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align="left"><br>
Kurban Bayrami'nda lisans ve lisansustu matematik ogrencilerine
yonelik cebir ve sayilar kurami agirlikli bir programimiz var.<br>
Lisansustu ve doktora ogrencileri icin TUBITAK'tan bu programa
destek aldik.<br>
Lisans ogrencilerine de biz destek verecegiz eger talep gelirse.<br>
Lutfen ilgili ogrenciler hemen basvurularini yapsinlar, yerimiz
oldukca kisitlidir. <br>
</p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left">Verilecek dersler:<br>
<span style="font-size: 9pt; font-family:
"Verdana","sans-serif";">Prof. Dr. Ali
Nesin, Permutation Groups.<br>
Yard. Doc. Ozlem Beyarslan, Around Chebotarev Density Theorem<br>
Dr. Kursat Aker, Lie Cebirleri Temsilleri</span><strong><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif"; font-weight:
normal;"><br>
MSc. Sermin Cam, Representation theory of compact and locally
compact groups</span></strong><b style=""><br style="">
</b></p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left">Programin ayrintilari asagida ve <a
href="http://matematikkoyu.org/kurban_lisansustu_2011">http://matematikkoyu.org/kurban_lisansustu_2011</a>
sayfasinda.<br>
Ali Nesin<br>
</p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left"><br>
<strong><span style="font-family:
"Calibri","sans-serif";">Tarih:</span></strong>
5-13 Kasim 2011 (Kurban Bayrami) <br>
<strong><span style="font-size: 9pt; font-family:
"Verdana","sans-serif";">Program
koordinatoru:</span></strong><span style="font-size: 9pt;
font-family: "Verdana","sans-serif";">
Selcuk Demir</span><b><span style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><strong><span
style="font-family:
"Verdana","sans-serif";"><br>
Hedef Kitle:</span></strong></span></b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> Matematik bolumu
ust seviye lisans, (doktora dahil) lisansustu ogrencileri ve
arastirmacilar.</span><span style="font-size: 12pt; font-family:
"Times New Roman","serif";"></span><b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><strong><span
style="font-family:
"Verdana","sans-serif";"><br>
Basvuru:</span></strong></span></b><span style="font-size:
9pt; font-family: "Verdana","sans-serif";">
Basvuru formunu <a href="mailto:emelaydin@nesinvakfi.org">emelaydin@nesinvakfi.org</a>
adresine mail ile gondermelisiniz. Basvurunuzun ulastigina dair
bir onay mesaji gonderilecektir. Basvuru formu icin <a
href="http://matematikkoyu.org/files/efm/files/Lisans_Lisansustu_Basvuru_yeni.doc"
title="Lisans_Lisansustu_Basvuru_yeni">tiklayin.</a> Eger uc
dort gun icinde mesaj almamissaniz lutfen bir daha yazin,
basvurunuz muhtemelen elimize gecmemistir<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong></span><span
style="font-size: 12pt; font-family: "Times New
Roman","serif";"></span><b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><strong><span
style="font-family:
"Verdana","sans-serif";"><br>
Kayit:</span></strong></span></b><span style="font-size:
9pt; font-family: "Verdana","sans-serif";">
Belli araliklarla basvurular degerlendirilir ve sonuclari
e-postayla iletilir. Odeme ve kayitla ilgili tum islemler
basvurunuz kabul edildikten sonra yapilacaktir. </span><span
style="font-size: 12pt; font-family: "Times New
Roman","serif";"></span><b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><strong><u><span
style="font-family:
"Verdana","sans-serif";"><br>
</span></u></strong></span></b></p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left"><b><span style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><strong><u><span
style="font-family:
"Verdana","sans-serif";">Egitmenler
ve Dersler</span></u></strong></span></b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> <br>
<br>
<span style="color: red;">Prof. Dr. Ali Nesin, Permutation
Groups.</span></span><strong><span style="font-size: 9pt;
font-family: "Verdana","sans-serif";"><br>
Ozet:</span></strong><span style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> 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.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Onkosul. </span></strong></b>Basic
group
theory.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Kaynak:</span></strong></b>
M. Bhattacharjee, D. Macpherson, R.G. Moller, P.M. Neumann, <strong><span
style="font-family:
"Verdana","sans-serif";">Notes on
Infinite Permutation Groups</span></strong>, Lecture Notes
in mathematics 1698, Springer 1998.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ayrintili
Program: </span></strong><br>
<strong><span style="font-family:
"Verdana","sans-serif";">5 Kasim (4
saat):</span></strong></b> Basic concepts: Group action,
orbit, transitivity, multiple transitivity, sharp transitivity,
primitive actions, homogeneity. Examples.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">6 Kasim (4
saat):</span></strong></b> Suborbits,<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong>orbital
graphs,
primitivity. Symmetric group. Wielandt’s theorem. Linear actions
and linear groups. Projective and affine groups and spaces.
Wreath products.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">7 Kasim (2
saat):</span></strong></b> Automorphisms of ordered
structures. Back and forth argument. Jordan groups.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">8 Kasim (2
saat):</span></strong></b> Examples of Jordan groups<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">9 Kasim (2
saat):</span></strong></b> Relations related to
betweenness.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">10 Kasim (2
saat):</span></strong></b> Classification of Jordan
groups.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">11 Kasim (2
saat):</span></strong></b> Homogeneous structures and
Fraissé’s theorem.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">12 Kasim (2
saat):</span></strong></b> The Hrushovski Construction I.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">13 Kasim (2
saat):</span></strong></b> The Hrushovski Construction II.
