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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

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

- Pseudoconvex domains spread over complex homogeneous manifolds
- Obstructions to Homogeneous Complex Manifolds being Kaehler
- Holomorphically Separable Homogeneous Complex Manifolds
- Levi Curvature of Flag Domains
- Finite Automorphism Groups of Compact Complex Surfaces
- Galois coverings via finite groups

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.

- 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

Our research is partially supported by an NSERC Discovery Grant

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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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

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