<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div class="WordSection1" style="-webkit-text-size-adjust: auto; page: WordSection1;"><div id="mail-editor-reference-message-container"><div id="mail-editor-reference-message-container"><div id="mail-editor-reference-message-container"><div id="mail-editor-reference-message-container"><div id="mail-editor-reference-message-container"><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 12pt; font-family: Helvetica;">Elyassaf Loyfer</span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;">Hebrew University of Jerusalem</span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><img width="229" height="293" id="Picture_x0020_1" src="cid:BEB6F213-CF10-40D2-96EA-E7F8243A5BAF" _mf_state="1" title="null" alt="image001.png" style="width: 2.3854in; height: 3.052in;"><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;"> </span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; font-family: Helvetica;"> </span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt;"><span dir="ltr">Tuesday, </span></span></b><b><span style="font-size: 11pt;"><span dir="ltr">October 8</span><span dir="ltr">, 202</span><span dir="ltr">4</span><span dir="ltr"> at 3:30pm</span></span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><span style="font-size: 11pt; background: yellow;">Location: Kent 102</span></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 11pt;"> </span><b><i><u><span style="font-size: 14pt;">Title:</span></u></i></b><i><span style="font-size: 14pt;"> </span></i><span style="font-size: 14pt;">Rate vs. Distance - Milestones and Obstacles Towards Improved Bounds*</span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 14pt;"> (*no bounds were harmed (yet) in the making of this research)</span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><i><span style="font-size: 14pt;"> </span></i></b><o:p></o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><b><i><span style="font-size: 14pt;">Abstract</span></i></b><i><span style="font-size: 14pt;">: </span></i><span style="font-size: 14pt;">The rate vs. distance problem is a major open problem of coding theory. Significant progress has stalled since 1977. The best-known upper bound, established by MRRW, is derived from Delsarte’s reformulation of the combinatorial question as a linear program (LP). This breakthrough sparked a line of research into stronger optimization problems. However, the more powerful formulations have remained difficult to analyze, and no improved bounds have been achieved yet. In this talk, I will present new results on the analysis of a recently developed LP hierarchy. I will discuss the techniques employed, current limitations, and possible strategies to deal with these challenges.</span><o:p></o:p></p><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 10pt; font-family: Calibri, sans-serif;"><o:p> </o:p></p><p class="MsoNormal" style="margin: 0in; font-size: 10pt; font-family: Calibri, sans-serif;"><span style="font-size: 14pt;">Based on joint work with Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones, and Nati Linial.</span></p><p></p></div></div></div></div></div></div><div dir="ltr"></div></body></html>