Speaker
Description
In 2001 Sir M. F. Atiyah formulated a conjecture $C1$ and later with P.Sutcliffe two stronger conjectures $C2$ and $C3$. These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of $n$ points in the Euclidean three space. The conjecture $C1$ is proved for $n = 3$ in [1] and for $n=4$ in [2], and $C1-C3$ in [3]. After two decades we succeeded in verifying $C1$ for arbitrary five points in the Euclidean plane. The computer symbolic certificate produces a new remarkable universal ('hundred pages long') positive polynomial invariant (for any five planar points), in terms of newly discovered shear coordinates. This refines the original Atiyah’s conjecture and we are optimistic for its verification for $n$ greater than five (less optimistic variant $\ldots$ 'It remains a conjecture for $300$ years (like Fermat)', see Atiyah: Edinburgh Lectures..2010). In 2013.\ Atiyah's conjectures were put on the new list of nine open problems [4] (hopefully easier than remaining nine millennium problems!).
[1] M. Atiyah. The geometry of classical particles. Surveys in Differential Geometry (International Press) 7 (2001).
[2] M. Eastwood and P. Norbury, A proof of Atiyah’s conjecture on configurations of four points in Euclidean three-space. Geometry \& Topology 5 (2001), 885–893.
[3] D. Svrtan, A proof of All three Euclidean Four Point Atiyah-Sutcliffe Conjectures, https://emis.de/journals/SLC/wpapers/s73vortrag/svrtan.pdf
[4] Open problems in Honor of Wilfried Schmied\\
https://legacy-www.math.harvard.edu/conferences/schmid\_2013/problems/index.html\\
