<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">The following might be of interest to many on this list.<div dir="ltr"></div><div><br></div><div><center style="box-sizing: border-box; -webkit-text-size-adjust: 100%; background-color: rgb(255, 255, 255);"><table border="0" cellpadding="0" cellspacing="0" height="100%" width="100%" id="bodyTable" style="border-collapse: collapse; background-color: rgb(244, 244, 244);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="bodyCell" align="center" valign="top" style="box-sizing: border-box; word-break: break-word; margin: 0px auto; padding: 0px; width: 640px;"><table id="root" border="0" cellpadding="0" cellspacing="0" width="100%" style="border-collapse: collapse;"><tbody class="mceWrapper" style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td align="center" valign="top" class="mceWrapperOuter" style="box-sizing: border-box; word-break: break-word;"><table border="0" cellpadding="0" cellspacing="0" width="100%" role="presentation" style="border-collapse: collapse; max-width: 660px;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="mceWrapperInner" valign="top" style="box-sizing: border-box; word-break: break-word; background-color: rgb(255, 255, 255); background-size: cover; background-position: center center; background-repeat: no-repeat no-repeat;"><table align="center" border="0" cellpadding="0" cellspacing="0" width="100%" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr class="mceRow" style="box-sizing: border-box;"><td valign="top" style="box-sizing: border-box; word-break: break-word; background-size: cover; background-position: center center; background-repeat: no-repeat no-repeat;"><table border="0" cellpadding="0" cellspacing="0" width="100%" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="mceColumn" valign="top" colspan="12" width="100%" style="box-sizing: border-box; word-break: break-word; padding-top: 0px; padding-bottom: 0px;"><table border="0" cellpadding="0" cellspacing="0" width="100%" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="mceSpacing-24" valign="top" style="box-sizing: border-box; word-break: break-word;"><div class="mceCode" style="box-sizing: border-box;"><table class="nl-container" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse; background-color: rgb(247, 247, 247);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row row-1" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse; background-size: auto;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(53, 61, 70); background-image: url("https://d15k2d11r6t6rl.cloudfront.net/public/users/Integrators/BeeProAgency/861155_845253/Math%20Header.jpg"); background-size: cover; color: rgb(0, 0, 0); background-repeat: no-repeat no-repeat;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="100%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; padding-top: 0px; padding-bottom: 0px; border: 0px;"><table class="image_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; width: 640px; padding: 45px 0px 50px;"><div class="alignment" align="center" style="box-sizing: border-box; line-height: 10px;"><img class="big" src="cid:4FFCA5EF-29C3-48BE-984D-E1752232DD10" width="680" alt="The University of Chicago Department of Mathematics Colloquium Series" title="The University of Chicago Department of Mathematics Colloquium Series" style="border: 0px; height: auto; outline: none; width: 680px; display: block;"></div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table><table class="row row-2" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(255, 255, 255); border-radius: 0px; color: rgb(0, 0, 0);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="50%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; border: 0px;"><table class="image_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; width: 640px; padding: 20px 0px 15px;"><div class="alignment" align="center" style="box-sizing: border-box; line-height: 10px;"><img src="cid:47958504-0F49-4664-95B4-F00AD2EE0CAD" width="204" alt="Photo of Nick Rozenblyum" title="Photo of Nick Rozenblyum" style="border: 0px; height: auto; outline: none; display: block; width: 204px;"></div></td></tr></tbody></table></td><td class="column column-2" width="50%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; border: 0px;"><table class="heading_block block-3" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; text-align: center; width: 640px; padding-top: 25px;"><h1 style="box-sizing: border-box; margin: 0px; padding: 0px; color: rgb(218, 154, 26); direction: ltr; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 38px; line-height: 45.599998px; text-align: left;"><span class="tinyMce-placeholder" style="box-sizing: border-box;">Jinyoung Park</span></h1></td></tr></tbody></table><table class="paragraph_block block-4" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse; word-break: break-word;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 20px;"><div style="box-sizing: border-box; color: rgb(16, 17, 18); direction: ltr; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 16px; letter-spacing: 0px; line-height: 19.200001px;"><p style="box-sizing: border-box; margin: 0px 0px 16px; padding: 0px; word-break: break-word; line-height: inherit;">Visiting Assistant Professor</p><p