Gregory D. Lyng

cv

education

• Ph.D., Indiana University, Bloomington, 2002.
  • Specialization: Mathematics
  • Ph.D. Thesis Title: One Dimensional Stability of Detonation Waves
  • Advisor: Kevin Zumbrun
• M.A., Mathematics, Indiana University, Bloomington, 1999.
• B.A. magna cum laude, Mathematics, Saint Olaf College, 1996.

professional history

• July 2010 - Present: Associate Professor, Department of Mathematics, University of Wyoming, Laramie.

• September 2005 - June 2010: Assistant Professor, Department of Mathematics, University of Wyoming, Laramie.

• September 2002 - May 2005: Assistant Professor (3-year Postdoctoral Position), Department of Mathematics, University of Michigan, Ann Arbor.
  Mentors: Peter Miller and Joel Smoller

• August 1996 - August 2002: Associate Instructor, Department of Mathematics, Indiana University, Bloomington.

research interests

Applied Analysis and Partial Differential Equations: nonlinear waves, existence & stability of traveling waves, Evans-function techniques, conservation and balance laws, gas dynamics, shock waves, and combustion, integrable equations.

funding & awards

• 2010: Extraordinary Merit in Teaching, College of Arts & Sciences, University of Wyoming.
• 2010: National Science Foundation (DMS-1005317), $25,000, Principal Investigator, Title of Project: Rocky Mountain Summer School: Conservation Laws & Applications.
• 2010: Institute for Mathematics and its Applications, $5,000, Principal Investigator, Title of Project: Rocky Mountain Summer School: Conservation Laws & Applications.
• 2009: Extraordinary Merit in Research, College of Arts & Sciences, University of Wyoming.
• 2009 - 2014: National Science Foundation (DMS-0845127), $409,998, Principal Investigator, Title of Project: CAREER: Wyoming Applied Analysis & Computing Group: Behavior of Solutions of Nonlinear Partial Differential Equations, (Faculty Early Career Development (CAREER) Program).
• 2008 - 2011: National Science Foundation (DMS-0755450), $245,574, Co-Principal Investigator, Title of Project: REU Site: Rocky Mountain Mathematical Research and Career Experiences (Research Experiences for Undergraduates Program), [PI: Bryan Shader].
• 2006: Basic Research Grant, College of Arts & Sciences, University of Wyoming, Principal Investigator, Title of Project: Evans-function Analysis for Realistic Models of Reacting Fluids.
• 2003 - 04: VIGRE Fellowship, Department of Mathematics, University of Michigan.
• 2003: Rackham Faculty Fellowship, Horace H. Rackham School of Graduate Studies, University of Michigan, Title of Project: Stability of Combustion Waves.
• 1999: Rothrock Teaching Award for Associate Instructors, Department of Mathematics, Indiana University.

