BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Some combinatorial applications of guided random processes -  Pete
 r Keevash (Oxford)
DTSTART:20230309T143000Z
DTEND:20230309T153000Z
UID:TALK197353@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:Random greedy algorithms became ubiquitous in Combinatorics af
 ter\nRodl's nibble (semi-random method)\, which was repeatedly refined for
 \nvarious applications\, such as iterative graph colouring algorithms\n(Mo
 lloy-Reed) and lower bounds for the Ramsey number R(3\,t) via the\ntriangl
 e-free process (Bohman-Keevash / Fiz Pontiveros-Griffiths-Morris).\nMore r
 ecently\, when combined with absorption\, they have played a key role\nin 
 many existence and approximate counting results for combinatorial\nstructu
 res\, following a paradigm established by my proofs of the Existence\nof D
 esigns and Wilson's Conjecture on the number of Steiner Triple Systems.\nH
 ere absorption (converting approximate solutions to exact solutions) is\ng
 enerally the most challenging task\, which has spurred the development of\
 nmany new ideas\, including my Randomised Algebraic Construction method\, 
 the\nKuhn-Osthus Iterative Absorption method and Montgomery's Addition\nSt
 ructures (for attacking the Ryser-Brualdi-Stein Conjecture). The design\na
 nd analysis of a suitable guiding mechanism for the random process can\nal
 so come with major challenges\, such as in the recent proof of Erdos'\nCon
 jecture on Steiner Triple Systems of high girth\n(Kwan-Sah-Sawhney-Simkin)
 . This talk will survey some of this background\nand also mention some rec
 ent results on the Queens Problem (Bowtell-Keevash\n/ Luria-Simkin / Simki
 n) and the Existence of Subspace Designs\n(Keevash-Sah-Sawhney). I may als
 o mention recent solutions of the Talagrand\n/ Kahn-Kalai Threshold Conjec
 tures (Frankston-Kahn-Narayanan-Park /\nPark-Pham) and thresholds for Stei
 ner Triple Systems / Latin Squares\n(Keevash / Jain-Pham)\, where the key 
 to my proof is constructing a suitable\nspread measure via a guided random
  process.
LOCATION:MR12
END:VEVENT
END:VCALENDAR