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New page: {| border=1 |- !Date!!General!! Uniformity !! Ergodic theory !! Small n |- | Jan 26 | Nielsen: [http://michaelnielsen.org/blog/?p=545 Doing science online] |- | Jan 27 | Gowers: [http://go...
 
Correcting spelling of my name
 
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A partial list of events occurring during the polymath1 project to date.
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Trevisan: [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics]
Trevisan: [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics]
Blank: [http://hyperpapeterie.wordpress.com/2009/02/01/massively-collaborative-mathematics/ Massively collaborative mathematics]
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Solymosi.2]: IP-corners problem proposed
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Solymosi.2]: IP-corners problem proposed


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| Feb 2
| Feb 2
|  
| Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/02/on-new-modes-of-mathematical-collaboration/ On new modes of mathematical collaboration]
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides?
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides?


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| Feb 5
| Feb 5
|
| Tea time: [http://virtualteatime.blogspot.com/2009/02/introspection.html Introspection]
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1853 Tao.130]: DHJ(2.5)?
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1853 Tao.130]: DHJ(2.5)?


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| Feb 6
| Feb 6
|  
|  
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1895 Solymosi.155] Pair removal for Kneser graphs
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1895 Solymosi.155]: Pair removal for Kneser graphs


Gowers: [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle removal approach] (300-399)
Gowers: [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle removal approach] (300-399)
|  
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35495 Neylon.201] Greedy algorithm
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35495 Neylon.201]: Greedy algorithm


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35528 Tao.206] Use <math>D_n</math>
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35528 Tao.206]: Use <math>D_n</math>
|-
|-
| Feb 7
| Feb 7
|  
|  
| [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-1945 Gowers.335] DHJ(j,k) introduced
| [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-1945 Gowers.335]: DHJ(j,k) introduced
|  
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35537 Jakobsen.207] <math>c_5 \geq 150</math>, <math>c_6 \geq 450</math>
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35537 Jakobsen.207]: <math>c_5 \geq 150</math>, <math>c_6 \geq 450</math>


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35585 Peake.217] <math>c_7 \geq 1308</math>, <math>c_8 \geq 3780</math>
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35585 Peake.217]: <math>c_7 \geq 1308</math>, <math>c_8 \geq 3780</math>


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35593 Peake.218] Lower bounds up to <math>c_{15}</math>
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35593 Peake.218]: Lower bounds up to <math>c_{15}</math>
|-
|-
| Feb 8
| Feb 8
|  
|  
| Gowers: [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/ Quasirandomness and obstructions to uniformity] (400-499)
| Gowers: [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/ Quasirandomness and obstructions to uniformity]: (400-499)
 
Ajtai-Szemeredi approach proposed
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2001 Tao.402]: Standard obstruction to uniformity?
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2002 Gowers.403]: Complexity 1 sets are more fundamental obstructions
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2019 Gowers.411]: Are global complexity 1 sets the only obstructions?
 
|  
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35597 Peake.219] <math>c_{99} \geq 3^{98}</math>
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35597 Peake.219]: <math>c_{99} \geq 3^{98}</math>


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35608 Tao.225] Spreadsheet set up
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35608 Tao.225]: Spreadsheet set up
|-
|-
| Feb 9
| Feb 9
| Nielsen: [http://michaelnielsen.org/blog/?p=555 Update on the polymath project]
| Nielsen: [http://michaelnielsen.org/blog/?p=555 Update on the polymath project]
| C
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2029 Bukh.412]: Negative answer to Gowers' question
| D
 
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35631 Kalai.233] Higher k?
[http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-2047 Gowers.365]: Equal slices measure introduced
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2056 Tao.419]:  Use low-influence instead of complexity 1?
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2057 Gowers.420]: Need DHJ(0,2)
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2072 Tao.431]: Use local obstructions rather than global obstructions?
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35631 Kalai.233]: Higher k?
|-
|-
| Feb 10
| Feb 10
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.439]: Use hypergraph regularity?
| D
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35662 Peake.241] <math>c_4 \leq 155</math>; xyz notation
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35662 Peake.241]: <math>c_5 \leq 155</math>; xyz notation


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35672 Peake.243] <math>c_4 \leq 154</math>
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35672 Peake.243]: <math>c_5 \leq 154</math>
|-
|-
| Feb 11
| Feb 11
| B
| le Bruyn: [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another Math 2.0 proposal]
| C
 
| Tao: [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on DHJ] (600-699)
[http://docs.google.com/Doc?id=dhs78pth_15dfw8jhz4 Tao.470]: Proto-wiki created
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.451]: 01-insensitive case OK
 
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2114 Kalai.455]: Hyper-optimistic conjecture
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2120 Tao.460]: Connections with ergodic approach
 
