<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div dir="ltr"></div><div dir="ltr">This may be of interest to many on this list.<br><br>Begin forwarded message:<br><br></div><blockquote type="cite"><div dir="ltr"><b>From:</b> Audra Herman <audrah1@uchicago.edu><br><b>Date:</b> February 3, 2025 at 4:21:14 PM CST<br><b>To:</b> razborov@uchicago.edu<br><b>Subject:</b> <b>Colloquium: Frederick Manners (UCSD)</b><br><b>Reply-To:</b> Audra Herman <audrah1@uchicago.edu><br><br></div></blockquote><blockquote type="cite"><div dir="ltr">
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<div style="max-width: 204px;"><img src="https://d15k2d11r6t6rl.cloudfront.net/pub/bfra/ewlkbmtv/1p9/34j/g6z/UChicago_Shield_1Color_DarkGreystone_RGB%20%281%29.png" style="display: block; height: auto; border: 0; width: 100%;" width="204" alt="Mehtaab Sawhney" title="Mehtaab Sawhney" height="auto" data-unique-identifier=""></div>
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<h1 style="margin: 0; color: #002a3a; direction: ltr; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 30px; font-weight: 700; letter-spacing: normal; line-height: 120%; text-align: center; margin-top: 0; margin-bottom: 0; mso-line-height-alt: 36px;"><span class="tinyMce-placeholder" style="word-break: break-word;">Frederick Manners</span></h1>
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<p style="margin: 0; margin-bottom: 16px;">University of California San Diego</p>
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<p style="margin: 0; mso-line-height-alt: 21.6px; letter-spacing: 1px;">A function $f : \mathbb{F}_2^n \to \mathbb{F}_2^n$ is linear if $f(x+y)=f(x)+f(y)$ for all pairs $(x,y)$.</p>
<p style="margin: 0; mso-line-height-alt: 21.6px; letter-spacing: 1px;">Now suppose $f$ is "a little bit linear" -- say, $f(x+y)=f(x)+f(y)$ for a 1% fraction of pairs $(x,y)$. What can you say about $f$? Must it be closely related to an actually linear function? If so, how closely?</p>
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<p style="margin: 0; mso-line-height-alt: 21.6px; letter-spacing: 1px;">This question turns out to be equivalent to asking for good quantitative bounds in the Freiman--Ruzsa theorem, a foundational result in additive combinatorics. Marton gave a formulation, equivalent to the statement above, which she conjectured should have polynomial bounds. I will discuss this conjecture, and its (comparatively) recent proof (joint with Timothy Gowers, Ben Green and Terence Tao).</p>
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<p style="margin: 0;">February 5th, 2025</p>
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<p style="margin: 0;"><span style="word-break: break-word; color: #000000;"><strong>Eckhart 202</strong></span></p>
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<p style="margin: 0;"><span style="word-break: break-word; color: #000000;"><u><strong>*3:00-4:00PM*</strong></u></span> Central</p>
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<p style="margin: 0;"><strong>Date: February 5th, 2025</strong></p>
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<p style="margin: 0;"><strong>Time</strong>: 3:00-4:00 PM Central</p>
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<p style="margin: 0;"><strong>Location:</strong> <span style="word-break: break-word; color: #000000;">Eckhart 202</span></p>
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Math Department · 5734 S University Ave Ste 108 · Chicago, IL 60637-1501 · USA
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<div style="display:none;"> ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏</div><!--[if !mso]><!--><div style="display:none; font-size:0px; line-height:0px; max-height:0px; max-width:0px; opacity:0; overflow:hidden; visibility:hidden; mso-hide:all;"><img src="https://uchicago.us2.list-manage.com/track/open.php?u=350fc31a7f826e3b52544f33a&id=f0e0a26fb9&e=d7c93c8cdd" height="1" width="1" style="display:none; font-size:0px; line-height:0px; opacity:0; overflow:hidden; visibility:hidden; mso-hide:all;" alt="" data-unique-identifier=""></div><!--<![endif]--></div></blockquote></body></html>