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<p class="MsoNormal" style="text-align: left; text-indent: 0cm;"
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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