Tao: [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on DHJ] (600-699)
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35691 Tao.249]: <math>\overline{c}^\mu_0 = 1</math>, <math>\overline{c}^\mu_1 = 2</math>, <math>\overline{c}^\mu_2 = 4</math>
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35691 Tao.249]: <math>\overline{c}^\mu_0 = 1</math>, <math>\overline{c}^\mu_1 = 2</math>, <math>\overline{c}^\mu_2 = 4</math>


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35709 Dyer.254] <math>\overline{c}^\mu_3 = 6</math>
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35709 Dyer.254]: <math>\overline{c}^\mu_3 = 6</math>
|-
|-
| Feb 12
| Feb 12
| [http://michaelnielsen.org/polymath1/index.php?title=Main_Page Wiki set up]
| [http://michaelnielsen.org/polymath1/index.php?title=Main_Page Wiki set up]
| C
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2143 O'Donnell.476]: Fourier-analytic Sperner computations
| D
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35728 Jakobsen.257] <math>\overline{c}^\mu_4 = 9</math>


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35733 Jakobsen.258] <math>\overline{c}^\mu_5 = 12</math>
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2149 McCutcheon.480]: Strong Roth theorem proposed


[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35749 Peake.262] Extremisers for <math>c_4</math>
|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35728 Jakobsen.257]: <math>\overline{c}^\mu_4 = 9</math>
 
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35733 Jakobsen.258]: <math>\overline{c}^\mu_5 = 12</math>
 
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35749 Peake.262]: Extremisers for <math>c_4</math>
|-
|-
| Feb 13
| Feb 13
| B
|  
| Gowers: [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (500-599)
| Gowers: [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (500-599)
|
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2179 McCutcheon.505]: IP uniformity norms?
 
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35801 Tao.614]: Carlson-Simpson not needed for stationarity
| Tao: [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for first few DHJ numbers] (700-799)
| Tao: [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for first few DHJ numbers] (700-799)
|-
|-
| Feb 14
| Feb 14
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2183 Gowers.496]: Equal slices implies uniform
| D
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2185 McCutcheon.508]: Ergodic proof strategy
 
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35821 Tao.618]: More randomness needed to invert maps
 
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35837 O'Donnell.622]: <math>[3]^n</math> should already provide enough randomness
 
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2188 Tao.510]: Finitary analogue of stationarity
 
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/14/a-proof-that-c_5154/ A proof that <math>c_5=154</math>?]
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/14/a-proof-that-c_5154/ A proof that <math>c_5=154</math>?]
|-
|-
| Feb 15
| Feb 15
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2195 Tao.498]: Uniform implies equal slices
| D
 
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2196 Tao.514]: DHJ(2.6) proposed
 
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2206 McCutcheon.518]: Ramsey proof of DHJ(2.6)
|  
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/15/a-new-strategy-for-computing-c_n/ A new strategy for computing <math>c_n</math>]
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/15/a-new-strategy-for-computing-c_n/ A new strategy for computing <math>c_n</math>]
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35853 Markström.706]: Integer program, <math>c_5=150</math>
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35865 Cantwell.708]: <math>c_6=450</math>
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35877 Tao.715]: Genetic algorithm?
|-
|-
| Feb 16
| Feb 16
| B
| C
| D
|  
|  
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2214 Tao.524]: Simplification of proof
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2222 O'Donnell 529]: Ramsey-free proof of DHJ(2.6)?
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2228 McCutcheon.533]: Ramsey theory incompatible with symmetry
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35921 Tao.626]: Ramsey theorems summarised
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35926 Peake.730]: <math>c_5</math> extremisers
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35927 Tao.731]: Human proof that <math>c_5 \leq 152</math>; <math>c_7 \leq 1348</math>
|-
|-
| Feb 17
| Feb 17
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2234 Tao.536]: Fourier-analytic proof of DHJ(2.6)
| D
 
| E
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2242 McCutcheon.541]: "Cave-man" proof of DHJ(2.6)
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35945 Chua.736]: <math>c'_5 \geq 124</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35951 Peake.738]: Connection between Moser(3) and sphere packing
 
|-
|-
| Feb 18
| Feb 18
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2255 Gowers.544]: Corners(1,3)?
| D
 
| E
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2260 Gowers.545]: Fourier computations on equal-slices measure begin
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35963 Markström.739]: <math>c_6</math> extremiser unique
|-
|-
| Feb 19
| Feb 19
| B
|  
| C
|  
| D
|  
| E
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36011 Markström.742]: 43-point Moser sets in <math>[3]^4</math> listed
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36017 Peake.743]: 43-point sets analysed
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36018 Cantwell.744]: <math>c'_5 \leq 128</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36024 Tao.745]: 50+ point line-free sets in <math>[3]^4</math> listed
 
