index.htm

Course 1.

The Classification of the Finite Simple Groups
A User's Manual

Lectures by Stephen D. Smith

1. An introduction to the groups in the CFSG;
2. An outline of the proof of the CFSG;
3. (Faliure of) Thompson factorization;
4. Recognition theorems for simple groups;
5. Representation theory for simple groups;
6. Maximal subgroups of simple groups;
7. Geometries for simple groups;
8. Some fusion techniques for classification problems;
9. Some more group-theoretic applications;
10. Some applications farther afield.

References

1. M. Aschbacher, R. Lyons, S. Smith, R. Solomon, The Classification of Finite Simple Groups - Groups of Characteristic 2 Type, AMS Mathematical Surveys and Monographs 172, 2011

2. R. Lyons, R. Solomon, The Classification of the Finite Simple Groups, AMS Mathematical Surveys and Monographs 40.3, 1994

A preliminary version of the lectures can be downloaded here:

www.math.uic.edu/~smiths/talkvh.pdf

Course 2.

G_2, Amalgams, and Fusion Systems

Lectures by Gernot Stroth

1. Quaternions;
2. Octonions;
3. The order of thr group G_2(q);
4. Subgroups of G_2(q);
5. Simplicity of G_2(q);
6. A general version of a parabolic subgroup of G_2(q);
7. Proof of the Main Theorem;
8. Amalgams;
9. Fusion Systems;
10. Exotic Fusion Systems.

References

1. R. A. Wilson, The Finite Simple Groups, Springer, 2009

2. C. Parker, G. Stroth, A family of fusion systems related to the groups $Sp_4(p^{a})$ and $G_2(p^{a})$, Archiv d. Mathematik 105 (2015), 311-323.

Beginning: Monday, 7th September, 2015 at 9.30am.

End: Friday, 18th September 2015 at 1.00pm.

Day schedule:

9.30am - 11.00am: Lecture 1
11.00am - 11.30am: Break
11.30am - 1.00pm: Lecture 2

Class problem sections on Wednesday 9th, Friday 11th, Monday 14th, and Wednesday Sep. 16th
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, September 17th