#### Group Theory Workshop

**Tarih**September 28 - October 6, 2008. (Eight full days)**Amaç**There will be two sessions, one at the basic level directed towards students and the other, more advanced, aiming researchers and graduate students.

The actual state of the program is below. Each talk will last 110 minutes with a break of 10 minutes in the middle. The timetable will be available later.

If you want to propose a lecture please write to Ali Nesin (anesin@bilgi.edu.tr) Single talks are welcome. Graduate students may expose their ongoing research.

We may arrange a bus from Istanbul to Sirince. Please register early so that we have time to do the necessary arrangements.

For registration write to aslicankorkmaz@nesinvakfi.org, for information anesin@bilgi.edu.tr.

**Ücret**No registration fee. For accomodation and three nefis meals a day: 20 YTL/day for students (or whatever they can afford), 30 YTL/day for assistants and staff, 60 YTL for those who have a research grant. There are some pensions at Sirince as well.

**1) Basic Advanced Group Theory by Ali Nesin (8 days): **

Sylow Theorems. Solvable and Nilpotent groups.

Decomposition theorems. Hall`s Theorem.

Permutation groups, sharply 2 and 3 transitive groups.

**Prerequisites:** A first year abstract algebra course.

**2) Classical Groups by Ali Nesin (8 days):**

Special linear, symplectic and orthogonal groups.

From scratch and as much as the time allows.

**Prerequisites:** Linear algebra and basic group theory.

**3) Kleinian and Fuchsian Groups by Andrei Ratiu (8 days): **These are discrete subgroups of PSL2(ℂ).

Mobius transformations of the extended complex plane.

Action of the Mobius transformations on the upper half-space in ℝ3.

Types of Mobius transformations.

The definition and the main properties of Kleinian groups and Fuchsian groups.

**Complex numbers and some rudiments of topology.**

Prerequisites:

Prerequisites:

**4) Jordan Automorphisms of Some Radical Rings by Feride Kuzucuoğlu (1 talk).**

**5) Centralizers in Locally Finite Simple Groups by Mahmut Kuzucuoğlu (1 talk).**

**6) Sylow Subgroups of Some Classical Groups over Finite Fields by Nedim Narman (4 days).**

Their description.

**Prerequisites:** Basic group theory and finite fields.

**7) Infinite Galois Theory and Profinite Groups by Özlem Beyarslan (3 days**).

Inverse limits, p-adic numbers and the Prüfer group.

The absolute Galois group of a finite field.

**Prerequisites:** Basic field theory.

**8) Compact Lie Groups by Selçuk Demir (8 days): **Topological groups. Lie groups. Compact Lie groups.

Tangent space and its Lie algebra structure.

Exponential mapping. Maximal tori. Root systems,

Weyl group, Dynkin diagram. Haar measure. Peter-Weyl Theorem.

**9) Simple Groups of Finite Morley Rank with a tight automorphism whose centralizer is pseudofinite by Pınar Uğurlu (1 talk).**

**10) Informal talks by master and doctorate students exposing their problems and research.**

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