|-
|-
| Feb 20
| Feb 20
| B
| Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/20/a-quick-review-of-the-polymath-project/ A quick review of the polymath project]
| C
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2296 Solymosi.563]: Moser(6) implies DHJ(3)
| D
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630]: IP convergence lemma
| E
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36031 Markström.747]: 42-point Moser sets listed
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36045 Peake.751]: Human proof of <math>c_5 \leq 151</math>
 
|-
|-
| Feb 21
| Feb 21
| Gowers: [http://gowers.wordpress.com/2009/02/21/to-thread-or-not-to-thread/ To thread or not to thread]
| Gowers: [http://gowers.wordpress.com/2009/02/21/to-thread-or-not-to-thread/ To thread or not to thread]
| C
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2327 Gowers.580]: Extreme localisation + density increment = DHJ(3)?
| D
 
| E
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2329 Gowers.581]: Multidimensional Sperner
|-
 
| Feb 22
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2331 Gowers.582]: Use Ajtai-Szemeredi argument to get density increment?
| B
 
| C
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36084 Tao.631]: Informal combinatorial translation of ergodic DHJ(2)
| D
 
| E
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2321 Tao.578]: Finitary ergodic proof of DHJ(2) proposed
 
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36085 Tao.632]: Special cases of DHJ(3) translated
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36051 Peake.752]: Human proof of <math>c_5=150</math>, <math>c_6=450</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36059 Tao.753]: Sequences submitted to OEIS
 
|-
|-
| Feb 23
| Feb 23
| B
|  
| Gowers: [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (800-849)
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2356 McCutcheon.593]: DHJ(2.7)
| D
 
| E
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2370 O'Donnell.596]: Fourier-analytic proof of DHJ(2)
 
Gowers: [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (800-849)
 
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2372 O'Donnell.800]: Fourier-analytic + density increment proof of DHJ(2)
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36112 Markström.463]: 42-point Moser sets analysed
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36115 Tao.464]: <math>c'_5 \leq 127</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36126 Chua.766]: 3D Moser sets with 222 have <math> \leq 13</math> points
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36127 Tao.767]: 4D Moser sets with 2222 have <math> \leq 39</math> points
|-
|-
| Feb 24
| Feb 24
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2400 Tao.809.2]: Low-influence implies Sperner-positivity
| D
 
| E
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2404 Gowers.812]: Fourier vs physical positivity
 
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2408 O'Donnell.814]: <math>\ell_1</math>, <math>\ell_2</math> equivalence
|  
|  
|-
|-
| Feb 25
| Feb 25
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2431 Gowers.820]: Density increment on complexity 1 set
| D
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2427 Tao.818]: Finitary ergodic sketch of DHJ(3)
| E
 
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2435 O'Donnell.821]: Simplified Fourier proof of DHJ(2) structure theorem
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36157 Cantwell.769]: 5D Moser sets with 2222* have <math> \leq 124</math> points
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36165 Peake.771]: Exotic 43-point Moser sets described
|-
|-
| Feb 26
| Feb 26
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2443 Gowers.824]: Complexity 1 + Ajtai-Szemeredi DHJ(3) sketch
| D
|  
| E
|  
|-
|-
| Feb 27
| Feb 27
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2447 Tao.826]: Non-Fourier proof of DHJ(2) structure theorem
| D
 
| E
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2453 Gowers.828]: Does correlation with 1-set imply density increment?
 
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2458 Tao.828.4]: Energy increment proof for Gowers Q?
 
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2469 McCutcheon.832.2]: Use dense fibres to answer Gowers Q?
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36188 Elsholtz.775]: Human proof of 2222* result
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36195 Cantwell.776]: <math>c'_5 \leq 126</math>
|-
|-
| Feb 28
| Feb 28
| B
|  
| C
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2476 Tao.834]: Use pullbacks for Gowers Q?
| D
 
| E
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2478 Gowers.835]: Pullbacks don't work
 
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2496 O'Donnell 839]: Increment-free Fourier proof of DHJ(2)
 
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2490 Tao.837.2]: Dense fibres argument for Gowers Q
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36216 Markström.779]: 41-point Moser sets listed
|-
|-
| Mar 1
| Mar 1
| B
|  
| C
|  
| D
|  
| E
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36246 Cantwell.782], [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36250 Peake.784]: <math>c'_5 \leq 125</math>
|-
|-
| Mar 2
| Mar 2
| B
|  
| Gowers: [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ 851-899]
| Gowers: [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ 851-899]
| D
 
| E
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2525 Tao.853] Mass increment; connection with Hahn decomposition
 
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2530 Gowers.854] Higher-D Ajtai-Szemeredi?
 