selected talks

• 2013 (scheduled), Viscous hyperstabilization of detonation waves, IIMAS Applied Math Colloquium, Universidad Nacional Autónoma de México: Mexico City, Mexico.
• 2013, The Gaussian semiclassical soliton ensemble, AMS Sectional Meeting, University of Colorado: Boulder, CO.
• 2013, The Evans function and stability of viscous detonation waves: an overview, Analysis & Convexity Seminar, University of Oklahoma: Norman, OK.
• 2012, The Gaussian semiclassical soliton ensemble, Applied Mathematics Seminar, Michigan State University: East Lansing, MI.
• 2012, The Gaussian semiclassical soliton ensemble, Applied & Interdisciplinary Mathematics Seminar, University of Michigan: Ann Arbor, MI.
• 2012, The semiclassical limit of the focusing nonlinear Schrödinger equation: overview & recent results, PDE Seminar, Indiana University: Bloomington, IN.
• 2012, Refined stability for combustion waves, AMS Sectional Meeting, University of Kansas: Lawrence, KS.
• 2011, The Evans function and the stability of viscous shock and detonation profiles, Math Department Colloquium, University of Colorado: Colorado Springs, CO.
• 2011, Refined Stability for gas-dynamical Shocks, Nonlinear Waves Seminar, University of Colorado: Boulder, CO.
• 2011, Refined stability for combustion Waves, PD11: SIAM Conference on Analysis of Partial Differential Equations: San Diego, CA.
• 2010, (Refined) stability for Navier–Stokes shocks, NW10: SIAM Conference on Nonlinear Waves and Coherent Structures: Philadelphia, PA.
• 2010, Spectral stability of ideal-gas shock layers, Rocky Mountain Mathematics Consortium Summer School: Laramie, WY.
• 2010, Spectral stability of combustion waves, DSPDEs'10: Emerging topics in dynamical systems and partial differential equations: Barcelona, Spain.
• 2009, Spectral stability of ideal-gas shock layers, Applied Mathematics Seminar, Colorado State University: Fort Collins, CO.
• 2008, Spectral stability of ideal-gas shock layers, Applied Mathematics Seminar, University of Wisconsin: Madison, WI.
• 2008, The Evans function and stability of detonation waves, NW08: SIAM Conference on Nonlinear Waves and Coherent Structures: Rome, Italy.
• 2008, Spectral stability of ideal-gas shock layers, Applied Mathematics & Computation Seminar, University of Massachusetts: Amherst, MA.
• 2007, Pointwise Green function bounds and stability of combustion waves, DS07:SIAM Conference on Applications of Dynamical Systems: Snowbird, UT.
• 2007, The large-N limit of N-solitons for the focusing NLS equation: the secondary caustic, Seventh Joint Meeting of the Sociedad Matemática Mexicana (SMM) and the American Mathematical Society (AMS): Zacatecas, Mexico.
• 2007, Toward the stability of combustion waves: pointwise Green function bounds, Taller de Ecuaciones Nolineales 2007 [2007 Workshop on Nonlinear Equations], Universidad Nacional Autónoma de México: Mexico City, Mexico.
• 2007, Pointwise Green function bounds and stability of combustion waves, Applied Math Seminar, Michigan State University: East Lansing, MI.
• 2006, The secondary caustic for the semiclassical limit of the focusing nonlinear Schrödinger equation, Applied Math Colloquium, University of Colorado: Boulder, CO.
• 2006, The secondary caustic for the semiclassical limit of the focusing nonlinear Schrödinger equation, CCAM Seminar on PDEs and Numerical Methods, Penn State University: State College, PA.
• 2006, Breaking curves for the large-N limit of the N-soliton of the focusing nonlinear Schrödinger equation, NW06: SIAM Conference on Nonlinear Waves and Coherent Structures: Seattle, WA.
• 2005, An Evans-function Approach to Studying Detonations: Stability and Beyond, Seminar, University of Louisville: Louisville, KY.
• 2005, An Evans-function Approach to Studying Detonations: Stability and Beyond, Seminar, Trinity College: Dublin, Ireland.
• 2004, Low-frequency stability of multidimensional viscous and inviscid planar detonation waves, Hyp2004: Tenth International Conference on Hyperbolic Problems, Kyushu University: Osaka, Japan.
• 2004, The N-soliton of the focusing nonlinear Schrödinger equation for N large, Differential Equations Seminar, North Carolina State University: Raleigh, NC.
• 2004, Low-frequency stability of multidimensional detonations in three models of combustion: A spectral equivalence theorem, Partial Differential Equations Seminar, Indiana University: Bloomington, IN.
• 2004, Low-frequency stability of multidimensional detonations in three models of combustion: A spectral equivalence theorem, Applied & Interdisciplinary Mathematics Seminar, University of Michigan: Ann Arbor, MI.
• 2004, The Evans function and the stability of viscous detonation waves, NC04: Tenth International Conference on Numerical Combustion, Society for Industrial and Applied Mathematics: Sedona, AZ.
• 2003, Another look at Majda's model for reacting flow, Differential Equations Seminar, North Carolina State University: Raleigh, NC.
• 2003, Stability of Detonation Waves,'' Equadiff2003: International Conference on Differential Equations, Limburgs Universitair Centrum: Hasselt, Belgium.
• 2003, The Evans function and stability of viscous detonation waves, Applied Math Seminar, Ohio State University: Columbus, OH.
• 2002, Stability of detonation waves, Differential Equations Seminar, University of Michigan: Ann Arbor, MI.
• 2002, Stability of detonation waves, Hyp2002: Ninth International Conference on Hyperbolic Problems, California Institute of Technology: Pasadena, CA.

