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<p style="margin: 0px; font-size: 15px; color: black; background-color: white;"><span style="margin:0px;font-size:12pt">Dear all,</span></p>
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<p style="margin: 0px; font-size: 15px; color: black; background-color: white;"><span style="margin:0px;font-size:12pt">We would like to cordially invite you to this week's mathematics seminar at Koç University. Everyone is welcome to attend. Please write
an email to me at</span><span style="margin:0px;font-size:12pt"> </span><a href="mailto:ajamneshan@ku.edu.tr" target="_blank" rel="noopener noreferrer" data-auth="NotApplicable" data-linkindex="0" style="margin:0px;font-size:14.67px;font-family:Calibri, sans-serif;text-align:justify"><span style="margin:0px;font-size:12pt;font-family:Arial, Helvetica, sans-serif">ajamneshan@ku.edu.tr</span></a><span style="margin:0px;font-size:12pt"> to
receive the zoom link. The details of this week's talk may be found below. </span></p>
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<p style="margin: 0px; font-size: 15px; color: black; background-color: white;"><span style="margin:0px;font-size:12pt">Best regards,</span></p>
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<p style="margin: 0px; font-size: 15px; color: black; background-color: white;"><span style="margin:0px;font-size:12pt">Asgar Jamneshan</span></p>
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<b><span lang="EN-US" style="margin: 0px; color: rgb(0, 32, 96);">KOÇ UNIVERSITY MATH SEMINAR</span></b></p>
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<b><span lang="EN-US" style="margin: 0px; color: rgb(0, 32, 96);">****************************</span></b></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Speaker :</span></b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Luka
Miliæeviæ, Mathematical Institute of the Serbian Academy of Sciences and Arts</span></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Title </span></b><b><span lang="EN-US" style="margin:0px;font-size:12pt"><span> </span><span style="margin: 0px; color: rgb(0, 32, 96);">:</span></span></b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Bilinear
Bogolyubov Argument in Abelian Groups</span><span style="margin:0px;font-size:12pt"></span></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Date :</span></b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Tuesday,
December 14, 2021</span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"></span></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Time </span></b><b><span lang="EN-US" style="margin: 0px; color: rgb(0, 32, 96);"> </span></b><b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">:</span></b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">14:30-15:40
(on Zoom)</span></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Abstract: <span> </span></span></b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"> </span></p>
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<span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">Bilinear Bogolyubov argument states that if we start with a dense set A of a product U x V of finite vector spaces and carry out sufficiently many steps where we replace every row or every column
of A by the set difference of it with itself, then inside the resulting set we obtain a bilinear variety of codimension bounded in terms of the density of A. In this talk, we focus on a generalization of this theorem to arbitrary finite abelian groups. Along
the way we also discuss analogues of a few linear-algebraic facts as well as quasirandomness of analogues of bilinear varieties in the setting of finite abelian groups.</span></p>
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<span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);">The Mathematics Seminar schedule can be found at<span> </span></span><a href="https://mysite.ku.edu.tr/math-sci/" target="_blank" rel="noopener noreferrer" data-auth="NotApplicable" data-linkindex="1" style="margin: 0px; color: rgb(5, 99, 193); text-decoration: underline;"><span style="margin:0px;font-size:12pt">https://mysite.ku.edu.tr/math-sci/</span></a><span style="margin:0px;font-size:12pt"><span> </span>.<span style="margin: 0px; color: rgb(0, 32, 96);"></span></span></p>
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<span style="margin:0px;font-size:12pt"> </span></p>
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<span style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">Asgar Jamneshan, </span><span style="color: rgb(0, 0, 0); font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Department of Mathematics, </span><span style="color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"></span><span style="color: rgb(34, 34, 34); font-family: Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255); display: inline !important;">Koç
University</span><span style="color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"></span></div>
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