|
|
|-
| Mar 3
|
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2555 McCutcheon.864] Caution: 12-sets not sigma-algebra!
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36277 Dyer.786] <math> \overline{c}^\mu_6 < 18</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36287 Cantwell.787] 125-sets have at most 41 points in middle slices
|-
| Mar 4
|
|
|
|[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36298 Markstrom.788]: <math> c^\mu_n = 4,6,9,12</math> for <math>n=2,3,4,5</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36303 Marc.791]: <math>\overline{c}^\mu_{10} \geq 29</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36310 Tao.793]: "score" introduced
 
Tao: [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers DHJ3 (900-999) Density Hales-Jewett type numbers]
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36331 Tao.901]: 125-sets have D=0
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36332 Dyer.902]: <math>\overline{c}^\mu_6 < 17</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36333 Carr.903]: Genetic algorithm implemented
|-
| Mar 5
|
|
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36343 Peake.904] Scores for 6D Moser?
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36349 Tao.908] Find Pareto-optimal and extremal statistics?
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36350 Dyer.909] Wildcard variants of Moser
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36360 Cantwell.912] 125-sets have at most 40 points in middle slices
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36362 Cantwell.913] 125-sets have D=0 (alternate proof)
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36379 Peake.914] Pareto-optimal 3D statistics
|-
| Mar 6
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2595 Gowers.873] 12-set density increment difficulty identified
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36399 Dyer.917] <math>\overline{c}^\mu_7 \leq 22</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36401 Cantwell.920] <math>c'_6 \leq 373</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36404 Cantwell.921] 125-sets have C=78 or 79
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36406 Markstrom.923] <math>\overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40</math> for <math>n=3,\ldots,12</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36417 Guest.930] GA without crossover?
|-
| Mar 7
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2609 Solymosi.880] Shelah-type flip-flop spaces?
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36421 Peake.931] 3D extremals and inequalities
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36431 Cantwell.932] 125-sets have a middle slice of at most 39 points
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36432 Cantwell.933] 125-sets have A=6,7,8
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36433 Cantwell.934] If C=78 then A=7,8
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36436 Tao.935] 125-sets have stats (6,40,79,0,0,0), (7,40,78,0,0) or (8,39,78,0,0)
 
|-
| Mar 8
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2613 Gowers.881] Iterative partitioning of 12-sets?
 
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2622 Gowers.882] New proof of Ajtai-Szemeredi
 
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2626 O'Donnell.884] Multidimensional Sperner written up
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36463 Peake.939] <math>c'_6 \leq 365</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36465 Carr.940] <math>c'_6 \geq 353; c'_7 \geq 978</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36469 Tao.941] Seeding GA?
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36475 Cantwell.942] (6,40,79,0,0) eliminated
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36481 Tao.943] Linear programming proof of <math>c'_4 =43</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36487 Tao.944] <math>c'_6 \leq 364</math>
|-
| Mar 9
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2633 Gowers.885] Sketch of DHJ(3)
 
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2636 Gowers.886] DHJ(4)?
 
[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2666 Gowers.897] Writing of DHJ(k) begins
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2656 Austin.894] New ergodic proof of DHJ(k)
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36508 Cantwell.945] (7,40,78,0,0) eliminated
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36515 Cantwell.949] (8,39,87,0,0) eliminated: <math>c'_5 = 124</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36519 Tao.950] <math>\overline{c}^\mu_n</math> submitted to OEIS
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36528 Carr.954] <math>c'_7 \geq 988</math>
|-
| Mar 10
| Gowers: [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics]
 
OU Math club: [http://oumathclub.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)]
| Gowers: [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)] (1000-1049)
 
[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2700 Gowers.1005.1] Tower-type bounds
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2689 Tao.1003] 1-sets, 2-sets locally independent
|
|-
| Mar 11
| Kalai: [http://gilkalai.wordpress.com/2009/03/11/polymath1-probable-success/ Polymath1: probable success]
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2713 Gowers.1007] Correlation component of DHJ(k) proof complete
 
[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2733 Solymosi.1011] Shelah-type argument?
 
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36575 Markstrom.961] Partial confirmation of HOC for n=6,7
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36577 Elsholtz.962] Analysis of GA solutions
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36599 Tao.969] Integer programming for Behrend sphere statistics
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36600 Tao.970] <math>c'_7 \leq 1086</math>
|-
| Mar 12
|
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2805 O'Donnell.1021] DHJ(k) => Varnavides completed
 
[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2799 Gowers.1020] No apparent obstacles to proving DHJ(k)
 
[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2826 O'Donnell.1025] Work exclusively with equal (non-degenerate) slices measure?
 