</span><span style="font-size: 12pt; font-family: "Times New
Roman","serif";"></span><span style="font-size:
9pt; font-family: "Verdana","sans-serif";"></span></p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left"><span style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> <span
style="color: red;">Yard. Doc. Ozlem Beyarslan, Around
Chebotarev Density Theorem</span><strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ozet: </span></strong></b>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 <em><span
style="font-family:
"Verdana","sans-serif";">K </span></em>of
the field </span><span style="font-size: 9pt; font-family:
"Lucida Sans Unicode","sans-serif";">ℚ</span><em><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> </span></em><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";">of rational
numbers. Generally speaking, a prime integer will factor into
several ideal primes in the ring of algebraic integers of <em><span
style="font-family:
"Verdana","sans-serif";">K</span></em>.
There are only finitely many patterns of splitting that may
occur. A special case that is easier to state says that if <em><span
style="font-family:
"Verdana","sans-serif";">K </span></em>is
an
algebraic number field which is a Galois extension of </span><span
style="font-size: 9pt; font-family: "Lucida Sans
Unicode","sans-serif";">ℚ</span><em><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> </span></em><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";">of degree <em><span
style="font-family:
"Verdana","sans-serif";">n</span></em>,
then the prime numbers that completely split in <em><span
style="font-family:
"Verdana","sans-serif";">K </span></em>have
density
1/<em><span style="font-family:
"Verdana","sans-serif";">n. </span></em>We
will first go over topics in number theory which are required
for the proof of the theorem.</span> <span style=""></span><strong><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><br>
Tarihler: </span></strong><span style="font-size: 9pt;
font-family: "Verdana","sans-serif";">5-12
Kasim gunde 2 saat.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Onkosul. </span></strong></b>Algebra,
Galois
Theory, Field Theory<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Kaynak:</span></strong></b>
Field Arithmetic, Fried and Jarden</span><span style="font-size:
9pt; font-family: "Verdana","sans-serif";"><span
style=""> </span></span><span style=""></span></p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left"><span style="font-size: 9pt; font-family:
"Verdana","sans-serif"; color: red;">Dr.
Kursat Aker, Lie Cebirleri Temsilleri</span><strong><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> </span></strong><b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ozet: </span></strong></span></b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";">Lie cebirlerinin
temsillerine giris niteliginde bir ders olacak.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ayrintili
Program: </span></strong><br>
<strong><span style="font-family:
"Verdana","sans-serif";">7 Kasim (4
saat):</span></strong></b> Dogrusal cebir: Kusegen
matrisler, nilpotent (sifirguclu, sifirlanir) matrisler, Jordsan
ayrismasi + uygulama saati<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">8 Kasim (4
saat): </span></strong></b>Temsil kuraminin temel
kavramlari + uygulama saati<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">9 Kasim (4
saat):</span></strong></b> sl(2) ve temsilleri + uygulama
saati<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">10 Kasim (4
saat): </span></strong></b>sl(3) ve temsilleri + uygulama
saati<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">11 Kasim (4
saat):</span></strong></b> Kristaller + uygulama saati<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">12 Kasim (2
saat): </span></strong></b>Littelman operatorleri +
uygulama saati<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">13 Kasim (2
saat): </span></strong></b>Tartisma</span><span
style="font-size: 12pt; font-family: "Times New
Roman","serif";"> </span></p>
<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
align="left"><strong><span style="font-size: 9pt; font-family:
"Verdana","sans-serif"; color: red;
font-weight: normal;">MSc. Sermin Cam, Representation theory
of compact and locally compact groups</span></strong><strong><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif"; font-weight:
normal;"> </span></strong><b><span style="font-size: 9pt;
font-family: "Verdana","sans-serif";"><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ozet: </span></strong></span></b><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";">An introductory
course on the representations ofcompact and locally compact
groups.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Onkosul:</span></strong></b>
Basic algebra, basic linear algebra, measure theory, basic
knowledge on Banach and Hilbert spaces.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">Ayrintili
Program: </span></strong><br>
<strong><span style="font-family:
"Verdana","sans-serif";">5 Kasim (2
saat):</span></strong></b> Topological groups, examples of
compact and locally compact groups.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">6 Kasim (2
saat):</span></strong></b> Haar measure on locally compact
groups with examples and basic properties.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">7-8 Kasim (4
saat):</span></strong></b> 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.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">9 Kasim (2
saat):</span></strong></b> Compact operators, Spectral
Theorem on Compact Operators.<strong><span style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">10 Kasim (2
saat):</span></strong></b> Vector valued integrals,
Orthogonality Relations for matrix coefficients.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">11 Kasim (2
saat):</span></strong></b> Peter-Weyl Theorem.<strong><span
style="font-family:
"Verdana","sans-serif";"> </span></strong><b><br>
<strong><span style="font-family:
"Verdana","sans-serif";">12 Kasim (2
saat):</span></strong></b> 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).</span></p>
<p class="MsoNormal" style="text-align: left;" align="left"><span
style="font-size: 9pt; font-family:
"Verdana","sans-serif";"> </span></p>
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