My main research concerns representation theory of finite groups, with particular emphasis on simple groups. They include the so called classical groups (linear, orthogonal, symplectic and unitary), groups of exceptional type, alternating groups and sporadic groups. These have been thoroughly studied in collaboration with Prof. Michler at IEM. According to a Theorem announced in 1980 there are no other such groups apart the trivial examples of cyclic groups of prime order. Unfortunately the proof of this statement is spread among many articles and does not seem to be complete as the recent 1300-page paper by Aschbacher and Smith shows. My efforts try to grasp the structure of the 26 (or maybe more) simple groups not belonging to an infinite series.

I will try to collect some data concerning a revision project about the construction of 25 out of 26 sporadic groups (we are scared of the Monster)

r, s, f, g as matrices in GL(495,3)
Magma code available

Unitriangular action on quadratic and sesquilinear forms

We make available code written under Magma V2.11.10 to calculate both directly and recursively the orbit size polynomial for the action of the unitriangular group K_n(F) in GL_n(F) on sesquilinear or quadratic forms (see my paper "Unitriangular action on quadratic and sesquilinear forms").

OrbitSizePolynomial.mag

Irreducible Constituents of Monomial and Permutation Characters

We make available code written under Magma V2.12.18 to calculate the irreducible constituents with multiplicities of a given monomial character. Files with code generating Tables 1 and 2 at the end of my paper "Irreducible constituents of monomial characters".

PermutationConstituents.mag

PermutationConstituentsExecutionTimes.mag

MonomialConstituents.mag

MonomialConstituentsExecutionTimes.mag