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2825 Tao.1024] Informal combinatorial translation of Austin's proof
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36609 Markstrom.972], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36614 Dyer.973], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36617 Tao.974], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36625 Markstrom.977]: Integer programming problem discovered, isolated, fixed
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36617 Tao.974]: <math>c'_6 \leq 361</math>, <math>c'_7 \leq 1078</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36624 Cantwell.976]: Partial recovery of 4D stats by hand
|-
| Mar 13
| Nielsen: [http://michaelnielsen.org/blog/?p=579 Biweekly links for 03/13/2009]
 
Galdino: [http://prafalardecoisas.wordpress.com/2009/03/13/links-semanais/ Links seminais]
 
Flaxman: [http://healthyalgorithms.wordpress.com/2009/03/13/gowers-polymath-experiment-problem-probably-solved/ Gowers' polymath experiment: problem probably solved]
|
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36652 Elsholtz.980]: Use e=1, f=1, etc. refinements
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36655 Peake.982]: xxyyzz inequalities
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36657 O'Bryant.984], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36680 O'Bryant.993]: <math>c_n \gg 3^{n - 4\sqrt{\log 2}\sqrt{\log n}+\frac 12 \log \log n}</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36659 Cantwell.985]: Human proof of <math>c^\mu_3=6</math> begins
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36666 Peake.989]: xxyyz inequalities
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36667 Tao.990]: <math>c'_7 \leq 1071</math>
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36672 Peake.991]: xxxyz, xxxxyz, xxxyyz inequalities
 
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36694 Seva.994]: Kakeya in [3]^n?
 
|-
| Mar 14
| Hariss: [http://maxwelldemon.wordpress.com/2009/03/14/polymath/ Polymath]
|
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2871 Tao.1035] Ramsey-free translation of Austin's proof
| Tao: [http://terrytao.wordpress.com/2009/03/14/dhj3-1100-1199-density-hales-jewett-type-numbers/ DHJ(3) 1100-1199]
 
|-
| Mar 15
| Neylon: [http://blog.openwetware.org/scienceintheopen/2009/03/15/there-are-crowds-and-then-there-are-crowds/ There are crowds, and then there are crowds...]
|
|
|
 
|-
| Mar 16
|  
| Gowers: [http://gowers.wordpress.com/2009/03/16/dhj3-and-related-results-1050-1099/ DHJ(3) and related results: 1050-1099]
|
|
 
|-
| Mar 18
| Polymath hits front page of Slashdot with [http://science.slashdot.org/article.pl?sid=09/03/18/194228  this article]
 
Nielsen: [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration]
|
|
|
 
|-
| Mar 20
| Nielsen: [http://michaelnielsen.org/blog/?p=584 The Polymath project: scope of participation]
|
|
|
 
|-
| Mar 21
| Gans: [http://economics.com.au/?p=3000 Something interesting is going on in Maths]
|
|
|
 
|-
| Mar 24
| Gowers: [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/#comments Can Polymath be scaled up?]
 
Vipulnaik: [http://whatisresearch.wordpress.com/2009/03/24/concluding-notes-on-the-polymath-project-and-a-challenge/ Concluding notes on the polymath project - and a challenge]
|
|
|
 
 
|-
| Mar 25
| Nielsen: [http://michaelnielsen.org/blog/?p=588 On scaling up the polymath project]
 
Dyer: [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the Polymath project]
|
|
|
 


|}
|}

Latest revision as of 15:47, 5 April 2009

A partial list of events occurring during the polymath1 project to date.

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

Nielsen: Is massively collaborative mathematics possible?

Feb 1 Gowers: Questions of procedure

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

Gowers: Why this particular problem?

Tao: A massively collaborative mathematical project

Trevisan: A people's history of mathematics

Blank: Massively collaborative 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 Vipulnaik: On new modes of mathematical collaboration Gowers.9: Reweighting vertices needed for Varnavides?

Tao.17: Should use [math]\displaystyle{ O(\sqrt{n}) }[/math] 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: [math]\displaystyle{ c_0=1 }[/math], [math]\displaystyle{ c_1=2 }[/math], [math]\displaystyle{ c_2=6 }[/math], [math]\displaystyle{ 3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n) }[/math]

Kalai.15: [math]\displaystyle{ c_n \gg 3^n/\sqrt{n} }[/math]

Tao.39: [math]\displaystyle{ c_n \geq 3^{n-O(\sqrt{\log n})} }[/math]

Tao.40: [math]\displaystyle{ c_3=18 }[/math]

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: [math]\displaystyle{ c_4 \geq 49 }[/math]

Tao.78: [math]\displaystyle{ c_4 \leq 54 }[/math]

Neylon.83: [math]\displaystyle{ 52 \leq c_4 \leq 54 }[/math], [math]\displaystyle{ 140 \leq c_5 \leq 162 }[/math]

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

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

Jakobsen.90: [math]\displaystyle{ c_4=52 }[/math]
Feb 5 Tea time: Introspection 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 [math]\displaystyle{ D_n }[/math]

Feb 7 Gowers.335: DHJ(j,k) introduced Jakobsen.207: [math]\displaystyle{ c_5 \geq 150 }[/math], [math]\displaystyle{ c_6 \geq 450 }[/math]

Peake.217: [math]\displaystyle{ c_7 \geq 1308 }[/math], [math]\displaystyle{ c_8 \geq 3780 }[/math]

Peake.218: Lower bounds up to [math]\displaystyle{ c_{15} }[/math]

Feb 8 Gowers: Quasirandomness and obstructions to uniformity: (400-499)

Ajtai-Szemeredi approach proposed

Tao.402: Standard obstruction to uniformity?

