Alexander Konovalov's personal homepage

Dr. Alexander Konovalov
(also known as Olexandr Konovalov)

University of St Andrews
School of Computer Science &
Centre for Interdisciplinary Research in Computational Algebra

Room 0.17, Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Tel +44/0 1334 461633
Fax +44/0 1334 463278

Email: see here at cs.st-andrews.ac.uk

Computational Algebra

I am working as a member of the EU Framework VI Project "SCIEnce - Symbolic Computation in Europe" in the area of symbolic computation software composability and symbolic computing on the Grid. Some information about the project is presented in my earlier posters:

"The OpenMath-based protocol for symbolic software composability" (jointly with Steve Linton and Dan Roozemond), presented at the 8th OpenMath Meeting at RISC, Schloss Hagenberg, University of Linz, 25-26 June, 2007.
"Symbolic computations as Grid and Web services" (jointly with Steve Linton and Kevin Hammond), Best Poster Award at the International Symposium on Symbolic and Algebraic Computation (ISSAC 2007) at the University of Waterloo, Waterloo, Ontario, Canada, July 29 - August 1, 2007.

My interests include computational group and group ring theory and software development for the computational algebra system GAP.

I developed the following packages for the GAP system:

LAGUNA - Lie AlGebras and UNits of group Algebras (jointly with V.Bovdi, R.Rossmanith and C.Schneider).
UnitLib - The Library of normalized unit groups of group algebras (jointly with E.Yakimenko)
Circle - Adjoint groups of finite rings (jointly with P.Soules)
SCSCP - Symbolic Computation Software Composability Protocol in GAP (jointly with S.Linton; see also slides about one of previous versions of this package and SCSCP specification)

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. Also I am one of the authors of the Wedderga package for the computation of the Wedderburn decomposition of group algebras, and I have a plan to finish the GAP package Congruence (see slides) for computations with congruence subgroups of SL(2,Z).

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 C₂wrG' 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 C₂wrG' 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 M₁₁, M₁₂, M₂₂, M₂₃, M₂₄
Janko groups J₁, J₂, J₃
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

The full (that is, periodically updated) list of my publications and talks (with some downloads) is available here.
You can also find a selection of my main publications in MathSciNet and arXiv.
My Erdös number is equal to 3, and its calculation is explained here.

Teaching

In 2008-2009 I am teaching:

First half of CS3103 Graphs and Algorithms in Semester 1 in the School of Computer Science
MT5829 Group Rings in Semester 2 in the School of Mathematics and Statistics

Coming conferences

You may find useful the information about some conferences in the areas of my research interests which I advertise on the homepage of the Ukrainian GAP User Group.

Memberships in professional organisations and other activities

Member of the Centre for Interdisciplinary Research in Computer Algebra (CIRCA), University of St Andrews
Member of the GAP Council
Member of the GAP Support group
Member of the Special Interest Group on Symbolic and Algebraic Manipulation of the Association of Computing Machinery (ACM SIGSAM)
Member of the Edinburgh Mathematical Society (EMS)
Member of the London Mathematical Society (LMS)
Member of the American Mathematical Society (AMS)
Reviewer for the American Mathematical Society MathSciNet (Mathematical Reviews on the Web). To see all my reviews click here
Chairman of the Ukrainian GAP User Group and editor of its mailing list

Last updated: 18 April 2009