**E-mail:**russell@math.mcgill.ca

**Office:** Burnside Hall, Room 1223

**Office Hours:** MWF 12:30-13:30 and by appointment

**Office Phone:** (514) 398-3835

**Office FAX:** (514) 398-3899

I am interested in the geometry of non-complete algebraic
varieties, in particular affine spaces or varieties that closely resemble them.
A central theme in my research over the past few years has been the
linearizability of algebraic group actions on affine spaces, actions of tori in
particular, which lead to quite fascinating geometric problems. Article (5)
below gives an overview of the proof that **C***-actions on **C ^{3}**
are linearizable, a result to which (3) and (4) make essential contributions.
In continuation of the work in (4), Koras and I in (14) characterize

- With S. M. Bhatwadekar. A note on geometric factoriality, Can. Math. Bull. 38 (4), 390-395, 1995.
- Sufficiently homogeneous
embeddings of
**A**into^{n-1}**A**are linear, Can. J. Math. 48 (6), 1286-1295, 1996.^{n} - With M. Koras. Contractible
threefolds and
**C***- actions on**C**, J. Alg. Geom. 6 671-695, 1997.^{3} - With M. Koras.
**C**: the smooth locus is not of hyperbolic type, J. Alg. Geom. 8, 603-694, 1999.^{3}/ C* - With S. Kaliman, M. Koras, L.
Makar-Limanov,
**C***- actions on**C**are linear, Electronic Research Announcements of the AMS 3, 63-71, 1997.^{3} - With D. Daigle. Affine rulings of normal rational surfaces, Osaka J. Math. 38 (2001), 37-100.
- With D. Daigle. On weighted projective planes and their affine rulings, Osaka J. Math. 38 (2001), 101-150.
- Normal crossing systems of plane curves with one place at infinity, Sitzungsberichte der Berliner Mathematischen Gesellschaft 1997-2000, 163-176, CICMA Reports 2000-01.
- Some formal aspects of the theorems of Mumford-Ramanujam, Proceedings of the International Colloquium in Algebra, Arithmetic and Geometry 2000, Tata Institute of Fundamental Research, Narosa Publishing, 2002, 557-584.
- Multiple planes ramified over
one-place curves, CICMA reports 2000-10, Algebra, Arithmetic and Geometry
with Applications, volume in honor of S.S. Abhyankar,s 70
^{th}birthday 673-685, Springer 2003, pp. 673-685. - With M. Koras. Linearization problems, in: Algebraic group actions and quotients, XXIII Autumn School in Algebraic Geometry, Wykno, Poland, pp. 91-107, Hindawi Publishing 2004.
- With D. Daigle. On log Q-homology planes and weighted projective planes, Can. J. Math. 56 no. 6, 1145-1189 (2004).
- Book Review: Open Algebraic Surfaces, by M. Miyanishi, CMS Notes, v. 33, no. 8, Dec. 2001, 18-20.
- With M. Koras. Contractible surfaces with quotient singularities, Transformation Groups 12 no. 2 (2007), 293-340.
- With P. Cassou-Nogues. Birational endomorphisms of the affine plane and affine-ruled surfaces, Proceedings of the Conference in Honor of M. Miyanishi, Kyoto University, T. Hibi, editor, Osaka U. Press 2007, 57-105.
- With R. Gurjar, K. Masuda and M. Miyanishi. Affine lines on affine surfaces and the Makar-Limanov invariant, Can. J. Math. 60 (2008), 109-139
- With P. Cassou-Nogues, M. Koras. Closed embeddings of C* in C^2, to appear in J. Algebra.
- Open Problems, Workshop on Group Actions on Rational Varieties, G. Freudenburg and P. Russell, editors, CICMA Reports 2002-04.
- Embedding problems in affine algebraic geometry, in Polynomial Automorphisms and related problems, Lecture notes of ICPA2006, Hanoi, Vietnam Publishing House for Science and Technology, 113-131.
- With R. Gurjar, M. Koras, M. Miyanishi, An affine Mumford theorem and related topics, submiited.
- With R. Gurjar, M. Koras, Two dimensional quotients of C^n by a reductive group, ERA-MS 15 (2008), 62-64.