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We would like to kindly invite you to this week's mathematics seminar at Koç. Everyone is welcome to attend! Details of the seminar can be found below. Please write an email at
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<span style="margin:0px;font-size:12pt">ajamneshan@ku.edu.tr</span></a> to receive the zoom link. </p>
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Best regards,</p>
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Asgar Jamneshan</p>
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<b><span lang="EN-US" style="margin: 0px; color: rgb(59, 32, 77);">KOÇ UNIVERSITY MATH SEMINAR</span></b></p>
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<b><span lang="EN-US" style="margin: 0px; color: rgb(59, 32, 77);">****************************</span></b></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Speaker: Or Shalom</span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);"> (Einstein Institute of Mathematics, Hebrew University of Jerusalem)</span><span lang="EN-US" style="margin: 0px; font-size: 12pt; font-size: 12pt;"></span></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; font-family: "Segoe UI", "Helvetica Neue", sans-serif; color: rgb(59, 32, 77);">Title</span><span lang="EN-US" style="margin: 0px; font-size: 12pt;"><span style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;">:</span></span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="font-family: "Segoe UI", "Helvetica Neue", sans-serif; color: rgb(59, 32, 77);">
</span></span><span lang="EN-US" style="margin: 0px; font-size: 12pt; font-family: "Segoe UI", "Helvetica Neue", sans-serif; color: rgb(0, 32, 96);"><span style="text-align: left; color: rgb(59, 32, 77); background-color: rgb(255, 255, 255);">A structure
theorem for Gowers-Host-Kra seminorms for non-finitely generated countable abelian groups of unbounded torsion</span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"></span></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Date:</span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="color: rgb(59, 32, 77);"> </span></span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Tuesday,
November 23, 2021</span></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Time: </span><span lang="EN-US" style="margin: 0px; color: rgb(59, 32, 77);"> </span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">14:30-15:40</span></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Place: </span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);"> </span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Hybrid
(SCI 103, Zoom)</span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><i></i></span></p>
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<b><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);">Abstract: </span><span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="color: rgb(59, 32, 77);"> </span></span></b></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77);"> </span></p>
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<span lang="EN-US" style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; text-align: left; background-color: rgb(255, 255, 255); display: inline !important; font-size: 12pt;">Furstenberg’s
famous proof of Szemeredi’s theorem leads to a natural question about the convergence and limit of some multiple ergodic averages. In the case of </span><img title="\mathbb{Z}" alt="\mathbb{Z}" width="10" height="11" style="height: auto; max-width: 100%; vertical-align: middle; font-family: Merriweather, Georgia, serif; text-align: left; color: rgb(26, 26, 26); background-color: rgb(255, 255, 255);" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cmathbb{Z}"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; text-align: left; background-color: rgb(255, 255, 255); display: inline !important; font-size: 12pt;">-actions
these averages were studied by Host-Kra and Ziegler. They show that the limiting behavior of such multiple ergodic average is determined on a certain factor that can be given the structure of an inverse limit of nilsystems (i.e. rotations on a nilmanifold).
This structure result can be generalized to </span><img title="\mathbb{Z}^d" alt="\mathbb{Z}^d" width="16" height="13" style="height: auto; max-width: 100%; vertical-align: middle; font-family: Merriweather, Georgia, serif; text-align: left; color: rgb(26, 26, 26); background-color: rgb(255, 255, 255);" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cmathbb{Z}%5Ed"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; text-align: left; background-color: rgb(255, 255, 255); display: inline !important; font-size: 12pt;"> actions
(where the average is taken over a Folner sequence), but the non-finitely generated case is still open. The only progress prior to our work is due to Bergelson Tao and Ziegler, who studied actions of the infinite direct sum </span><img title="\mathbb{Z}/p\mathbb{Z}" alt="\mathbb{Z}/p\mathbb{Z}" width="37" height="16" style="height: auto; max-width: 100%; vertical-align: middle; font-family: Merriweather, Georgia, serif; text-align: left; color: rgb(26, 26, 26); background-color: rgb(255, 255, 255);" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cmathbb{Z}/p%5Cmathbb{Z}"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; text-align: left; background-color: rgb(255, 255, 255); display: inline !important; font-size: 12pt;">.
In our work we generalize this further to the case where the sum is taken over different primes (the most interesting case is when the multiset of primes is unbounded). We will explain how this case is significantly different from the work of Bergelson Tao
and Ziegler by describing a new phenomenon that only happens in these settings. Moreover, we will discuss a generalized version of nilsystems that plays a role in our work and some corollaries. If time allows, we will also discuss the group actions of other
abelian groups.</span></span></p>
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<span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><span style="font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;"> </span></p>
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<span class="x_SpellE" style="margin:0px"><span style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;">The </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span class="x_SpellE" style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">Mathematics</span><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><span class="x_SpellE" style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">Seminar</span><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><span class="x_SpellE" style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">schedule</span><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;">can
be</span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><span class="x_SpellE" style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">found</span><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span></span><span style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;">at</span><span style="margin: 0px; font-size: 12pt; color: rgb(0, 32, 96);"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </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"><span style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;">https://mysite.ku.edu.tr/math-sci/</span></a><span style="margin:0px;font-size:12pt"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><span class="x_SpellE" style="margin: 0px; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">and</span><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;"> </span><a href="https://researchseminars.org/seminar/kocuniversitymathseminar" target="_blank" rel="noopener noreferrer" data-auth="NotApplicable" data-linkindex="2" style="margin:0px"><span style="color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif; font-size: 12pt;">https://researchseminars.org/seminar/kocuniversitymathseminar</span></a></span><span style="margin: 0px; font-size: 12pt; color: rgb(59, 32, 77); font-family: "Segoe UI", "Helvetica Neue", sans-serif;"> .</span></p>
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