[geometry-ml:04718] 学習院・早稲田 幾何学セミナー 6/8 16:00-

[sumio yamada]

みなさま、

以下の通り、対面のセミナーを行います。
https://pc1.math.gakushuin.ac.jp/~hosono/GWGS/GWGS.html

ご興味のある方は、是非ご参加ください。

山田澄生

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2022年6月8日（水）16:00～17:30
講演者： John Loftin (Rutgers University)

題目: Cubic Differentials, Harmonic Maps, and Real Buildings
於：学習院大学 南1号館103教室

概要：Consider a Riemann surface S of genus g at least 2 equipped with a
holomorphic cubic differential U.  This pair (S,U) induces, via the theory
of Higgs bundles, a rank-3 bundle with a flat connection, which induces a
representation of the fundamental group into SL(3,R), and these
representations comprise the Hitchin component.  In addition, there is a
harmonic map, equivariant under this representation, from the universal
cover of S into the symmetric space SL(3,R)/SO(3).  This parametrization of
the Hitchin component is not explicit but involves the a system of PDEs.
For nonzero U, we study the case sU as s approaches infinity.  In
particular, we show the geometry in this limit can be read off explicitly
from U, in terms of an embedding of the universal cover of S into the real
building given by the asymptotic cone of the symmetric space
SL(3,R)/SO(3).  We are able to provide explicit pictures for most triangle
groups.

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