Gowers.403: Complexity 1 sets are more fundamental obstructions

Gowers.411: Are global complexity 1 sets the only obstructions?

Peake.219: [math]\displaystyle{ c_{99} \geq 3^{98} }[/math]

Tao.225: Spreadsheet set up

Feb 9 Nielsen: Update on the polymath project Bukh.412: Negative answer to Gowers' question

Gowers.365: Equal slices measure introduced

Tao.419: Use low-influence instead of complexity 1?

Gowers.420: Need DHJ(0,2)

Tao.431: Use local obstructions rather than global obstructions?

Kalai.233: Higher k?
Feb 10 Tao.439: Use hypergraph regularity? Peake.241: [math]\displaystyle{ c_5 \leq 155 }[/math]; xyz notation

Peake.243: [math]\displaystyle{ c_5 \leq 154 }[/math]

Feb 11 le Bruyn: Yet another Math 2.0 proposal

Tao.470: Proto-wiki created

Tao.451: 01-insensitive case OK

Kalai.455: Hyper-optimistic conjecture

Tao.460: Connections with ergodic approach

Tao: A reading seminar on DHJ (600-699)

Tao.249: [math]\displaystyle{ \overline{c}^\mu_0 = 1 }[/math], [math]\displaystyle{ \overline{c}^\mu_1 = 2 }[/math], [math]\displaystyle{ \overline{c}^\mu_2 = 4 }[/math]

Dyer.254: [math]\displaystyle{ \overline{c}^\mu_3 = 6 }[/math]

Feb 12 Wiki set up O'Donnell.476: Fourier-analytic Sperner computations

McCutcheon.480: Strong Roth theorem proposed

Jakobsen.257: [math]\displaystyle{ \overline{c}^\mu_4 = 9 }[/math]

Jakobsen.258: [math]\displaystyle{ \overline{c}^\mu_5 = 12 }[/math]

Peake.262: Extremisers for [math]\displaystyle{ c_4 }[/math]

Feb 13 Gowers: Possible proof strategies (500-599) McCutcheon.505: IP uniformity norms?

Tao.614: Carlson-Simpson not needed for stationarity

Tao: Bounds for first few DHJ numbers (700-799)
Feb 14 Gowers.496: Equal slices implies uniform McCutcheon.508: Ergodic proof strategy

Tao.618: More randomness needed to invert maps

O'Donnell.622: [math]\displaystyle{ [3]^n }[/math] should already provide enough randomness

Tao.510: Finitary analogue of stationarity

Sauvaget: A proof that [math]\displaystyle{ c_5=154 }[/math]?
Feb 15 Tao.498: Uniform implies equal slices

Tao.514: DHJ(2.6) proposed

McCutcheon.518: Ramsey proof of DHJ(2.6)

Sauvaget: A new strategy for computing [math]\displaystyle{ c_n }[/math]

Markström.706: Integer program, [math]\displaystyle{ c_5=150 }[/math]

Cantwell.708: [math]\displaystyle{ c_6=450 }[/math]

Tao.715: Genetic algorithm?

Feb 16 Tao.524: Simplification of proof

O'Donnell 529: Ramsey-free proof of DHJ(2.6)?

McCutcheon.533: Ramsey theory incompatible with symmetry

Tao.626: Ramsey theorems summarised Peake.730: [math]\displaystyle{ c_5 }[/math] extremisers

Tao.731: Human proof that [math]\displaystyle{ c_5 \leq 152 }[/math]; [math]\displaystyle{ c_7 \leq 1348 }[/math]

Feb 17 Tao.536: Fourier-analytic proof of DHJ(2.6)

McCutcheon.541: "Cave-man" proof of DHJ(2.6)

Chua.736: [math]\displaystyle{ c'_5 \geq 124 }[/math]

Peake.738: Connection between Moser(3) and sphere packing

Feb 18 Gowers.544: Corners(1,3)?

Gowers.545: Fourier computations on equal-slices measure begin

Markström.739: [math]\displaystyle{ c_6 }[/math] extremiser unique
Feb 19 Markström.742: 43-point Moser sets in [math]\displaystyle{ [3]^4 }[/math] listed

Peake.743: 43-point sets analysed

Cantwell.744: [math]\displaystyle{ c'_5 \leq 128 }[/math]

Tao.745: 50+ point line-free sets in [math]\displaystyle{ [3]^4 }[/math] listed

Feb 20 Vipulnaik: A quick review of the polymath project Solymosi.563: Moser(6) implies DHJ(3) Tao.630: IP convergence lemma Markström.747: 42-point Moser sets listed

Peake.751: Human proof of [math]\displaystyle{ c_5 \leq 151 }[/math]

Feb 21 Gowers: To thread or not to thread Gowers.580: Extreme localisation + density increment = DHJ(3)?

