# Timeline

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Date General Uniformity Ergodic theory Small n
Jan 26 Nielsen: Doing science online
Jan 27 Gowers: Is massively collaborative mathematics possible?
Jan 28 Kalai: Mathematics, science, and blogs
Jan 30 Gowers: Background to a polymath project
Feb 1 Gowers: Questions of procedure

Gowers: A combinatorial approach to DHJ (1-199)

Gowers: Why this particular problem?

Trevisan: A people's history of mathematics

Solymosi.2: IP-corners problem proposed

Tao.4: Analytic proof of Sperner? Regularisation needed?

Hoang.4: Naive Varnavides for DHJ fails

Gowers.1: Carlson-Simpson theorem useful?

Tao.4: Stationarity useful?

Feb 2 Gowers.9: Reweighting vertices needed for Varnavides?

Tao.17: Should use $O(\sqrt{n})$ wildcards

Tao.18: Use rich slices?

Gowers.19: Collect obstructions to uniformity!

Kalai.29: Fourier-analytic proof of Sperner?

O'Donnell.32: Use uniform distribution on slices

Gowers.38: Can't fix # wildcards in advance

Tao.39: Can take # wildcards to be O(1)

Bukh.44: Obstructions to Kruskal-Katona?

Tao.8: $c_0=1$, $c_1=2$, $c_2=6$, $3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n)$

Kalai.15: $c_n \gg 3^n/\sqrt{n}$

Tao.39: $c_n \geq 3^{n-O(\sqrt{\log n})}$

Tao.40: $c_3=18$

Elsholtz.43: Moser(3)?

Feb 3 Nielsen: The polymath project Gowers.64: Use local equal-slices measure?

Gowers.70: Collection of obstructions to uniformity begins

Tao.86: Use Szemeredi's proof of Roth?

Jakobsen.59: $c_4 \geq 49$

Tao.78: $c_4 \leq 54$

Neylon.83: $52 \leq c_4 \leq 54$, $140 \leq c_5 \leq 162$

Feb 4 Gowers: Quick question Tao.100: Use density incrementation?

Tao.118: Szemeredi's proof of Roth looks inapplicable

Jakobsen.90: $c_4=52$
Feb 5 Tao.130: DHJ(2.5)?

Bukh.132, O'Donnell.133, Solymosi.135: Proof of DHJ(2.5)

Tao.148: Obstructions to uniformity summarised

Tao: Upper and lower bounds for DHJ (200-299)
Feb 6 Solymosi.155 Pair removal for Kneser graphs

Gowers: The triangle removal approach (300-399)

Neylon.201 Greedy algorithm

Tao.206 Use $D_n$

Feb 7 Gowers.335 DHJ(j,k) introduced Jakobsen.207 $c_5 \geq 150$, $c_6 \geq 450$

Peake.217 $c_7 \geq 1308$, $c_8 \geq 3780$

Peake.218 Lower bounds up to $c_{15}$

Feb 8 Gowers: Quasirandomness and obstructions to uniformity (400-499) Peake.219 $c_{99} \geq 3^{98}$

Tao.225 Spreadsheet set up

Feb 9 Nielsen: Update on the polymath project C D Kalai.233 Higher k?
Feb 10 B C D Peake.241 $c_5 \leq 155$; xyz notation

Peake.243 $c_5 \leq 154$

Feb 11 B C Tao: A reading seminar on DHJ (600-699) Tao.249: $\overline{c}^\mu_0 = 1$, $\overline{c}^\mu_1 = 2$, $\overline{c}^\mu_2 = 4$

Dyer.254 $\overline{c}^\mu_3 = 6$

Feb 12 Wiki set up C D Jakobsen.257 $\overline{c}^\mu_4 = 9$

Jakobsen.258 $\overline{c}^\mu_5 = 12$

Peake.262 Extremisers for $c_4$

Feb 13 B Gowers: Possible proof strategies (500-599) Tao: Bounds for first few DHJ numbers (700-799)
Feb 14 B C D Sauvaget: A proof that $c_5=154$?
Feb 15 B C D Sauvaget: A new strategy for computing $c_n$
Feb 16 B C D
Feb 17 B C D E
Feb 18 B C D E
Feb 19 B C D E
Feb 20 B C D E
Feb 21 Gowers: To thread or not to thread C D E
Feb 22 B C D E
Feb 23 B Gowers: Brief review of polymath1 (800-849) D E
Feb 24 B C D E
Feb 25 B C D E
Feb 26 B C D E
Feb 27 B C D E
Feb 28 B C D E
Mar 1 B C D E
Mar 2 B Gowers: DHJ 851-899 D E