Harmonic maps, renormalized energy and random matrices
演讲者
Antoine Song
时间
2025年06月10日 14:45 至 16:30
地点
A3-4-301
线上
Zoom 815 762 8413
(BIMSA)
摘要
I will discuss a new geometric concentration phenomenon for equivariant harmonic maps from surfaces to Euclidean spheres. Specifically, for any unitary representation of the fundamental group of a Riemann surface S, one can associate a renormalized energy and an equivariant harmonic map from the universal cover of S to a unit sphere. The main result of this talk is that when the unitary representation is chosen at random, with high probability, the renormalized energy is close to an explicit constant and the shape of the harmonic map is close to a unique limit shape.