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SUMMARY:A conjecture at the heart of Ramsey theory\, and surrounding quest
 ions on tensors and polynomials.
DTSTART:20240117T140000
DTEND:20240117T150000
DTSTAMP:20260916T044052Z
UID:bc0f80667c74cc7419abce6bab25a8626182dbfd69a1d94925732cba
CATEGORIES:Conferences - Seminars
DESCRIPTION:Thomas Karam – Oxford University     \nSeminar in Mathe
 matics\nThis talk will primarily involve two phases. In the first half\, w
 e will focus on describing how the polynomial density Hales-Jewett conject
 ure\, a central open problem in combinatorics\, motivates a succession of 
 three probabilistic and analytic results\, where the proof of each result 
 uses the next result as a black box: an approximation theorem on sets defi
 ned by polynomial conditions\, a generalisation of the theorem of Green an
 d Tao on the equidistribution of polynomials\, and the existence of high-r
 ank subtensors of high-rank tensors. In the second half\, we will present 
 additional results within the two nascent areas encompassing the previous 
 results: the basic properties of the ranks of tensors\, and the structure 
 of objects defined in terms of linear forms and polynomials restricted to 
 power sets such as the Boolean cube.\n\n 
LOCATION:https://epfl.zoom.us/j/63047925658
STATUS:CONFIRMED
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