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VENEZIA AUGUST 19th-30th 2019 |
SUMMER SCHOOL on FINITE GROUPS AND RELATED GEOMETRICAL STRUCTURES |
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Axial
Algebras and 3-Transposition groups
Joint lectures by Hans Cuypers and Jonathan I. Hall Special guest lectures on Axial Algebras by Sergey Shpectorov
Monday,
August 19th
Introduction to 3-transpositions
The basic theory of 3-transpositions, their diagram,
commuting graph,
\theta- and \tau-relations and their connections
with normal subgroups will be discussed. Various examples of
3-transposition groups as well as an overview of the classfi cation of
all 3-transposition groups will be given.
Tuesday, August 20th:
As a warm up a characterization of the ( finitary)
symmetric group as 3-transposition
groups in which any four 3-transpositions with
connected diagram
generate a subgroup of Sym_5 is given. Moreover, the
permutation action of a
3-transposition group on its class of 3-transpositions
is analyzed, which gives
inside in the structure of the group.The general theory of 3-transposition groups
Wednesday, August 21st
Groups of symplectic type
A characterization of the symplectic and orthogonal
groups over the field with 2 elements as groups generated
by 3-transpositions is presented. Some applications in graph theory
and geometry are discussed.
Thursday, August 22ndt
A characterization of the orthogonal groups over the
field with 3 elements as groups generated by 3-transpositions is
given. Connections with affine polar spaces are discussed.Groups of orthogonal type.
Friday, August 23rd
Groups of unitary
type
Monday, August 26th
Sporadic 3-transposition groups
We discuss the existence and uniqueness of the three
sporadic Fischer
groups and their relations with some other sporadic
simple groups.
Tuesday, August 27th
Generalizations in Groups Theory and Geometry
Generalizations, both in Group Theory and Geometry,
of the concepts,theory
and methods used in the study of 3-transposition
groups are discussed.
Wednesday, August 28th
3-transpositions and algebras
We study the relation between 3-transposition groups
and various types of
algebras. Today, our focus will be on the relation
between 3-transpositions
and Lie algebras.
Thursday, August 29th
:Axial algebras and 3-transpositions
Axial algebras and their relation with
3-transposition groups will be discussed.
Friday, August 30th
More on axial algebras
We continue the study of axial algebras and their
relation with 3-transposition
groups.
Beginning:
Monday, 19th August, 2019
at 9.30am.
End: Friday, 30th August, 2019 at 1.00pm. Day schedule from Monday 19th to Friday 30th August: 9.30am - 11.00am: Lecture 1 11.00am - 11.30am: Break 11.30am - 1.00pm: Lecture 2 Class problem sections on Wednesday 21st, Friday 23rd, Monday 26th, and Wednesday 28th August. with the following schedule: 15.30pm - 16.30pm: Class problem section 1 16.30pm - 17.00pm: Break 17.00pm - 18.00pm: Class problem section 2 Course Banquet on Thursday, 29th August |