory).
Postdoctoral Mentorship:
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Current faculty mentorship for postdoctoral
assistant professors
- Karl Liechty (2011-Present)
- Organization of a Working Group on Integrability and Asymptotics, involving several postdocs and graduate students. Joint work originating in this working group has resulted in several publications.
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Former faculty mentorship for postdoctoral assistant professors
- Robert Jenkins (2009-2012), now at SISSA, Trieste, Italy.
- Richard Kollar (2005-2009), now tenure-track at Comenius University, Bratislava, Slovakia.
- Robert Buckingham (2005-2008, now tenure-track at the University of Cincinnati.
- Jeffery DiFranco (2004-2007, now tenure-track at Seattle University)
- Guadalupe Teran-Lozano (2004-2007, now at the University of New Mexico)
- Gregory Lyng (2002-2005, now Associate Professor at the University of Wyoming).
Service:
- Associate Editor, SIAM Journal of Mathematical Analysis (2009-Present).
- Guest Editor, special issue of Comm. Math. Sci. in honor of the 60th birthday of C. D. Levermore (2010-2011).
- Program Director, SIAM Activity Group on Nonlinear Waves and Coherent Structures (2009-2010).
- Academic Program Review Committee, Department of Mathematics, University of Arizona (2009).
- National Science Foundation Review Panel service (2005, 2006, 2011).
- Rackham Distinguished Dissertation Award Committee (2001).
- Departmental committees: Admissions and Fellowships (2001-2002, 2008), AIM Graduate / Admissions and Fellowships (chair, 2008-Present), Doctoral (2008-Present), Education (2008-Present), Executive (2005-2006), Masters (2008-Present), Personnel (2003-2005), Applied Analysis Qualifying Review Exam committee: (2001-2006), Long Range Planning Committee (2010-2015).
- Peer referee for: AMS, Cambridge University, CRC, and London Mathematical Society Presses, Advances in Theoretical and Mathematical Physics, Annals of Mathematics, ANZIAM Journal of Applied Mathematics, International Mathematics Research Notices, CHAOS, Communications in Mathematical Physics, Communications on Pure and Applied Mathematics, Constructive Approximation, Electronic Transactions on Numerical Analysis, Journal of Approximation Theory, Journal of the Faculty of Science, United Arab Emirates University, Journal of Mathematical Analysis and Applications, Journal of Mathematical Physics, Journal of Nonlinear Science, Mathematical Reviews, Nonlinearity, Optics Communications, Photonics Technology Letters, Physica D, Physica Scripta, Physical Review E, Physical Review Letters, and Physics Letters A.
Synergistic Activities:
- Organization (with D. Viswanath) of departmental Applied and Interdisciplinary Mathematics Seminar (2001-Present).
- Organization (with P. Duren) of departmental Complex Analysis Seminar (2008-2009).
- Organization of departmental Working Group in Integrable Systems and Asymptotics (2004-Present).
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Frequent organization of minisymposia and special sessions at large
meetings. Most recently:
- Co-chair, SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, PA, August 2010.
- Organization (joint with J. Bronski and K. McLaughlin) of a special session on Asymptotics of Nonlinear Waves and Related Problems as part of the 6th IMACS conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, March 2009. Also service on the scientific program committee for this conference and organization of a Tutorial lecture series.
- Organization (joint with A. Tovbis) of a special session on Direct and Inverse Scattering Transforms for Integrable Systems and their Semiclassical Limits as part of the 2008 International Workshop on Operator Theory and its Applications (IWOTA), College of William and Mary, Williamsburg, VA, July 2008.
- Organization (joint with R. Buckingham, J. DiFranco, and R. Kollar) of a special session on Nonselfadjoint Spectral Problems as part of the 5th IMACS conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, April 2007. Also, service on the scientific program committee for this conference.
- Organization (joint with E. Basor) of a special session on New Developments and Directions in Random Matrix Theory as part of the AMS sectional meeting in Tucson, AZ, April 2007.