<div dir="ltr"><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif">Hi folks, <span style="font-family:Arial,Helvetica,sans-serif;font-size:large"><br></span></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><br></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif">We're continuing theory lunch this quarter, and will be having our first meeting today! Meetings will still be held at our normal time (Wednesdays 12.30), in last quarter's room (JCL 298).</div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><br></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif">Sorry for the late notice everyone, we're trying to set up a system for automating the announcements, and are still working through some bugs. Abstract to follow below.</div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><br></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif">Happy New Year, and hope your holidays were restful,</div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif">Antares & Chris</div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><span style="font-family:Arial,Helvetica,sans-serif;font-size:large"><br></span></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">******************************</span><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">******************************</span><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">**************************</span><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></b></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></b></div><div style="color:rgba(0,0,0,0.87);font-size:14px;font-family:Calibri,Arial,Helvetica,sans-serif"><div><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4">Date</font></b><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-size:1.13em;color:rgb(49,49,49);word-spacing:1px">:</b><span style="font-size:1.13em;color:rgb(49,49,49);word-spacing:1px"> </span><span style="color:rgb(49,49,49);word-spacing:1px"><font size="4">January 11, 2022</font></span><br></div><div style="font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="color:rgb(32,31,30);margin:0px"><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Time: </b>12:30pm CT</font></div><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Location: </b>JCL 298</font></div></div></div></div></div></div></div></div></div><div style="color:rgba(0,0,0,0.87);font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:14px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="color:rgb(32,31,30);margin:0px"><div dir="auto" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><b><font style="font-size:1.13em"><br></font></b></div><div dir="auto" style="margin:0px;color:rgb(49,49,49);word-spacing:1px"><font size="4"><font face="Calibri, Arial, Helvetica, sans-serif" style="font-weight:bold">Speaker: </font><font face="Calibri, Arial, Helvetica, sans-serif" style="">Jesse Stern</font></font></div><div dir="auto" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></div></div><div style="margin:0px"><span style="color:rgb(49,49,49);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;word-spacing:1px"><font style="font-size:1.13em"><b>Title: </b>The Sumset Cover Problem</font></span></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><b style="color:rgb(49,49,49);font-size:16px;word-spacing:1px"><font style="font-size:1.13em"><br></font></b></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><span style="margin:0px;font-size:16px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Zoom: </b>[<a href="https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09">link</a>]</font></span></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><br></div><div style="margin:0px"><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="color:rgb(49,49,49);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:13pt;margin:0px"><b>Abstract:</b></span><span style="color:rgb(32,31,30);font-family:"trebuchet ms",sans-serif;font-size:12pt;margin:0px;word-spacing:0px"> </span></font><span style="color:rgb(51,51,51);font-family:-apple-system,"system-ui","Segoe UI",Roboto,Oxygen,Ubuntu,Cantarell,"Fira Sans","Droid Sans","Helvetica Neue",sans-serif;font-size:16px">We define the Sumset Cover Problem which, at a high level, is the problem of determining pairs of sets (A,B) such that A+B=C for some target set C. Some simple sumset cover examples for C={1,2,3,4} would be {1,2}+{0,2} or {1,3}+{0,1}. We discuss our proof of a nearly tight bound on the number of such covers when C=[n] as well as briefly discussing our progress towards extending the bound to general C. Not only does this allow one to count the number of covers, but it also allows one to enumerate the exact coverings efficiently with respect to the to the number of distinct sumset covers.</span></div><div dir="auto" style="margin:0px"><span style="color:rgb(51,51,51);font-family:-apple-system,"system-ui","Segoe UI",Roboto,Oxygen,Ubuntu,Cantarell,"Fira Sans","Droid Sans","Helvetica Neue",sans-serif;font-size:16px"><br></span></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">[</span><a href="https://urldefense.com/v3/__https://orecchia.net/event/theory-lunch/__;!!BpyFHLRN4TMTrA!pwdRh9yLA-IBD6NCNvREJGd9Nj5jtC6_N-AowF6HSwIQeb1FPAmu0L_tAswwp_F5nRs$" rel="noopener noreferrer nofollow" title="https://orecchia.net/event/theory-lunch/" target="_blank" style="text-decoration-line:none;color:rgb(26,115,232);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large;margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Theory</span></span></span></span></span> <span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Lunch</span></span></span></span> Webpage</a><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">]</span><br style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">[</span><a href="https://urldefense.com/v3/__https://calendar.google.com/calendar/u/0/embed?src=c_osgf1c1qemdras8mu7l7pdhjrs@group.calendar.google.com&ctz=America*Chicago__;Lw!!BpyFHLRN4TMTrA!pwdRh9yLA-IBD6NCNvREJGd9Nj5jtC6_N-AowF6HSwIQeb1FPAmu0L_tAsww4XtIRnQ$" rel="noopener noreferrer nofollow" title="https://calendar.google.com/calendar/u/0/embed?src=c_osgf1c1qemdras8mu7l7pdhjrs@group.calendar.google.com&ctz=America/Chicago" target="_blank" style="text-decoration-line:none;color:rgb(26,115,232);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large;margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Theory</span></span></span></span></span></span></span><span style="margin:0px"> </span><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Lunch</span></span></span></span></span><span style="margin:0px"> </span>Calendar</a><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">]</span></span></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large"><br></span></span></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="font-size:large">******************************</span><span style="font-size:large">******************************</span><span style="font-size:large">**************************</span></span></font></div></div></div></div></div></div></div></div></div>