[Turkmath:9235] GSU Genel Seminer duyurusu: 25 Eylul S.Yalcinkaya

[Ayberk Zeytin]

Deg(erli Liste Üyeleri;

Galatasaray Üniversitesi Matematik Bölümü Seminerleri kapsam?nda 25 
Eylül Carsamba günü Sukru Yalcinkaya konus,mac? olacakt?r. Konus,ma ile 
ilgili detayl? bilgiler soyledir:

Gün: 25 Eylül, 15:00.

Yer:  Galatasaray Üniversitesi FEF 10.

Titre/ bas,l?k: Black Box Groups

Abstract/Özet: Black box groups are introduced as an idealised setting 
for randomised algorithms for solving permutation and matrix group 
problems in computational group theory. A black box group G is a finite 
group whose elements are encoded as 0-1 strings of uniform length and 
the group operations are performed by an oracle ('black box'). Given 
strings representing g, h in G, the black box can compute the strings 
representing gh, g^{-1} and decide whether g = h. 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, called constructive recognition 
algorithms, are the ones producing an isomorphism between a black box 
copy of a finite group and its natural copy.
A simple observation on the recognition algorithms in black box group 
theory is that procedures are based on checking whether some first order 
formulae satisfied by the given black box group. I will focus on this 
observation and discuss constructive recognition of black box groups of 
Lie type. Along the way, I will explain how we define a standard 
Frobenius automorphism in a black box group isomorphic to (P)SL(2, q) 
and construct (or interpret) of a black box field in black box groups 
using only black box group operations. If time permits, I will talk 
about the interpretation of inverse transpose map and graph 
automorphisms, and the corresponding constructions in the black box 
groups of Lie type.
This is a joint work with Alexandre Borovik.

Sayg?lar?mla,

-- 
Ayberk Zeytin
Matematik Bölümü
Galatasaray Üniversitesi
http://math.gsu.edu.tr/azeytin/

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