[Turkmath:8608] MSGSÜ Genel Seminerleri ve İstanbul Model Teori Seminerleri

[Ayse Berkman]

Sayın turkmath Listesi Üyeleri,

Bu hafta bölümümüzde iki genel seminer yapılacaktır. Ayrıca bu haftanın
İstanbul Model Teori Seminerleri serisinde, yurtdışından gelen iki
konuşmacı yer alacağı için bu konuşmaların duyurularını da sizlerle
paylaşmak istedim. Bu dört seminerle ilgili tüm ayrınıtları aşağıda
bulabilirsiniz.

Selamlar,
Ayşe Berkman

1 Kasım 2012 Perşembe 15.30
Tuna Altınel (Université Claude Bernard Lyon-1) "A Jordan decomposition for
minimal simple groups of finite Morley rank"
İstanbul Model Teori Seminerleri

1 Kasım 2012 Perşembe 16.45
Adrien Deloro (Université Paris 6) "Representations of finite Morley rank"
İstanbul Model Teori Seminerleri

2 Kasım 2012 Cuma 14.30
Alexandre Borovik (The University of Manchester) "Oracles and Revelations"
MSGSÜ Matematik Bölümü Genel Semineri

2 Kasım 2012 Cuma 16.00
Özgür Kişisel (ODTÜ - Kuzey Kıbrıs) "Constructing Quantum Groups"
MSGSÜ Matematik Bölümü Genel Semineri

Tüm konuşmalar, Mimar Sinan Üniversitesi Matematik Bölümü Seminer Odası'nda
yapılacaktır.

Harita: http://math.msgsu.edu.tr/iletisim.html

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*Konuşma Özetleri*

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*A Jordan decomposition for minimal simple groups of finite Morley rank,
Tuna Altınel*


The Jordan decomposition of a matrix as the sum of two multiplicatively
commuting matrices, one diagonalizable and the other nilpotent (or
unipotent if the matrix is invertible), is fundamental in the analysis of
semisimple Lie algebras and simple algebraic groups. It connects algebraic
and geometric aspects of these structures.


Infinite simple groups of finite Morley rank, of which the only known
examples are simple linear algebraic groups over algebraically closed
fields, motivate the question whether one can propose an abstract Jordan
decomposition using only group-theoretic properties, said more
model-theoretically a decomposition definable in the group language.


In a joint work with Jeffrey Burdges and Olivier Frecon, we have proposed
an approach for a Jordan decomposition of finite Morley rank coherent with
the one in algebraic groups. The definition, quite natural for the expert,
involves Carter subgroups. We have established that the decomposition
enjoys the expected basic properties over a subclass of minimal simple
groups of finite Morley rank. This subclass is rather restricted. The
amount of effort is considerable. In my talk, I will try to illustrate why
one has to work so much for so little, as well as why one can still expect
much more with so little.

* *

*Representations of finite Morley rank, Adrien Deloro*


The Cherlin-Zilber conjecture has received most of the attention devoted to
groups of finite Morley rank. But groups of fMR are not interesting only as
abstract groups, also as permutation groups. The talk is about modules of
finite Morley rank, i.e. groups acting on abelian groups. I shall review
the various results obtained in this vein.

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*Oracles and Revelations, Alexandre Borovik*


This is joint work with Şükrü Yalçınkaya. The talk will discuss some
approaches to a systematic development of black box algebra. The talk will
be at an elementary level.

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*Constructing Quantum Groups, Özgür Kişisel*


Quantum groups are the group objects of noncommutative geometry. They are
known to have applications in diverse areas of mathematics such as knot
theory, representation theory and mathematical physics. The two main
techniques for constructing quantum groups use deformations and bicrossed
products. We will attempt to propose another method for constructing
quantum groups and give some examples.
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