Gowers.581: Multidimensional Sperner

Gowers.582: Use Ajtai-Szemeredi argument to get density increment?

Tao.631: Informal combinatorial translation of ergodic DHJ(2)

Tao.578: Finitary ergodic proof of DHJ(2) proposed

Tao.632: Special cases of DHJ(3) translated

Peake.752: Human proof of [math]\displaystyle{ c_5=150 }[/math], [math]\displaystyle{ c_6=450 }[/math]

Tao.753: Sequences submitted to OEIS

Feb 23 McCutcheon.593: DHJ(2.7)

O'Donnell.596: Fourier-analytic proof of DHJ(2)

Gowers: Brief review of polymath1 (800-849)

O'Donnell.800: Fourier-analytic + density increment proof of DHJ(2)

Markström.463: 42-point Moser sets analysed

Tao.464: [math]\displaystyle{ c'_5 \leq 127 }[/math]

Chua.766: 3D Moser sets with 222 have [math]\displaystyle{ \leq 13 }[/math] points

Tao.767: 4D Moser sets with 2222 have [math]\displaystyle{ \leq 39 }[/math] points

Feb 24 Tao.809.2: Low-influence implies Sperner-positivity

Gowers.812: Fourier vs physical positivity

O'Donnell.814: [math]\displaystyle{ \ell_1 }[/math], [math]\displaystyle{ \ell_2 }[/math] equivalence

Feb 25 Gowers.820: Density increment on complexity 1 set Tao.818: Finitary ergodic sketch of DHJ(3)

O'Donnell.821: Simplified Fourier proof of DHJ(2) structure theorem

Cantwell.769: 5D Moser sets with 2222* have [math]\displaystyle{ \leq 124 }[/math] points

Peake.771: Exotic 43-point Moser sets described

Feb 26 Gowers.824: Complexity 1 + Ajtai-Szemeredi DHJ(3) sketch
Feb 27 Tao.826: Non-Fourier proof of DHJ(2) structure theorem

Gowers.828: Does correlation with 1-set imply density increment?

Tao.828.4: Energy increment proof for Gowers Q?

McCutcheon.832.2: Use dense fibres to answer Gowers Q? Elsholtz.775: Human proof of 2222* result

Cantwell.776: [math]\displaystyle{ c'_5 \leq 126 }[/math]

Feb 28 Tao.834: Use pullbacks for Gowers Q?

Gowers.835: Pullbacks don't work

O'Donnell 839: Increment-free Fourier proof of DHJ(2)

Tao.837.2: Dense fibres argument for Gowers Q Markström.779: 41-point Moser sets listed
Mar 1 Cantwell.782, Peake.784: [math]\displaystyle{ c'_5 \leq 125 }[/math]
Mar 2 Gowers: DHJ 851-899

Tao.853 Mass increment; connection with Hahn decomposition

Gowers.854 Higher-D Ajtai-Szemeredi?

Mar 3 McCutcheon.864 Caution: 12-sets not sigma-algebra! Dyer.786 [math]\displaystyle{ \overline{c}^\mu_6 \lt 18 }[/math]

Cantwell.787 125-sets have at most 41 points in middle slices

Mar 4 Markstrom.788: [math]\displaystyle{ c^\mu_n = 4,6,9,12 }[/math] for [math]\displaystyle{ n=2,3,4,5 }[/math]

Marc.791: [math]\displaystyle{ \overline{c}^\mu_{10} \geq 29 }[/math]

Tao.793: "score" introduced

Tao: DHJ3 (900-999) Density Hales-Jewett type numbers

Tao.901: 125-sets have D=0

Dyer.902: [math]\displaystyle{ \overline{c}^\mu_6 \lt 17 }[/math]

Carr.903: Genetic algorithm implemented

Mar 5 Peake.904 Scores for 6D Moser?

Tao.908 Find Pareto-optimal and extremal statistics?

Dyer.909 Wildcard variants of Moser

Cantwell.912 125-sets have at most 40 points in middle slices

Cantwell.913 125-sets have D=0 (alternate proof)

Peake.914 Pareto-optimal 3D statistics

Mar 6 Gowers.873 12-set density increment difficulty identified Dyer.917 [math]\displaystyle{ \overline{c}^\mu_7 \leq 22 }[/math]

Cantwell.920 [math]\displaystyle{ c'_6 \leq 373 }[/math]

Cantwell.921 125-sets have C=78 or 79

Markstrom.923 [math]\displaystyle{ \overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40 }[/math] for [math]\displaystyle{ n=3,\ldots,12 }[/math]

Guest.930 GA without crossover?

