University of Regina

Department of Mathematics and Statistics

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Dr. B.C. Gilligan

Professor, Ph.D. 1972 (Toronto)

Primary Field of Research. Complex analysis and complex manifolds.

Complex analysis in several variables, particularly function theoretic conditions on complex homogeneous spaces and their relationships to the geometry of the spaces, and the existence of Kaehler metrics on homogeneous spaces.

Secondary Field of Research. Family History of the PEADS

 

Selected Publications.

* B. Gilligan, Structure of complex homogeneous spaces with respect to topological invariants, 75 pp., Heft Nr. 218, Schriftenreihe, Forschungsschwerpunkt Komplexe Mannigfaltigkeiten, Bochum, 1994.

* B. Gilligan, Complex homogeneous spaces of real groups with top homology in codimension two, Ann. Global Anal. Geom. 13 (1995), 303-314.

* B. Gilligan and P. Heinzner, Globalization of holomorphic actions on principal bundles, Math. Nachr. 189 (1998), 145-156.

* B. Gilligan, Homology invariants of homogeneous complex manifolds. in Lie Groups and Lie Algebras, B.P. Komrakov et al (eds.), Kluwer Academic Publishers (1998), 163-179.

* B. Gilligan, Lectures on Complex Analysis, 229 pages; textbook for Math 312 in 200330 and for Math 412 in 200210 This is an ongoing project.

* B. Gilligan, Invariant analytic hypersurfaces in complex Lie groups, Bull. Austral. Math. Soc. 70 (2004), 343 - 349.

* B. Gilligan, An obstruction to homogeneous manifolds being Kaehler, Ann. Inst. Fourier, Grenoble, 55 (2005), 229 - 241.

* B. Gilligan and K. Oeljeklaus, Two Remarks on Kahler Homogeneous Manifolds, Annales Fac. Sci. Toulouse, vol. 17, No. 1, (2008) 73-80.

* Symmetries in Complex Analysis, editors: Bruce Gilligan and Guy Roos; Workshop "Several complex variables, analysis on complex Lie groups and homogeneous spaces", Zhejiang University, Hangzhou (P.R. China), Oct. 17-29, 2005, CONM, A.M.S., vol. 468 (2008).

* B. Gilligan and A.T. Huckleberry, Fibrations and Globalizations of Compact Homogeneous CR-Manifolds, Izvestiya: Mathematics, 73:3,(2009) 501 - 553.

This file can be downloaded from Arxiv.

* B. Gilligan and K. Oeljeklaus, Compact CR-solvmanifolds as Kaehler obstructions, 15 pp ms.

This file can be downloaded from here.

* Bruce Gilligan, Christian Miebach, and Karl Oeljeklaus, Homogeneous Kaehler and Hamiltonian manifolds, 11 pp ms.

This file can be downloaded from here. See also arxiv:1001.1209

 

Other Professional Activities

Reviewer for Mathematical Reviews

Reviewer for Zentralblatt fuer Mathematik und ihre Grenzgebieten

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gilligan[at]math[dot]uregina[dot]ca

 

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Courses for Winter Semester 2010:

 

Math 111-001: The webpage can be found here

Math 412/812-001: The webpage can be found here.

Office Hours during the 201010 Semester

10:30 - 12:00 MWF

 

Some Background

An interesting site containing a wealth of information, including a lot of history of mathematics, has URL: http://www-groups.dcs.st-and.ac.uk/~history/index.html This is not required, as part of any course, to be read by the students. But it does illustrate how mathematicians have struggled with various ideas over the centuries and sometimes it took several years, and the work of several different people, in order to develop most topics which are now a part of what we call modern mathematics.

 

Latest update of this webpage was on 26 January 2010