CURRICULUM VITAE

Robert Alan Gardner
born: 10/21/50
place: N.Y.,  N.Y.,  USA

Education:

1973                University of Michigan              A.B.
1978                University of Michigan              Ph.D.

 
Employment:

1973-1978        University of Michigan          Teaching Assistant
1978-1979        Math. Res. Center/Madison    Assistant Scientist
1979-1980        Heriot-Watt University           Research Associate
1980-1984        Univ. of Massachusetts           Assistant Professor
 Fall 1982          Tulane University                  Visiting Assoc. Professor
1984-1985        SFB, Univ. Heidelberg           Gastprofessor
1984-1990        Univ. of Massachusetts           Associate Professor
1990-                Univ. of Massachusetts            Professor

Research Interests: Nonlinear partial differential equations, dynamical systems, mathematical biology

Grants and Fellowships:

1978-1979   MRC postdoctoral fellowship
1979-1980   Science Research Council  postdoctoral fellow
1981-1983   NSF grant: "Qualitative behavior of reaction-diffusion systems"
1984-1986   NSF grant: "Semilinear parabolic and elliptic equations"
1986-1988   NSF grant: "Reaction-diffusion equations and conservation laws"
1988-1990   NSF grant: "Elliptic and parabolic systems of nonlinear equations"
1990-1992   NSF grant: "Stability of solutions of nonlinear p.d.e."
1993-1996   NSF grant: "Dynamical systems arising in the stability analysis of travelling waves"
2003-2005   NSF grant: "Forumulation and analysis of  deterministic models of predation in acarine populations"
 

Invited Presentations:

Summary prior to  Fall 1999:
31 invited seminar/colloquium talks
17  invited talks at U.S. conferences
9  invited talks at international conferences:
Extended visits at: MRC/Madison Minneapolis, Warwick, Tulane, University of Leiden, Heriot-Watt, Sonderforschungsbereich 123- Heidelberg,Universidad Compultense (Madrid), Maryland- College Park, Brown, Tel-Aviv,Utrecht, University of Mexico


Selected invited presentations:
International Conference in Nonlinear Diffusion (pleanary lecture) and 3 seminars on nonlinear wave stability at Heriot-Watt Univ,  1988, Edinburgh, Scotand

Taniguchi International Workshop and Symposium (plenary lecture) on Nonlinear PDE,   1989, Katata and Kyoto, Japan

Conference on nonlinear PDE  (plenary lecture) (Trieste, Italy 1989)

US-Chinese Conference on Recent Developments on Differential Equations and Applications (plenary lecture) ,1996, Hangzhou, China

Conference on Asymptotics in Nonlinear Diffusive Systems (plenary lecture), 1998, Sendai, Japan

Oberwolfach , Germany: 1985, 1987, 1989, (2004, but unable to attend)

1st Joint AMS - SMF conference,  (plenary lecture)  (2001, Lyons, France)

Americas Conference on Differential Equations and Nonlinear Dynamics (plenary lecture) , (2002, Edmonton, Canada)




Ph.D. Students:

Patrick Miller (1994), "Stability of Travelling Waves for a Three-Component Reaction-Diffusion System"

Edgardo Eszter (1998), "On the Stability of Periodic Travelling Waves Associated with the FitzHugh-Nagumo System"




Selected Publications:

•  Stability index analysis of 1-D patterns of the Gray-Scott model,  (with Doelman,Arjen and  Kaper, Tasso J. A), Mem. Amer. Math. Soc. 155 (2002), no. 737, xii+64 pp.

• Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach, (with Doelman,Arjen and  Kaper, Tasso J. A) , Physica . D 122 (1998), no. 1-4, 1--36

•   The gap lemma and geometric criteria for instability of viscous shock profiles, (with Zumbrun, Kevin), Comm. Pure and Appl. Math. 51 (1998), no. 7, 797--855.

• [Spectral analysis of long wavelength periodic waves and applications, J. Reine Angew. Math. 491 (1997), 149--181.

• On the structure of the spectra of periodic travelling waves. J. Math. Pures Appl. (9) 72 (1993), no. 5, 415--439.\

• Stability of travelling waves for nonconvex scalar viscous conservation laws, (with Jones, C. K. R. T. and Kapitula, Todd), Comm. Pure and Appl. Math. 46 (1993), no. 4, 505--526. 

•   A stability index for steady state solutions of boundary value problems for parabolic systems,  (with C. K. R. T.), J. Differential Equations 91(1991), no. 2, 181--203.

• Stability of travelling wave solutions of diffusive predator-prey systems, (with Jones, C. K. R. T.), Trans. Amer. Math. Soc. 327 (1991), no. 2, 465--524.

• A topological invariant arising in the stability analysis of travelling waves, (with Alexander, J. and Jones, C. ), J. Reine Angew. Math.
  

• [Existence of multidimensional travelling wave solutions of an initial-boundary value problem. J. Differential Equations 61 (1986), no. 3, 335--379.

• An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, (with Conley, C.),  Indiana Univ. Math. J. 33 (1984), no. 3, 319--343.

•   On the detonation of a combustible gas. Trans. Amer. Math. Soc. 277 (1983), no. 2, 431--468.

• The existence of periodic travelling waves for singularly perturbed predator-prey equations via the Conley index. (with Smoller, J.), J. Differential Equations 47 (1983), no. 1, 133--161.

• Existence and stability of travelling wave solutions of competition models: a degree theoretic approach, J. Differential Equations 44 (1982), no. 3, 343--364. 

 

  Summary of Recent Service:

  Department:
  Faculty Selection Committee (99--03, chair in 02)
  Personnel Committee (97-99, 04-07) 
  Qualifying exam committee (continuing)
  Head Search Comitttee (chair, Spr. 01)
  NSF  panelist  for peer review of  applied math proposals, (Jan, 2002 and Jan, 2003)