I am very happy about today’s result by Sam Mattheus and Jacques Verstraete proving an almost tight bound on the off-diagonal Ramsey number r(4, t). This beats the bound by Bohman and Keevash using the random process. See Anurag’s post above for details. Just yesterday I gave a plenary talk at CanaDAM about off-diagonal Ramsey numbers and my main point was that finite geometry will be able to help!
(Also, I and others had research projects criticized with the argument that the random process should be tight. There is no evidence for this. To the contrary, this adds to the evidence that one can beat the random process using algebra.)
Ratio Bound – A Combinatorics Blog 