Mar 7 Solymosi.880 Shelah-type flip-flop spaces? Peake.931 3D extremals and inequalities

Cantwell.932 125-sets have a middle slice of at most 39 points

Cantwell.933 125-sets have A=6,7,8

Cantwell.934 If C=78 then A=7,8

Tao.935 125-sets have stats (6,40,79,0,0,0), (7,40,78,0,0) or (8,39,78,0,0)

Mar 8 Gowers.881 Iterative partitioning of 12-sets?

Gowers.882 New proof of Ajtai-Szemeredi

O'Donnell.884 Multidimensional Sperner written up

Peake.939 [math]\displaystyle{ c'_6 \leq 365 }[/math]

Carr.940 [math]\displaystyle{ c'_6 \geq 353; c'_7 \geq 978 }[/math]

Tao.941 Seeding GA?

Cantwell.942 (6,40,79,0,0) eliminated

Tao.943 Linear programming proof of [math]\displaystyle{ c'_4 =43 }[/math]

Tao.944 [math]\displaystyle{ c'_6 \leq 364 }[/math]

Mar 9 Gowers.885 Sketch of DHJ(3)

Gowers.886 DHJ(4)?

Gowers.897 Writing of DHJ(k) begins

Austin.894 New ergodic proof of DHJ(k) Cantwell.945 (7,40,78,0,0) eliminated

Cantwell.949 (8,39,87,0,0) eliminated: [math]\displaystyle{ c'_5 = 124 }[/math]

Tao.950 [math]\displaystyle{ \overline{c}^\mu_n }[/math] submitted to OEIS

Carr.954 [math]\displaystyle{ c'_7 \geq 988 }[/math]

Mar 10 Gowers: Polymath1 and open collaborative mathematics

OU Math club: Problem solved (probably)

Gowers: Problem solved (probably) (1000-1049)

Gowers.1005.1 Tower-type bounds

Tao.1003 1-sets, 2-sets locally independent
Mar 11 Kalai: Polymath1: probable success Gowers.1007 Correlation component of DHJ(k) proof complete

Solymosi.1011 Shelah-type argument?

Markstrom.961 Partial confirmation of HOC for n=6,7

Elsholtz.962 Analysis of GA solutions

Tao.969 Integer programming for Behrend sphere statistics

Tao.970 [math]\displaystyle{ c'_7 \leq 1086 }[/math]

Mar 12 O'Donnell.1021 DHJ(k) => Varnavides completed

Gowers.1020 No apparent obstacles to proving DHJ(k)

O'Donnell.1025 Work exclusively with equal (non-degenerate) slices measure?

Tao.1024 Informal combinatorial translation of Austin's proof Markstrom.972, Dyer.973, Tao.974, Markstrom.977: Integer programming problem discovered, isolated, fixed

Tao.974: [math]\displaystyle{ c'_6 \leq 361 }[/math], [math]\displaystyle{ c'_7 \leq 1078 }[/math]

Cantwell.976: Partial recovery of 4D stats by hand

Mar 13 Nielsen: Biweekly links for 03/13/2009

Galdino: Links seminais

Flaxman: Gowers' polymath experiment: problem probably solved

Elsholtz.980: Use e=1, f=1, etc. refinements

Peake.982: xxyyzz inequalities

O'Bryant.984, O'Bryant.993: [math]\displaystyle{ c_n \gg 3^{n - 4\sqrt{\log 2}\sqrt{\log n}+\frac 12 \log \log n} }[/math]

Cantwell.985: Human proof of [math]\displaystyle{ c^\mu_3=6 }[/math] begins

Peake.989: xxyyz inequalities

Tao.990: [math]\displaystyle{ c'_7 \leq 1071 }[/math]

Peake.991: xxxyz, xxxxyz, xxxyyz inequalities

Seva.994: Kakeya in [3]^n?

Mar 14 Hariss: Polymath Tao.1035 Ramsey-free translation of Austin's proof Tao: DHJ(3) 1100-1199
Mar 15 Neylon: There are crowds, and then there are crowds...
Mar 16 Gowers: DHJ(3) and related results: 1050-1099
Mar 18 Polymath hits front page of Slashdot with this article

Nielsen: How changing the technology of collaboration can change the nature of collaboration

Mar 20 Nielsen: The Polymath project: scope of participation
Mar 21 Gans: Something interesting is going on in Maths
Mar 24 Gowers: Can Polymath be scaled up?

Vipulnaik: Concluding notes on the polymath project - and a challenge


Mar 25 Nielsen: On scaling up the polymath project

Dyer: A gentle introduction to the Polymath project


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