Some Recent Publications, Preprints
See also Publication List for a more complete list.

Irreducible geometric subgroups of classical algebraic groups,
with Tim Burness and Soumaïa Ghandour
preprint (pdf)
Let G be a simple
classical algebraic group over an algebraically closed field K of
characteristic p≥0 with natural module W. Let H be a closed subgroup of G
and let V be a nontrivial irreducible tensorindecomposable prestricted
rational KGmodule such that the restriction of V to H is irreducible. In this
paper we classify all such triples (G;H; V ), where H is a maximal closed
disconnected positivedimensional subgroup of G and H preserves a natural
geometric structure on W.

Unipotent overgroups in simple algebraic groups,
with Iulian Simion (pdf), to appear in
the proceedings of Groups and Geometries: Indian Statistical Institute, Bangalore

Irreducible almost simple subgroups of classical algebraic groups,
with Tim Burness, Soumaïa Ghandour, and Claude Marion
(pdf), to appear in Memoirs of the Amer. Math. Soc.
Let G be a simple
classical algebraic group over an algebraically closed field K of
characteristic p≥0 with natural module W. Let H be a closed subgroup of G
and let V be a nontrivial irreducible tensorindecomposable prestricted
rational KGmodule such that the restriction of V to H is irreducible. In this
paper we classify all such triples (G;H; V ), where H is a maximal closed
disconnected positivedimensional subgroup of G and H lies in the socalled S family of subgroups of G, that is, those whose connected component is simple and acts
irreducibly and tensorindecomposably on W.

On the irreducibility of symmetrizations of
crosscharacteristic representations of finite classical groups
with Kay Magaard and Gerhard Roehrle, J. Pure Appl. Algebra,217
(2013), no. 8, 14271446.
(pdf)
Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple
group of Lie type of characteristic $p = {\rm char}(k)$ acting irreducibly on $W$ . Suppose also
that $G$ is a classical group with natural module $W$ , chosen minimally with respect to
containing the image of $H$ under the associated representation. We consider the question
of when H can act irreducibly on a $G$constituent of $W^{\times e}$ and study its relationship to
the maximal subgroup problem for finite classical groups.

Irreducibility in algebraic groups and regular unipotent elements ,
with Alexandre Zalesski, to appear in Proc. Amer. Math. Soc. (pdf)
Let H be a connected reductive algebraic group. We study closed connected reductive subgroups G of H, where
G contains a regular unipotent element of H. The main result states that G does not lie in a proper parabolic subgroup of H. This builds on earlier work of Saxl and Seitz, who determined all maximal closed
subgroups of H containing a regular unipotent element of H.

Linear Algebraic Groups and Finite Groups of Lie Type, with Gunter
Malle, Cambridge University Press,
(Cambridge studies in advanced mathematics 133),
This textbook is based upon a series of lectures given by the authors in the Venice
Group Theory summer school, in September 2007.
Please see (here) for an errata list.

Centres of centralizers of unipotent elements in simple algebraic groups,
with Ross Lawther, Memoirs Amer. Math. Society,
210 (2011), no. 988, pp. 1188.
(pdf)
Let G be a simple algebraic group
defined over an algebraically closed field k whose characteristic is either 0
or a good prime for G, and let u be a unipotent element of G. We study the
centralizer C(u), especially its centre Z(C(u)). We calculate the Lie algebra
of Z(CG(u)), in particular determining its dimension; in the case where G is of
exceptional type we find the upper central series of the Lie algebra of the
unipotent radical of C(u), writing each term explicitly as a direct sum of
indecomposable tilting modules for a reductive complement to the radical in
C(u). The dimension of the centre of the centralizer is a surprisingly simple
function of the labelled diagram for the class of u and seems not to have been
known even in characteristic 0.

Nilpotent Subalgebras of Semisimple Lie algebras,
with Paul Levy and George McNinch,
C. R. Acad. Sci. Paris, Ser. I 347 (2009) pp. 477482,
(pdf)
In this note, we answer a question posed by JeanPierre Serre concerning
nil subalgebras of
semisimple Lie algebras. One can show that under certains restrictions on the
characteristic of the underlying field, any nil subalgera of the Lie algebra of
a reductive group lies in a Borel subalgebra. Indeed, the proof etablishes that
any unipotent subgroup scheme lies in a Borel subgroup. Serre asked if there
exist examples of nil subalgebras (or of `infinitesimal' unipotent subgroup
schemes) not lying in a Borel subalgebra (respectively a Borel subgroup) when
the restrictions on the characteristic are relaxed.

Nilpotent centralizers and Springer Isomorphisms, with George McNinch,
Journal of Pure and Applied Algebra, 213 (2009),
pp. 13461363.
(pdf)
In this article we investigate properties of centralizers in algebraic
groups. In addition, we verify certain properties of Springer isomorphisms
with regards to the centralizer of a regular nilpotent
element.

Group representation theory, edited by Meinolf Geck (Aberdeen),
Donna Testerman (EPFL), Jacques Thévenaz (EPFL),
EPFL
Press, Lausanne, 2007, 454 pages.
This volume
gives a general outline of the various activities which took place during the
research semester
Group Representation Theory, held in Lausanne, Switzerland,
from January to June, 2005. There are contributions by :
J.F. Carlson, R. Kessar, M. Linckelmann, J. Thévenaz, P. Webb,
M. Broué, S. Donkin, M. Geck, G. Seitz, J.P. Serre.

Completely reducible SL(2)homomorphisms,
with George McNinch, Trans. American Math. Society
359 (2007), pp. 44894510.
(pdf)
Let G be a semisimplelinear algebraic group over a field K. Suppose
the characteristic of K is positive and is very good for G. We describe all
group scheme homomorphisms from SL_2 to G whose image is geometrically
Gcompletely reducible, in the sense of Serre; the description resembles that
of irreducible modules given by Steinberg's tensor product theorem. In case K
is algebraically closed and G is simple, the result proved here was previously
obtained by Liebeck and Seitz using different methods.

Irreducible subgroups of algebraic groups, with M. Liebeck,
Quarterly Journal of Mathematics 55 (2004),
pp. 4755.
(pdf)

Subgroups of type A_{1} containing a fixed unipotent
element in an algebraic group, with R. Proud and J. Saxl,
Journal of Algebra 231 (2000), pp. 5366.
(pdf)

$A_1$ subgroups of exceptional algebraic groups,
with Ross Lawther, Memoirs of the American Mathematical Society
674 pp. 1131. (1999).