{"657188":{"#nid":"657188","#data":{"type":"news","title":"External News: Incoming Faculty Jinyoung Park Proves the Kahn-Kalai Expectation Threshold Conjecture","body":[{"value":"\u003Cp\u003EJinyoung Park, an incoming faculty member for Fall 2023, together with her coauthor Huy Tuan Pham have proven the Expectation Threshold Conjecture of Kahn and Kalai from 2006.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003EFor the full article please \u003C\/em\u003E\u003Ca href=\u0022https:\/\/gilkalai.wordpress.com\/2022\/04\/02\/amazing-jinyoung-park-and-huy-tuan-pham-settled-the-expectation-threshold-conjecture\/?fbclid=IwAR3Wt4_73iRwFAyMx6zL7MCnMYfYheZJWk8318r766OR7VDu-d_jR3FayNY\u0022 style=\u0022font-style: italic;\u0022\u003Eclick here\u003C\/a\u003E\u003Cem\u003E, an\u0026nbsp;excerpt is below.\u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cblockquote\u003E\r\n\u003Cp\u003EThe 2006\u0026nbsp;\u003Ca href=\u0022https:\/\/arxiv.org\/abs\/math\/0603218\u0022\u003Eexpectation threshold conjecture\u003C\/a\u003E\u0026nbsp;gives a justification for a naive way to estimate the threshold probability of a random graph property. Suppose that you are asked about the critical probability for a random graph in G(n,p) for having a perfect matching (or a Hamiltonian cycle). You compute the expected number of perfect matchings and realize that when p is C\/n this expected number equals 1\/2. (For Hamiltonian cycles it will be C\u0026rsquo;\/n.) Of course, if the expectation is one half, the probability for a perfect matching can still be very low; indeed, in this case, an isolated vertex is quite likely but when there is no isolated vertices the expected number of perfect matchings is rather large. Our 2006 conjecture boldly asserts that the gap between the value given by such a naive computation and the true threshold value is at most logarithmic in the number of vertices. Jeff and I tried hard to find a counterexample but instead we managed to find more general and stronger forms of the conjecture that we could not disprove.\u003C\/p\u003E\r\n\u003C\/blockquote\u003E\r\n\r\n\u003Ch3\u003EJinyoung Park\u003C\/h3\u003E\r\n\r\n\u003Cp\u003EJinyoung Park is a Szeg\u0026ouml; Assistant Professor at \u003Ca href=\u0022https:\/\/www.google.com\/url?q=https%3A%2F%2Fmathematics.stanford.edu%2F\u0026amp;sa=D\u0026amp;sntz=1\u0026amp;usg=AOvVaw35OJgxIfPZM2Gdh5o11An-\u0022 target=\u0022_blank\u0022\u003EStanford University\u003C\/a\u003E, working with her mentor\u0026nbsp;\u003Ca href=\u0022https:\/\/www.google.com\/url?q=https%3A%2F%2Fstanford.edu%2F~jacobfox%2F\u0026amp;sa=D\u0026amp;sntz=1\u0026amp;usg=AOvVaw12HQPG0s7RYk_ZNoT-td-w\u0022 target=\u0022_blank\u0022\u003EJacob Fox\u003C\/a\u003E. Previously a postdoctoral member of \u003Ca href=\u0022https:\/\/www.google.com\/url?q=https%3A%2F%2Fwww.ias.edu%2F\u0026amp;sa=D\u0026amp;sntz=1\u0026amp;usg=AOvVaw0mYVBHDid-oCM0SF8D4sOi\u0022 target=\u0022_blank\u0022\u003EInstitute for Advanced Study\u003C\/a\u003E (\u003Ca