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<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Assist. Prof. Umud Devrim Yalcin<o:p></o:p></span></font></b></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;margin-bottom:
12.0pt;text-align:center'><font size=3 face=Tahoma><span style='font-size:12.0pt;
font-family:Tahoma'>(Ä°stanbul Bilgi University)<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;margin-bottom:
12.0pt;text-align:center'><font size=3 face=Tahoma><span style='font-size:12.0pt;
font-family:Tahoma'>19 February Friday, at <font color=blue><span
style='color:blue'>14:00</span></font>;<br>
Bilgi Üniversitesi Dolapdere Kampüsü, Room:<font color=blue><span
style='color:blue'>135.</span></font></span></font><o:p></o:p></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Title:</span></font></b><o:p></o:p></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Tahoma><span style='font-size:12.0pt;font-family:Tahoma'>Symplectic
Rank 3 Theorem<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'> Abstract:<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='text-align:justify;text-autospace:none'><font size=3
face=Tahoma><span style='font-size:12.0pt;font-family:Tahoma'>Let b be a
nondegenerate symplectic form on a vector space V over a finite feld. Let G be
a symplectic group containing all the b-similarities; i.e. Sp(V; b) ≤ G ≤ </span></font><font
size=2><span style='font-size:10.0pt'>Γ</span></font><font face=Tahoma><span
style='font-family:Tahoma'>Sp(V; b). Then G is Rank 3 on the projective space
P(V ). That is, for any x Ñ” P(V ), the one point stabilizer Gx has 3 orbits in
P(V ); namely: {x}, x<sup>í¯€</sup>_{x} (set of all the points that are
b-orthogonal to x other than x) and P(V ) _ x<sup>í¯€</sup>?. Symplectic Rank 3
Theorem states that this Rank 3 property characterizes all the intermediate
groups between Sp(V; b) and </span></font><font size=2><span style='font-size:
10.0pt'>Γ</span></font><font face=Tahoma><span style='font-family:Tahoma'>Sp(V;
b).<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-align:justify;text-autospace:none'><font size=3
face=Tahoma><span style='font-size:12.0pt;font-family:Tahoma'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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