Scientists / Open questions
Michael Francis Atiyah
Geometric topology; index theory; mathematical physics
1966 Fields Medal
9 questions
Yang-Baxter solutions from monopole spectral curves: star-triangle weights beyond the chiral Potts family and the quantum interpretation of the hyperbolic-monopole mass
The Atiyah–Sutcliffe conjectures on configurations of points: linear independence of the direction polynomials and the determinant volume inequalities for general n
Existence and moduli of irreducible self-dual connections on the four-sphere for compact simple gauge groups at low instanton number
Open core of the Atiyah–Hitchin low-energy monopole scattering problems: the general geodesic flow on the two-monopole moduli space and explicit metrics on higher-charge monopole moduli spaces
Open problems of the geometric models of matter: energy functional, spin- states, refined particle models, and geometric particle processes
Open problems in the Atiyah–Manton complex-geometry model of nuclei and atoms: metrics, energy functionals, quantization, neutrons, and dynamics
Integral cohomology of moduli spaces of principal G-bundles on a Riemann surface: torsion and integral relations beyond the unitary case
Ground-state edge-cone metrics and template-topology reflection for anyon tensor networks in geometric models of matter (Atiyah-Marcolli, 2021)
A truly decoupled pure four-dimensional super Yang-Mills limit from M-theory on -holonomy flop geometries