graduate student mentorship

• Yi-Hung Kuo (PhD Student, 2012 - Present, Co-Advisor with Long Lee)
• Eric Quade
  PhD, 2012
  Thesis Title: A new construction of viscous weak detonation profiles
  First Position: Faculty, Laramie County Community College (Albany County Campus)
• Michael Bostick
  MS, 2009
  Thesis Title: Combustion waves with multistep chemistry
  First Position: Faculty, Central Wyoming College

undergraduate research students

• George Wheeler (Summer 2013), Topic: Refined stability for systems.
• Yeongjoh Kim (Summer 2013, Co-mentor with Long Lee), Topic: Eigenvalues of the Zakharov-Shabat problem.
• Allison Lindgren (Summer 2012), Topic: Refined stability.
• Samuel Pasco (Summer 2011), Topic: Supercontinuum generation.
  After Wyoming: Basin Electric
• Irena Vankova (Spring & Summer 2011, Co-mentor with Long Lee), Topics: Semiclassical soliton ensembles & supercontinuum generation.
  After Wyoming: Graduate School, Applied Mathematics, New York University
• Stephen Bagley (Summer 2010), Topic: Refined stability.
  After Wyoming: Graduate School, Mathematics, University of Utah
• Nicholas Anderson (Summer 2010), Topic: Refined stability.
  After Wyoming: Graduate School, Mathematics, University of Wyoming
• Brian Kim (Summer 2004), Topic: Traveling-wave solutions of a diffusive predator-prey system

courses taught

Complete List of Courses

peer reviewer

• Book Proposals: J. Wiley & Sons, Inc.
• Journal Articles: Applicable Analysis, Discrete and Continuous Dynamical Systems (supplement), International Mathematics Research Notices, Journal of Differential Equations, Journal of Mathematical Physics, Journal of Physics A, Mathematical Models and Methods in Applied Sciences, Mathematische Nachrichten, Michigan Mathematics Journal, Nonlinear Analysis: Real World Applications, Nonlinearity, Physica D, Proceedings of the Royal Society A, SIAM Journal on Mathematical Analysis, Zeitschrift für Naturforschung A.
• Grant Proposals: National Science Foundation (USA)

professional associations

• Member, American Mathematical Society
• Member, Society for Industrial and Applied Mathematics
• Affiliate Faculty, Science & Mathematics Teaching Center, University of Wyoming: 2009 - 2012.
• Member, Advisory Board, Interdisciplinary Mentoring Program in Analysis, Computation, & Theory (IMPACT), Brigham Young University: 2009 - Present.

outreach & other activities

• Co-organizer, Rocky Mountain Mathematics Consortium Summer School: Conservation Laws & Applications, Laramie, WY: June 2010.
• Judge, Wyoming State Science Fair, Laramie, WY: March 2010.
• Co-director, Rocky Mountain Mathematical Research and Career Experiences, University of Wyoming REU Program: Summers 2009 - 2011.
• Co-instructor, Wyoming Math Teachers Circle: Problem Solving, Teton Science Schools, Jackson, WY: July 2009.

service

• Committee Service (American Mathematical Society): Short Course Subcommittee (1 Feb 2013 - 31 Jan 2016)
• Committee Service (College of Arts and Sciences): Ad hoc General Education Requirements Committee (Fall 2011)
• Committee Service (Department of Mathematics, *=committee chairman): Faculty Evaluation and Advisory Committee (elected, 2006-7, 2009-10, 2010-11, 2011-2012*), Undergraduate Committee (2010-11,2011-12), Graduate Committee (2005-6, 2006-7, Fall 2007, 2008-9), Colloquium Committee (2005-6, 2006-7, Fall 2007, 2008-9*, 2009-10*), Tenure & Promotion Committee (2009-10), Hiring Committee (2011-12*)