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<div align="center"><big><b><big>Welcome to the 2025 Fall
talks of ODTÜ-Bilkent Algebraic Geometry Seminars</big></b></big><b><br>
</b></div>
<div align="center"><i>since 2000</i><br>
</div>
<div align="center"><b><b>=================================================================</b></b><br>
<br>
This week the <a
href="http://www.bilkent.edu.tr/~sertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTÜ-Bilkent
Algebraic Geometry Seminar</a> is <b>online</b><br>
<br>
<i><font color="#ff00ff">This talk will begin at <u><b>15:40</b></u><u> (GMT+3)</u></font></i><br>
<a
href="https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20251128T1540&p1=19&ah=1"
target="_blank" moz-do-not-send="true">Please check
your time difference between Ankara and your city here</a><br>
<b>=================================================================<br>
<br>
</b></div>
<div align="center">
<div align="center"><img
src="cid:part1.UowLFNkv.IBBXRSgL@bilkent.edu.tr"
alt=""></div>
</div>
<div align="center"><br>
</div>
<div align="center"><i>Gustave Boulanger (1824-1888)<br>
</i></div>
<div align="center"><i><br>
</i></div>
<div align="center"><i><br>
</i>
<div align="left">
<div align="left"><b><b moz-do-not-send="true"
href="https://fens.sabanciuniv.edu/tr/faculty-members/detail/3419"><font
color="#ff0000">Speaker: </font> <a
moz-do-not-send="true"
href="https://sites.google.com/view/swshah/home">Syed Waqar Ali Shah</a></b></b></div>
<b><b><font color="#ff0000"><font color="#000000"> </font></font></b></b><b><b><font
color="#ff0000">Affiliation: </font><i>Bilkent<br>
<br>
</i></b></b></div>
<div align="left"><b><b><font color="#ff0000"> Title:<font
color="#000000"> Euler systems for exterior
square motives</font></font></b></b></div>
<div align="left"><b><b><font color="#ff0000"><font
color="#000000"><br>
</font></font></b></b></div>
</div>
<div align="justify"><b><b><font color="#ff0000">Abstract:
</font></b></b>The Birch–Swinnerton-Dyer conjecture
relates the behavior of the L-function of an elliptic
curve at its central point to the rank of its group of
rational points. The Bloch–Kato conjecture generalizes
this principle to a broad family of motivic Galois
representations, predicting a precise relationship
between the order of vanishing of motivic L-functions at
integer values and the structure of the associated
Selmer groups. Since the foundational work of Kolyvagin
in the nineties, Euler systems have played a central
role in approaching these conjectures, and in recent
years their scope has expanded significantly within the
automorphic setting of Shimura varieties.<br>
<br>
In this talk, I will focus on unitary Shimura varieties
GU(2,2), whose middle-degree cohomology realizes the
exterior square of the four-dimensional Galois
representations attached to certain automorphic
representations of GL_4. The period integral formula of
Pollack–Shah for exterior square L-functions has a
natural motivic interpretation, suggesting the
feasibility of constructing a nontrivial Euler system. A
key obstacle to this construction is the failure of a
suitable multiplicity-one property, which has long
prevented the verification of the certain norm relations
required for Euler system methods. I will present a new
approach that overcomes this difficulty. The resulting
Euler system in the middle-degree cohomology of GU(2,2)
provides the first nontrivial evidence toward the
Bloch–Kato conjecture for exterior square motives and
opens several promising avenues for further arithmetic
applications. This is joint work with Andrew Graham and
Antonio Cauchi. </div>
<br>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Date:<font
color="#000000"> 28 November 2025, Friday</font></font></b></font></font></div>
<div align="left"><font color="#ff0000"><font
color="#000000"><b><font color="#ff0000">Time: </font>15:40 <i>(GMT+3)</i></b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom</b></font></font></font></font></div>
<blockquote>
<p><i><b>Participants who have registered will receive
the Zoom link via email one day before the
seminar.</b></i></p>
<p><i><b>If you registered for a previous talk in this
series, there's no need to register again—you'll
automatically receive the link for this session.</b></i></p>
<p><i><b moz-do-not-send="true"
href="mailto:sertoz@bilkent.edu.tr">If you haven't
registered yet, please contact <a
href="mailto:sertoz@bilkent.edu.tr"
class="moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
to be added to the mailing list.</b></i></p>
</blockquote>
<div align="left">You are most cordially invited to
attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz</div>
<div align="left"><br>
</div>
<div align="center">
<div align="center"><b><font color="#0080c0"><i><b><font
color="#0080c0"><i>This seminar series is
organized by a joint team from ODTÜ and
Bilkent<br>
<br>
Alexander Degtyarev (Bilkent)<br>
Ali Sinan Sertöz (Bilkent) contact person<br>
Ali Ulaş Özgür Kişisel (ODTÜ)<br>
Yıldıray Ozan (ODTÜ)<br>
</i></font></b></i></font></b></div>
<div align="left"><br>
</div>
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<hr>
<pre cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail: <a href="mailto:sertoz@bilkent.edu.tr" target="_blank"
class="gmail-moz-txt-link-freetext moz-txt-link-freetext"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" target="_blank"
moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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