BEGIN:VCALENDAR VERSION:2.0 PRODID:-//talks.cam.ac.uk//v3//EN BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT TZOFFSETFROM:+0000 TZOFFSETTO:+0100 TZNAME:BST DTSTART:19700329T010000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0100 TZOFFSETTO:+0000 TZNAME:GMT DTSTART:19701025T020000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:Combinatorics Seminar SUMMARY:The (non-)concentration of the chromatic number - Oliver Riordan (University of Oxford) DTSTART;TZID=Europe/London:20191031T143000 DTEND;TZID=Europe/London:20191031T153000 UID:TALK131377AThttp://talks.cam.ac.uk URL:http://talks.cam.ac.uk/talk/index/131377 DESCRIPTION:Let $G(n\,1/2)$ be the random graph on $n$ vertice s in which each edge is present with probability $1/2$\, independently of the others. A classical qu estion is: what is the chromatic number $X_n$ of $G(n\,1/2)$\, i.e.\, how many colours do we need to colour all vertices so that adjacent vertices rec eive different colours? Of course\, $X_n$ is a ran dom variable: one main thrust of past work is prov ing better and better upper and lower bounds that hold with high probability (probability tending to 1)\, starting with the asymptotic formula proved by Bollob\\'as in the 1980s. A separate direction asked: even if we can't pin down the value of $X_n$ precisely\, can we bound how much it varies? A n owadays standard argument gives an upper bound of $O(n{1/2})$. Surprisingly\, until very recently \\emph{no} meaningful lower bounds were\n known\, although this natural question was raised by Bollob\\'as many years ago.\nRecently\, Annika Heckel made a breakthrough\, establishing a lower bound of\n$n{1/4-o(1)}$. She and I have now extended this to $n{1/2-o(1)}$\, a lmost\nmatching the upper bound.\n LOCATION:MR12 CONTACT:Andrew Thomason END:VEVENT END:VCALENDAR