style="box-sizing: border-box; margin: 0px 0px 16px; padding: 0px; word-break: break-word; line-height: inherit;">Courant Institute of Mathematical Sciences</p><p style="box-sizing: border-box; margin: 0px; padding: 0px; word-break: break-word; line-height: inherit;">New York University</p></div></td></tr></tbody></table><table class="button_block block-5" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 15px; padding-bottom: 5px;"><div class="alignment" align="left" style="box-sizing: border-box;"><a href="https://uchicago.us2.list-manage.com/track/click?u=350fc31a7f826e3b52544f33a&id=85940c441a&e=a52274294a" target="_blank" style="box-sizing: border-box; word-break: keep-all; text-decoration: none; display: inline-block; color: rgb(218, 154, 26); border-radius: 0px; width: auto; border: 1px solid rgb(53, 61, 70); padding-top: 0px; padding-bottom: 0px; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 16px; text-align: center;"><span style="box-sizing: border-box; padding-left: 30px; padding-right: 30px; display: inline-block;"><span dir="ltr" style="box-sizing: border-box; word-break: break-word; line-height: 32px;">Learn More</span></span></a></div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table><table class="row row-3" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="100%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; padding: 5px 40px 10px; vertical-align: top; border: 0px;"><table class="divider_block block-1" width="100%" border="0" cellpadding="10" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word;"><div class="alignment" align="center" style="box-sizing: border-box;"><table border="0" cellpadding="0" cellspacing="0" role="presentation" width="100%" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="divider_inner" style="box-sizing: border-box; word-break: break-word; font-size: 1px; line-height: 1px; border-top-width: 4px; border-top-style: solid; border-top-color: rgb(85, 85, 85);"><span style="box-sizing: border-box;"> </span></td></tr></tbody></table></div></td></tr></tbody></table><table class="heading_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-bottom: 15px; text-align: center; width: 560px;"><h2 style="box-sizing: border-box; margin: 0px; padding: 0px; color: rgb(139, 0, 33); direction: ltr; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 30px; line-height: 36px; text-align: left;">Thresholds</h2></td></tr></tbody></table><table class="text_block block-3" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse; word-break: break-word;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word;"><div style="box-sizing: border-box; font-family: Arial, sans-serif;"><div class="" style="box-sizing: border-box; font-size: 12px; color: rgb(53, 61, 70); line-height: 1.8; font-family: Arial, "Helvetica Neue", Helvetica, sans-serif;"><p style="box-sizing: border-box; margin: 0px; padding: 0px; word-break: break-word; line-height: inherit;"><span style="box-sizing: border-box; font-size: 16px;">For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). In this talk, I will present recent progress on this topic. </span></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; word-break: break-word; line-height: inherit;"> </p><p style="box-sizing: border-box; margin: 0px; padding: 0px; word-break: break-word; line-height: inherit;"><span style="box-sizing: border-box; font-size: 16px;">Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.</span></p><p style="box-sizing: border-box; margin: 0px; padding: 0px; word-break: break-word; line-height: inherit;"> </p></div></div></td></tr></tbody></table><table class="heading_block block-4" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 20px; text-align: center; width: 560px;"><h1 style="box-sizing: border-box; margin: 0px; padding: 0px; color: rgb(218, 154, 26); direction: ltr; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 38px; line-height: 45.599998px; text-align: left;"><span class="tinyMce-placeholder" style="box-sizing: border-box;">Details:</span></h1></td></tr></tbody></table><table class="divider_block block-5" width="100%" border="0" cellpadding="10" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word;"><div class="alignment" align="center" style="box-sizing: border-box;"><table border="0" cellpadding="0" cellspacing="0" role="presentation" width="100%" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="divider_inner" style="box-sizing: border-box; word-break: break-word; font-size: 1px; line-height: 1px; border-top-width: 4px; border-top-style: solid; border-top-color: rgb(85, 85, 85);"><span style="box-sizing: border-box;"> </span></td></tr></tbody></table></div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table><table class="row row-6" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(255, 255, 255); border-radius: 0px; color: rgb(0, 0, 0);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="25%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; border: 0px;"><table class="button_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 5px; padding-bottom: 5px;"><div class="alignment" align="left" style="box-sizing: border-box;"><a href="https://uchicago.us2.list-manage.com/track/click?u=350fc31a7f826e3b52544f33a&id=ab8a64b39c&e=a52274294a" target="_blank" style="box-sizing: