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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
2023/4/21
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
Proper affine actions and geodesic flows of hyperbolic surfaces
hyperbolic surfaces geodesic fl ows
2015/9/29
Let €0 O.2; 1/ be a Schottky group, and let † D H
2=€0 be the corresponding
hyperbolic surface. Let C.†/ denote the space of unit length geodesic currents
on †. The cohom...
Trace coordinates on Fricke spaces of some simple hyperbolic surfaces
simple hyperbolic surfaces Fricke spaces
2015/9/29
The work of Fricke-Klein [20] develops the deformation theory of hyperbolic
structures on a surface Σ in terms of the space of representations of its fundamental group damental group π = π1(Σ) in SL(...
Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
Horocyclic Flows Complete Hyperbolic Surfaces Finite Area
2015/8/26
We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution ...
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
Growth of Weil-Petersson volumes random hyperbolic surfaces of large genus
2011/1/20
In this paper, we investigate the geometric properties of hyperbolic surfaces by studying the lengths of simple closed geodesics. The moduli space Mg,n of complete hyperbolic surfaces of genus g ≥ 2 w...