Alexander Konovalov's personal homepage
Computational Algebra
I am involved in the EPSRC project
"HPC-GAP: High Performance Computational Algebra and Discrete Mathematics"
and the EU Framework VI Project
"SCIEnce - Symbolic Computation in Europe".
I am interested in the GAP
system and other software for computational abstract algebra and constraint
programming, in parallel symbolic computation in various contexts, in groups
and group rings and their applications in discrete mathematics.
I developed the following packages for the computational algebra system
GAP:
Since 2007 I became a maintainer and continued the development of the
OpenMath package which adds OpenMath functionality
to GAP and is used by the SCSCP package.
Later since 2011 I became a maintainer and continued the development of the
Example package which provides a demo/template
of a GAP package and further guidelines to package authors.
Also I am one of the authors of the Wedderga
package for the computation of the Wedderburn decomposition of group algebras.
Finally, I am one of the authors of the the Congruence
package for computations with congruence subgroups of SL(2,Z). This
package is not yet redistributed with the GAP system, but this is expected soon.
Besides this, I maintain the
Experimental GAP Installer for Windows, which provides standard installation
procedure that will guide you through all steps of the GAP installation. There
is also a clickable graph
that illustrates dependencies between the GAP packages and some
notes about installation of GAP packages in Mac OS X.
Group Rings
In my PhD thesis, I proved that the normalized unit group of the modular
group algebra of a 2-group of maximal class G has a section isomorphic
to the wreath product C_{2}wrG' of the cyclic group of
order 2 and the derived group G' of G, giving for such groups a
positive answer on a question formulated by Aner Shalev. Recently I gave a
construction of the wreath product C_{2}wrG' for
another class of 2-groups.
Later I became also interested in the Modular Isomorphism Problem.
My current interests in the area of group rings are concentrated around
torsion units of integral group rings of finite groups. The long-standing
conjecture of Hans Zassenhaus (ZC-1) says that every torsion
unit in the integral group ring of the finite group G is rationally
conjugate to an element in G. Wolfgang Kimmerle proposed to relate
(ZC) with some properties of graphs associated with groups.
The Gruenberg - Kegel graph (or the prime graph) of G is the graph
with vertices labelled by the prime divisors of the order of G
with an edge from p to q if and only if there is an element
of order pq in the group G. Then Kimmerle's conjecture
(KC) asks whether G and the notmalized unit group of its
integral group ring have the same prime graph.
Jointly with Victor Bovdi, we started the program of verifying (KC)
for sporadic simple groups. Currently we are able to report on the
checking (KC) for the following 13 out of 26 sporadic simple groups:
- Mathieu groups M_{11},
M_{12}, M_{22},
M_{23}, M_{24}
- Janko groups J_{1},
J_{2}, J_{3}
- Higman-Sims group HS
- McLaughlin group McL
- Held group He
- Rudvalis group Ru
- Suzuki group Suz
For more details, please see publications and preprints following the links given below.
Publications and talks
See my entry in the Research@StAndrews portal.
Earlier publications and talks (with some downloads) are also available here.
You can also find a selection of my main publications in
MathSciNet,
arXiv
and
DBLP.
My Erdös number is equal to 3,
and its calculation is explained here.
Teaching
In 2009-2010 I taught:
Coming conferences
For conferences of my immediate interest, I publish a calendar here. Feel free to subscribe
to it (best viewed with Apple iCal - events will even have URLs of conference webpages). I also advertise a wider selection of conferences in this mailing list of the Ukrainian GAP User Group.
Memberships in professional organisations and other activities
Most recent minor incomplete update: 7 November 2013