[MD-sorular] Matematik Koyu'nde Grup Teori

[Ali Nesin]

28 Eylul – 5 Ekim arasinda (yani Seker Bayrami’nda) Matematik Koyu’nde Grup Teorisi Calistayi yapilacak.

Toplam 8 gun.

Hedef Kitle: Ileri duzeyde lisans ogrencileri, lisansüstü öğrenciler ve arastirmacilar.

Calistayda konusma vermek ya da calistaya katilmak isteyenler bana yazabilirler.

Lisansustu ogrencileri problemlerini ve calismalarini sunabilirler.

Simdilik program asagidaki gibi. Daha da zenginlesecegini umuyoruz.

“Registration fee” yok. Ogrencilere gunde 20 YTL, ucretlilere 30 YTL. kalma ve gunde uc ogun yemek ve her sey dahil

http://matematikkoyu.org/grup_teori

Ali

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. Prerequisites: Complex numbers and some rudiments of topology. 

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.