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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. Kazım Büyükboduk<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'>Koç 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'> Max-Planck-Institut für Mathematik, Bonn, Germany
(Visiting)<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'><br>
4 December 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'>130.</span></font></span></font><font color=red><span
style='color:red'><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'>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'>Zeta-functions
and arithmetic: From Euler to Wiles<o:p></o:p></span></font></p>
<p class=MsoNormal align=center style='text-align:center;text-autospace:none'><font
size=3 face=Arial><span lang=EN-US style='font-size:12.0pt;font-family:Arial'><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 lang=EN-US
style='font-size:12.0pt;font-family:Arial;font-weight:bold'> </span></font></b><b><font
face=Arial><span style='font-family:Arial;font-weight:bold'>Abstract:<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='text-align:justify;text-indent:35.4pt;text-autospace:
none'><font size=3 face=Tahoma><span style='font-size:12.0pt;font-family:Tahoma'>The
purpose of this expository talk is to discuss an important theme in Number
Theory: The relation between zeta-functions (objects of analytic nature) and
certain objects (which we generally call them Selmer groups) of arithmetic
nature. Kummer was first to recognize the arithmetic significance of the
special values of the classical zeta-function, using which he was able to
deduce an important portion of the "Fermat's Last Theorem". Kummer's
ideas were much later generalized by Ribet and Wiles (in a certain sense) to
conclude with the full proof. An important portion of this talk will be devoted
to explaining Kummer's ideas, and if time permits, say a few words about their
influence in modern number theory (e.g., towards Birch-Swinnerton Dyer
conjectures (one of the Clay Millenium Problems) and its utmost generalization,
the Bloch-Kato conjectures).<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 style='text-align:justify'><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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