[mk-duyuru] Kurban Bayrami'nda Lisans ve Lisansustu Programi

[Ali Nesin]

Kurban Bayrami'nda lisans ve lisansustu matematik ogrencilerine yonelik 
cebir ve sayilar kurami agirlikli bir programimiz var.
Lisansustu ve doktora ogrencileri icin TUBITAK'tan bu programa destek aldik.
Lisans ogrencilerine de biz destek verecegiz eger talep gelirse.
Lutfen ilgili ogrenciler hemen basvurularini yapsinlar, yerimiz oldukca 
kisitlidir.

Verilecek dersler:
Prof. Dr. Ali Nesin, Permutation Groups.
Yard. Doc. Ozlem Beyarslan, Around Chebotarev Density Theorem
Dr. Kursat Aker, Lie Cebirleri Temsilleri*
MSc. Sermin Cam, Representation theory of compact and locally compact 
groups**
*

Programin ayrintilari asagida ve 
http://matematikkoyu.org/kurban_lisansustu_2011 sayfasinda.
Ali Nesin


*Tarih:* 5-13 Kasim 2011 (Kurban Bayrami)
*Program koordinatoru:*Selcuk Demir**
Hedef Kitle:**Matematik bolumu ust seviye lisans, (doktora dahil) 
lisansustu ogrencileri ve arastirmacilar.**
Basvuru:**Basvuru formunu emelaydin at nesinvakfi.org 
<mailto:emelaydin at nesinvakfi.org> adresine mail ile gondermelisiniz. 
Basvurunuzun ulastigina dair bir onay mesaji gonderilecektir. Basvuru 
formu icin tiklayin. 
<http://matematikkoyu.org/files/efm/files/Lisans_Lisansustu_Basvuru_yeni.doc> 
Eger uc dort gun icinde mesaj almamissaniz lutfen bir daha yazin, 
basvurunuz muhtemelen elimize gecmemistir****
Kayit:**Belli araliklarla basvurular degerlendirilir ve sonuclari 
e-postayla iletilir. Odeme ve kayitla ilgili tum islemler basvurunuz 
kabul edildikten sonra yapilacaktir. **_
_**

**_Egitmenler ve Dersler_**

Prof. Dr. Ali Nesin, Permutation Groups.*
Ozet:*We will concentrate on infinite permutation groups, on which much 
progress has been made in the last three decades. Our main aim is to 
classify Jordan groups. Time permitting, we will show the existence of 
certain Jordan groups by constructing new geometries using amalgamation 
methods of Hrushovski.***
*Onkosul. **Basic group theory.***
*Kaynak:** M. Bhattacharjee, D. Macpherson, R.G. Moller, P.M. Neumann, 
*Notes on Infinite Permutation Groups*, Lecture Notes in mathematics 
1698, Springer 1998.***
*Ayrintili Program: *
*5 Kasim (4 saat):** Basic concepts: Group action, orbit, transitivity, 
multiple transitivity, sharp transitivity, primitive actions, 
homogeneity. Examples.***
*6 Kasim (4 saat):** Suborbits,**orbital graphs, primitivity. Symmetric 
group. Wielandt's theorem. Linear actions and linear groups. Projective 
and affine groups and spaces. Wreath products.***
*7 Kasim (2 saat):** Automorphisms of ordered structures. Back and forth 
argument. Jordan groups.***
*8 Kasim (2 saat):** Examples of Jordan groups***
*9 Kasim (2 saat):** Relations related to betweenness.***
*10 Kasim (2 saat):** Classification of Jordan groups.***
*11 Kasim (2 saat):** Homogeneous structures and Fraissé's theorem.***
*12 Kasim (2 saat):** The Hrushovski Construction I.***
*13 Kasim (2 saat):** The Hrushovski Construction II.

Yard. Doc. Ozlem Beyarslan, Around Chebotarev Density Theorem***
*Ozet: **Our aim in this course is to understand Chebotarev Density 
Theorem. The major connection between the theory of finite fields and 
atithmetic of function fields. Chebotarev's density theorem in algebraic 
number theory describes statistically the splitting of primes in a given 
Galois extension /K /of the field Q//of rational numbers. Generally 
speaking, a prime integer will factor into several ideal primes in the 
ring of algebraic integers of /K/. There are only finitely many patterns 
of splitting that may occur. A special case that is easier to state says 
that if /K /is an algebraic number field which is a Galois extension of 
Q//of degree /n/, then the prime numbers that completely split in /K 
/have density 1//n. /We will first go over topics in number theory which 
are required for the proof of the theorem. *
Tarihler: *5-12 Kasim gunde 2 saat.***
*Onkosul. **Algebra, Galois Theory, Field Theory***
*Kaynak:** Field Arithmetic, Fried and Jarden

Dr. Kursat Aker, Lie Cebirleri Temsilleri***
*Ozet: **Lie cebirlerinin temsillerine giris niteliginde bir ders olacak.***
*Ayrintili Program: *
*7 Kasim (4 saat):** Dogrusal cebir: Kusegen matrisler, nilpotent 
(sifirguclu, sifirlanir) matrisler, Jordsan ayrismasi + uygulama saati***
*8 Kasim (4 saat): **Temsil kuraminin temel kavramlari + uygulama saati***
*9 Kasim (4 saat):** sl(2) ve temsilleri + uygulama saati***
*10 Kasim (4 saat): **sl(3) ve temsilleri + uygulama saati***
*11 Kasim (4 saat):** Kristaller + uygulama saati***
*12 Kasim (2 saat): **Littelman operatorleri + uygulama saati***
*13 Kasim (2 saat): **Tartisma

*MSc. Sermin Cam, Representation theory of compact and locally compact 
groups****
*Ozet: **An introductory course on the representations ofcompact and 
locally compact groups.***
*Onkosul:** Basic algebra, basic linear algebra, measure theory, basic 
knowledge on Banach and Hilbert spaces.***
*Ayrintili Program: *
*5 Kasim (2 saat):** Topological groups, examples of compact and locally 
compact groups.***
*6 Kasim (2 saat):** Haar measure on locally compact groups with 
examples and basic properties.***
*7-8 Kasim (4 saat):** Finite dimensional representations of compact 
groups: unitarizability, completereducibility and Schur's lemma. We will 
also see Schur's lemma for topologically irreducibleunitary 
representations of locally compact groups.***
*9 Kasim (2 saat):** Compact operators, Spectral Theorem on Compact 
Operators.***
*10 Kasim (2 saat):** Vector valued integrals, Orthogonality Relations 
for matrix coefficients.***
*11 Kasim (2 saat):** Peter-Weyl Theorem.***
*12 Kasim (2 saat):** We will describe the irreducible representations 
and thedecomposition of L2 for the group SU(2), then use the results to 
obtain the irreducible representations of SO(3) and U(2).

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