John Ryan's Home Page

John Ryan

Telephones etc.

Office: SCEN 356
Office Telephone: 479 575 6334
Office Fax: 479 575 8630
e-mail address: jryan@uark.edu
Address: Department of Mathematics, University of Arkansas, Fayetteville, AR 72703.

Research

Keywords:

Clifford analysis, Dirac operators, Dirac type operators, Moebius transformations, conformally flat manifolds, Hardy spaces.

Brief Description:

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

Degrees and Awards:

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

Publications:

Here is a list of my publications

Coursework

Spring 2012

Senior Seminar: Clifford Algebras, An Introduction

In Spring 2008 I taught a topics course on Dirac Operators in Analysis and Geometry, the notes for that course can be found at

http://comp.uark.edu/~jryan/notes.doc

Office Hours: Monday, Wednesday, Friday: 2-3pm.

Some Campus Resources

UARKinfo

University of Arkansas, Fayetteville, Mathematical Sciences home page.

University of Arkansas, Fayetteville, Math Resource and Tutoring Center (MRTC)

University of Arkansas, Fayetteville, Mathematics Department Colloquia

University of Arkansas, Fayetteville, Mathematics Department Research Reports

Faculty Senate.

Journals etc

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

Conferences

Spring Lecture Series

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 occassion 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).

Memeber of Organizing Committe 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 (Sposored by NSF).