Bruce Gilligan -- Homepage
Department of Mathematics & Statistics
University of Regina

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Dr. B.C. Gilligan; Professor, Ph.D. 1972 University of Toronto, M.Sc. 1966 University of Toronto, A.B. 1965 Princeton University

 

Primary Field of Research: Symmetries in complex analysis:

 

We are currently working on the following, all of which involve the study of the symmetries of complex manifolds under additional assumptions.

 

Secondary Field of Research:

Family History of the PEADS; particularly, in England

 

Selected Publications:

Otto Forster, Lectures on Riemann Surfaces. Translated from the 1977 German original by Bruce Gilligan. Reprint of the 1981 English translation.
Graduate Texts in Mathematics, 81. Springer-Verlag, New York, 1991.

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

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., Mathematische Zeitschrift, 269 (2011), 179 - 191.
This file can be downloaded from here.

Bruce Gilligan, Christian Miebach, and Karl Oeljeklaus, Homogeneous Kaehler and Hamiltonian manifolds, Math. Ann., vol. 349 (2011), 889 -- 901.
This file can be downloaded from here. See also arxiv:1001.1209

Bruce Gilligan, Christian Miebach, and Karl Oeljeklaus, Pseudoconvex domains spread over complex homogeneous manifolds, Manuscripta Math. 142 (2013), 35 -- 59.
This file can be downloaded from here. See also arxiv:1204:1163

S. Ruhallah Ahmadi and Bruce Gilligan, Complexifying Lie group actions on homogeneous manifolds of non--compact dimension two. Canadian Mathematical Bulletin, 57 (2014), 673 - 682.
This file can be downloaded from here.

S. Ruhallah Ahmadi and Bruce Gilligan, Classification of Kaehler homogeneous manifolds of non--compact dimension two. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), to appear.

Bruce Gilligan, Levi's Problem for Pseudoconvex Homogeneous Manifolds. Canadian Mathematical Bulletin, to appear.
This file can be downloaded from here.

 

Student Supervision:

  • Ruhi Ahmadi, Ph.D. Program in Mathematics; Ruhi's home page
  • Jeremy Lane, USRA, Summer 2011, co-supervised
  • Larissa Richards, USRA, Summer 2011, co-supervised
  • Drew Johnstone, USRA, Summer 2013

 

Research Funding:

Our research is partially supported by an NSERC Discovery Grant

 

Other Professional Activities:

Reviewer for Mathematical Reviews

Reviewer for Zentralblatt für Mathematik und ihre Grenzgebieten

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email: gilligan[at]math.uregina.ca

 

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Courses in 201710:

Math 412/812 (Complex Analysis II)

If you are a student in one of these courses, please consult UR Courses for details

 

Office Hours during the 201710 Semester TBA

or by appointment - please email me

 

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 08 February 2017