XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019 VIII School on Geometry and Physics 24-28.06.2019
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# Armen Sergeev

## Adiabatic limit in Yang–Mills equation and harmonic spheres conjecture

Harmonic spheres conjecture establishes a correspondence between Yang–Mills fields on $\mathbb R^4$ with gauge group $G$ and harmonic maps of the Riemann sphere $S^2$ into the loop space $\Omega G$ of the group $G$. This conjecture is an extension to general Yang–Mills $G$-fields of the Atiyah–Donaldson theorem relating $G$-instantons on $\mathbb R^4$ with holomorphic maps $S^2\to\Omega G$.

In our talk we shall analyze a possible way of the proof of this conjecture, proposed by Popov, based on the adiabatic limit construction. This construction employs a nice parametrization of the sphere $S^4\setminus S^1$ without a circle found by Jarvis and Norbury. Using his construction we can associate with arbitrary Yang–Mills $G$-field on $S^4$ harmonic map $S^2\to\Omega G$.

 Event sponsored by: University of Bialystok

Webpage by: Tomasz Golinski