John Ryan

John Ryan

Distinguished Professor

(ARSC)-Arts & Sciences

(MASC)-Mathematical Sciences

Phone: 479-575-6334

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I work in the area of Clifford analysis. Clifford analysis is the study and application of Dirac type operators in analysis and geometry. I have a particular interest in the links between Dirac type operators and conformal structure. For a more detailed description of Clifford analysis see the Wikipedia page on Clifford analysis

Clifford analysis, Dirac operators and their applications

D. Phil. University of York, UK, and D. Sc. University of York, UK.

Journals etc.

  • Member of editorial board of Complex Analysis and Operator Theory.
  • Member of editorial board Complex Variables and Elliptic Equations.
  • Member of editorial board Analele Universitaii Din Oradea, Fascicula Matematica.
  • Assistant editor of Advances in Applied Clifford Algebra.
  • Trustee of I.S.A.A.C. - The International Society for Analysis its Applications and Computation, 1996-2010.
  • von Humboldt Research Fellow


Principle member of organizing committee for Clifford Algebras in Analysis and Related Topics, main speaker Alan McIntosh, Spring Lecture Series, University of Arkansas, April 1993. 

Together with Daniele Struppa, Dean of Arts and Sciences, George Mason University, I organized the special section on "Dirac Operators in Analysis" as part of the first congress of ISAAC, University of Delaware, June, 1997.

Together with Daniele Struppa, George Mason University, Virginia, and Vladimir Soucek, Charles University, Prague, Czech Republic, I organized the meeting Clifford Analysis, Cetraro, Italy, October 1998.

Member of the International Advisory Committee for the 5th International conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 1999.

Memeber of organizing committee for conference on Clifford Analysis, its Applications in Mathematical Physics, and Related Topics a conference in memory of L. K. Hua on the occasion of his 90th birthday, Beijing, China, August 2000.

Member of international advisory committee for the NATO sponsored conference on Clifford analysis in honor of Richard Delanghe on his 60th birthday, Czech Republic, October 2000.

Member of the international advisory committee for the third ISAAC congress, Free University, Berlin, Germany, August 2001.

Together with Rafal Ablamowicz I was a main organizer for the Sixth International Conference on Clifford Algebras and their Applications in Mathematical Physics, Tennessee Technical University, Cookeville, TN, May 2002. (Conference sponsored by NSF and AMS).

Member of Organizing Committee and Scientific Committee of the 2002 International Congress of Mathematicians Satellite Meeting on Clifford Analysis, University of Macau, August 2002.

Main organizer of the Mid-West Geometry Conference, University of Arkansas, 25-27 March, 2004. (sponsored by NSF)

Co-organizer of a section on "Dirac operators in analysis and geometry" at the regional meeting of the AMS, Fayetteville, AR, November, 2006.

With Craig A. Nolder I organized a section on "Hypercomplex analysis" at the regional meeting of the AMS in November 2009 in Boca Raton.

Main organizer of the 36th Spring Lecture Series, "Conformal Differential Geometry and its Interactions with Representation Theory", University of Arkansas, April 2011. Main speaker, Michael Eastwood, ANU, Canberra, Australia (Sponsored by NSF).

Master Researcher Award (Fulbright College of Arts and Sciences, University of Arkansas, USA, 2010), D. Sc. (University of York, U.K., 2008), D. Phil. (University of York, U.K., 1982), M. Sc. (University of Warwick, U.K., 1978), B. A. (University of York, U.K., 1976), von Humboldt Fellowship (Technical University of Freiberg, Germany, 1995).

My Mathematical Genealogy