报告人：Wenyuan Yang (Peking University)
时间：2018-11-28 10:40-11:30
地点：Room 1304, Sciences Building No. 1
Abstract: In this talk, we shall derive an asymptotic formula for the number of conjugacy classes of elements
for a class of statistically convex-cocompact actions with contracting elements. Denote by $\mathcal C(n)$
(resp. $\mathcal C'(n)$) the set of (resp. primitive) conjugacy classes of stable length at most $n$. The main
result is an asymptotic formula as follows: $$\sharp \mathcal C(n) \asymp \sharp \mathcal C'(n) \asymp \frac
{\exp(\omega(G))}{n}.$$ As a consequence of the formulae, the conjugacy growth series is transcendental
for all non-elementary relatively hyperbolic groups, graphical small cancellation groups with finite components.
As by-product of the proof, we establish several useful properties for an exponentially generic set of elements.
In particular, it yields a positive answer to a question of Maher that an exponentially generic elements in
mapping class groups have their Teichm\"{u}ller axis contained in the principal stratum. This is a joint work
with Ilya Gekhtman (U. Toronto).
