[MD-sorular] Bayramda Cebir ve Sayilar Kurami

[Ali Nesin]

Kurban Bayrami'nda ileri seviyede lisans ve lisansustu matematik
ogrencilerine yonelik cebir ve sayilar kurami agirlikli bir programimiz
var. Önümüzdeki Cumartesi basliyor.
Program http://matematikkoyu.org/kurban_lisansustu_2011 sayfasinda ve
asagida.
Lisansustu ve doktora ogrencileri icin TUBITAK'tan bu programa (henüz
bilmedig(imiz bir miktar) destek aldik. Yani bu seviyedeki
ög(rencilerden bir ücret talep etmiyoruz.
Lisans ogrencilerine de biz destek verecegiz eger istenirse.
Yani gelin!
Ilgili ogrenciler hemen basvurularini yapsinlar:
http://matematikkoyu.org/kurban_lisansustu_2011
Ali Nesin

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.
Tarih: 5-13 Kasim 2011 (Kurban Bayrami)
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. 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).