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<p class="MsoNormal"><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Sayin Liste Uyeleri,<br>
<br>
Gebze Teknik Üniversitesi (GTU</span>) <span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">
Matematik Bölümü Genel Seminerleri kapsamında,<br>
31 Mart Cuma günü saat 14:00'da </span><span>Michel Lavrauw </span><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">(Sabancı
Üniversitesi) bir seminer verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.<br>
<br>
Saygılarımızla.<o:p></o:p></span></p>
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Dear all,<br>
<br>
There will be a seminar in Gebze Technical University (GTU) on 31th of<br>
March by </span><span>Michel Lavrauw</span><span style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"> (Sabancı
University)<br>
Time and place: At 14:00 in Department of Mathematics, Building I, Seminar room.<br>
<br>
Title: <span style="font-size: 12pt;">The geometry of nite non-associate division a</span><span style="font-size: 12pt;">lgebras.</span></span></p>
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Abstract:</span></p>
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<div>Finite non-associative division algebras (also called semifields) were first studied<br>
by L. E. Dickson in 1905 as axiomatically defined algebraic structures satisfying<br>
almost all of the axioms in the definition of a finite field. A study which naturally<br>
arose in the aftermath of the well-known theorem: A finite skew-field is a field.<br>
This theorem essentially says that the axiom of commutativity of multiplication<br>
is implied by the other axioms of a finite field.<br>
Dickson showed that this does not hold true for the axiom of associativity of multiplication, by constructing explicit examples of finite non-associative division algebras. Later, when the coordinatisation of projective planes was established<br>
(1940's), it turned out that Dickson's examples also implied the existence of projective planes in which Desarques configuration does not hold, a configuration of points and lines, whose importance emerged from Hilbert's axiomatisation of geometry (1899).<br>
Once this connection between the theory of semifields and the theory of projective planes was established, the topic received a considerable amount of attention from both geometers and algebraists. A good survey of the state of the<br>
art at that time, can be found in the book Projective planes (1970) by Hughes<br>
and Piper, the book Finite Geometries (1968) by Dembowski, or in Knuth's<br>
dissertation Finite semifields and finite projective planes (1963).<br>
In the last decade a second wave of interest in the theory of semifields arrived,<br>
partly due to applications, partly due to new connections between the algebra<br>
and the geometry of semifields, e.g. [1], [2]. For a survey, see [3]. In this<br>
talk we will elaborate on the geometry of finite semifields, and explain how<br>
the interplay between algebra and geometry has allowed us to obtain many<br>
new results, e.g. [4, 5], including the classification of 8-dimensional rank two<br>
commutative semifields.</div>
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