Abstract: This talk will primarily involve two phases. In the first half, we will focus on describing how the polynomial density Hales-Jewett conjecture, a central open problem in combinatorics, provides an independent external motivation to a succession of three results, where the proof of each result uses the next result as a black box: an internal approximation theorem on sets defined by polynomial conditions, a local generalisation of the theorem of Green and Tao on the equidistribution of polynomials, and the existence of some kinds of high-rank 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.
Zoom Information:
Link: https://us02web.zoom.us/j/88563732575?pwd=N3VXeGl3dC9tQklpMFNLV21UZ2x3UT09
Meeting ID: 885 6373 2575
Password: 146751
