# New directions in additive combinatorics: day 3

Yesterday, we had four 90 minute talks! We began with more of the details of Peter Keevash’s proof, that uses some interesting results on hypergraphs and counting paths. After morning tea, Aart Blokhuis delved into t-fold blocking sets, followed by Simeon’s introduction to the links with coding theory. In the afternoon, we moved to the Department of Mathematics (at NUS) to see a colloquium by Ben Green on “Permutations and Number Theory”; a fabulous talk, one of the best I’ve ever seen him give. Finally, the “young person’s talk” was given by Ameera Chowdhury who spoke on a cool way to view and prove the MDS conjecture for prime fields and in the De Beule – Ball bound case.

In the evening, I spent two hours with Qing Xiang, Tao Feng, and Koji Momihara chatting about some interesting directions and problems we could look at in finite geometry. These guys are very good with Gauss sums and cyclotomic constructions, and so we are looking for more problems of this kind. Watch this space … work is now underway to construct some interesting objects in finite geometry! What was most interesting in our two hour session was the bottomless amount of notes and random pieces of paper that Qing seems to have stashed in his bag. Often I would be at the whiteboard saying something like “and from some work I did ten years ago …” and then Qing would pull out the relevant pages of information from his mystery bag. It is conjectured that he could also find a rabbit in there with some extra effort.