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, visit https://en.wikipedia.org/wiki/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)
Coursework
Spring 2017
- Elementary Differential Equations, Discrete Mathematics.
- In Spring 2008 I taught a topics course on Dirac Operators in Analysis and Geometry, the notes for that course can be found here.
Office Hours
Monday, Wednesday, Friday: 11:45am – 12:35pm and 12:45pm – 1:35pm
Some Campus Resources
- University of Arkansas – Home Page
- University of Arkansas – Mathematical Sciences – Home Page
- University of Arkansas – Math Resource and Teaching Center – Home Page
- University of Arkansas – Mathematics Department – Colloquia Page
- University of Arkansas – Mathematics Department – Research Areas
- University of Arkansas – Faculty Senate – Home Page
Journals, etc.
Member of the editorial board of Complex Analysis and Operator Theory
Member of the editorial board of Complex Variables and Elliptic Equations, 2001-2010
Member of the editorial board of 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
Principle member of the 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.
Member of the organizing conference committee for 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 the 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 the 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.
The 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.
The 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).
The main organizer of the 37th Spring Lecture Series, “Higher Codimensional Elliptic Boundary Problems”, University of Arkansas, April 2012. Main speaker, Rafe Mazzeo, Stanford University (Sponsored by NSF).
With Craig Nolder, I organized the conference Clifford Analysis and Related Topics, a Conference in Honor of Paul A. M. Dirac, Florida State University, Tallahassee, Florida, December 2014 (Sponsored by NSF).
