The longer the conference goes, the more time I spend doing research with some of the participants, and I tend to day-dream more in the lecture, so the quality of reporting will inevitably be low. Ben Green completed his mini-course on finite field models in additive combinatorics, with many many applications of the Cauchy-Schwarz inequality. We then had a session of short talks by Peter Sin and Xiang-dong Hou. The former spoke on generalised adjacency matrices of graphs and when two such matrices of the same graph can be similar and be “Smith Normal Form” equivalent. The latter outlined a proof of a conjecture on “monomial” graphs, which has connections to generalised quadrangles (since the conjecture is about a girth 8 bipartite graph). After lunch, Peter Keevash finished off the proof of his fabulous theorem by wrapping up the strategy that he outlined in the first lecture. We then completed the day by a very nice session of short talks by Alice Hui and Sebastian Cioabă. The former gave a very nice result on switching strongly regular graphs arising from geometric configurations in symplectic spaces, and the latter gave a stimulating summary of the speaker’s work on different types of connectivity and expansion properties of distance-regular graphs and graphs coming from association schemes.

# New directions in additive combinatorics: day 4

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Does the conference website provide access to the speakers’ slides (for talks using them)? I would like to see some of them, but cannot find anything.

The conference is still going. The slides will be put up once it is finished.

Some of the PDFs are already up. See: http://www2.ims.nus.edu.sg/Programs/016combin/wk.php