[Turkmath:2852] HATIRLATMA-MSGSÜ Matematik Bölümü Semineri- Şükrü Yalçınkaya -22.03.2018, 16:00

[Sibel Şahin]

 Sayın liste üyeleri,

*22 Mart, Perşembe 16:00'**da* MSGSÜ Matematik Bölümü Semineri'nde İstanbul
Üniversitesi Matematik Bölümü'nden *Şükrü Yalçınkaya* " Recognition of
black box  groups and unipotent elements " başlıklı bir konuşma verecektir.
Konuşmanın özeti aşağıda yer almaktadır.

Seminerde görüşmek dileğiyle,
Sibel ŞAHİN


*Başlık:*  Recognition of black box  groups and unipotent elements

*Özet:  *A black box group is a black box (or an oracle, or a device, or an
algorithm) operating with binary strings of uniform length which encrypt
(not necessarily in a unique way) elements of some finite group. Group
operations, taking inverses and deciding whether two strings represent the
same group elements are done by the black box. In this context, a natural
task is to find a probabilistic algorithm which determines the isomorphism
type of a group within given arbitrarily small probability of error. More
desirable algorithms, constructive recognition algorithms, are the ones
producing an isomorphism between a black box copy of a finite group and its
natural copy.
In this talk, I will discuss the recognition problem for the black box
groups  PSL_2 over fields of odd characteristic. Our approach to this
problem involves the construction of a black box projective plane and its
coordinatization by using the geometry of involutions (elements of order
2). This construction produces the best possible recognition for these
groups and also produces a solution to a long standing open problem in
computational group theory, that is, construction of a unipotent element in
black box groups of Lie type.
This is a joint work with Alexandre Borovik.
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