href=\u0022https:\/\/www.google.com\/url?q=https%3A%2F%2Fwww.math.ias.edu%2Fcsdm\u0026amp;sa=D\u0026amp;sntz=1\u0026amp;usg=AOvVaw2phk_Cu-UKlEqxt1Tuv6R9\u0022 target=\u0022_blank\u0022\u003ECSDM\u003C\/a\u003E program, led by \u003Ca href=\u0022https:\/\/www.google.com\/url?q=https%3A%2F%2Fwww.math.ias.edu%2Favi%2F\u0026amp;sa=D\u0026amp;sntz=1\u0026amp;usg=AOvVaw11yNNfwUk26spS1P7wwsaZ\u0022 target=\u0022_blank\u0022\u003EAvi Wigderson\u003C\/a\u003E), Dr. Park will be joining SoM as an incoming faculty member in 2023.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Park\u0026#39;s\u0026nbsp;research interests include\u003C\/p\u003E\r\n\r\n\u003Cul\u003E\r\n\t\u003Cli\u003E\r\n\t\u003Cp\u003Eextremal and probabilistic combinatorics,\u003C\/p\u003E\r\n\t\u003C\/li\u003E\r\n\t\u003Cli\u003E\r\n\t\u003Cp\u003Easymptotic enumeration, and\u003C\/p\u003E\r\n\t\u003C\/li\u003E\r\n\t\u003Cli\u003E\r\n\t\u003Cp\u003Egraph theory.\u003C\/p\u003E\r\n\t\u003C\/li\u003E\r\n\u003C\/ul\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003EJinyoung Park, an incoming faculty member for Fall 2023, has proven the the Kahn-Kalai\u0026nbsp;Expectation Threshold Conjecture with coauthor Huy Tuan Pham.\u003C\/p\u003E\r\n","format":"limited_html"}],"field_summary_sentence":[{"value":"Jinyoung Park, an incoming faculty member for Fall 2023, has proven the Kahn-Kalai Expectation Threshold Conjecture with coauthor Huy Tuan Pham."}],"uid":"34518","created_gmt":"2022-04-12 14:31:38","changed_gmt":"2022-04-12 14:38:01","author":"sbarone7","boilerplate_text":"","field_publication":"","field_article_url":"","dateline":{"date":"2022-04-12T00:00:00-04:00","iso_date":"2022-04-12T00:00:00-04:00","tz":"America\/New_York"},"extras":[],"hg_media":{"657187":{"id":"657187","type":"image","title":"Jinyoung Park","body":null,"created":"1649773839","gmt_created":"2022-04-12 14:30:39","changed":"1649773839","gmt_changed":"2022-04-12 14:30:39","alt":"","file":{"fid":"249079","name":"headshot_jinyoung_park.jpeg","image_path":"\/sites\/default\/files\/images\/headshot_jinyoung_park.jpeg","image_full_path":"http:\/\/www.tlwarc.hg.gatech.edu\/\/sites\/default\/files\/images\/headshot_jinyoung_park.jpeg","mime":"image\/jpeg","size":158638,"path_740":"http:\/\/www.tlwarc.hg.gatech.edu\/sites\/default\/files\/styles\/740xx_scale\/public\/images\/headshot_jinyoung_park.jpeg?itok=Pb7qt1Qq"}}},"media_ids":["657187"],"related_links":[{"url":"https:\/\/gilkalai.wordpress.com\/2022\/04\/02\/amazing-jinyoung-park-and-huy-tuan-pham-settled-the-expectation-threshold-conjecture\/?fbclid=IwAR3Wt4_73iRwFAyMx6zL7MCnMYfYheZJWk8318r766OR7VDu-d_jR3FayNY","title":"External News: Jinyoung Park"},{"url":"https:\/\/sites.google.com\/view\/jinyoungpark","title":"Jinyoung Park\u0027s Homepage"}],"groups":[{"id":"1279","name":"School of Mathematics"}],"categories":[],"keywords":[{"id":"173647","name":"_for_math_site_"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003E\u003Ca href=\u0022mailto:comm@math.gatech.edu\u0022\u003ESal Barone\u003C\/a\u003E\u003C\/p\u003E\r\n","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}