border-box; word-break: keep-all; text-decoration: none; display: inline-block; color: rgb(139, 0, 33); border-radius: 0px; width: auto; border: 2px solid rgb(0, 0, 0); padding-top: 0px; padding-bottom: 0px; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 16px; text-align: center;"><span style="box-sizing: border-box; padding-left: 20px; padding-right: 20px; display: inline-block;"><span dir="ltr" style="box-sizing: border-box; word-break: break-word; line-height: 32px;">Add to Google</span></span></a></div></td></tr></tbody></table></td><td class="column column-2" width="25%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; border: 0px;"><table class="button_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 5px; padding-bottom: 5px;"><div class="alignment" align="left" style="box-sizing: border-box;"><a href="https://uchicago.us2.list-manage.com/track/click?u=350fc31a7f826e3b52544f33a&id=a20b86149a&e=a52274294a" target="_blank" style="box-sizing: border-box; word-break: keep-all; text-decoration: none; display: inline-block; color: rgb(139, 0, 33); border-radius: 0px; width: auto; border: 2px solid rgb(0, 0, 0); padding-top: 0px; padding-bottom: 0px; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 16px; text-align: center;"><span style="box-sizing: border-box; padding-left: 20px; padding-right: 20px; display: inline-block;"><span dir="ltr" style="box-sizing: border-box; word-break: break-word; line-height: 32px;">Add to Outlook</span></span></a></div></td></tr></tbody></table></td><td class="column column-3" width="50%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; border: 0px;"><table class="button_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; text-align: center; padding-top: 5px; padding-bottom: 5px;"><div class="alignment" align="center" style="box-sizing: border-box;"><a href="https://uchicago.us2.list-manage.com/track/click?u=350fc31a7f826e3b52544f33a&id=9033bc26c9&e=a52274294a" target="_blank" style="box-sizing: border-box; word-break: keep-all; text-decoration: none; display: inline-block; color: rgb(218, 154, 26); border-radius: 0px; width: auto; border: 2px solid rgb(0, 0, 0); padding-top: 0px; padding-bottom: 0px; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 16px;"><span style="box-sizing: border-box; padding-left: 30px; padding-right: 30px; display: inline-block;"><span dir="ltr" style="box-sizing: border-box; word-break: break-word; line-height: 32px;"><strong style="box-sizing: border-box;">Join Zoom</strong></span></span></a></div></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table><table class="row row-7" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(255, 255, 255); border-radius: 0px; color: rgb(0, 0, 0);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="100%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; vertical-align: top; padding-top: 5px; padding-bottom: 5px; border: 0px;"><div class="spacer_block" style="box-sizing: border-box; height: 20px; line-height: 20px; font-size: 1px;"> </div></td></tr></tbody></table></td></tr></tbody></table><table class="row row-8" align="center" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td style="box-sizing: border-box; word-break: break-word;"><table class="row-content stack" align="center" border="0" cellpadding="0" cellspacing="0" role="presentation" width="680" style="border-collapse: collapse; width: 680px; background-color: rgb(53, 61, 70); border-radius: 0px; color: rgb(0, 0, 0);"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="column column-1" width="50%" style="box-sizing: border-box; word-break: break-word; width: 640px; display: block; padding-left: 60px; padding-right: 40px; vertical-align: top; border: 0px;"><table class="heading_block block-2" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 55px; text-align: center; width: 540px;"><h3 style="box-sizing: border-box; margin: 0px; padding: 0px; text-align: left; color: rgb(255, 255, 255); direction: ltr; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: 400; line-height: 14.4px;"><span class="tinyMce-placeholder" style="box-sizing: border-box;">Department of Mathematics </span></h3></td></tr></tbody></table><table class="heading_block block-3" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 5px; text-align: center; width: 540px;"><h3 style="box-sizing: border-box; margin: 0px; padding: 0px; text-align: left; color: rgb(255, 255, 255); direction: ltr; font-family: Poppins, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: 400; line-height: 14.4px;"><span class="tinyMce-placeholder" style="box-sizing: border-box;"><span dir="ltr" style="box-sizing: border-box; word-break: break-word; font-size: inherit !important; font-family: inherit !important; line-height: inherit !important;">5734 S University Ave</span></span></h3></td></tr></tbody></table><table class="heading_block block-4" width="100%" border="0" cellpadding="0" cellspacing="0" role="presentation" style="border-collapse: collapse;"><tbody style="box-sizing: border-box;"><tr style="box-sizing: border-box;"><td class="pad" style="box-sizing: border-box; word-break: break-word; padding-top: 5px; text-align: center; width: 540px; padding-bottom: 20px;"><h3 style="box-sizing: border-box; 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