An action of the cactus group

Canonical abelianization of finite group actions

In these notes we present a corrected version of the algorithm for abelianization of stabilizers of finite group actions on smooth manifolds using equivariant blow ups.

A note on group actions on algebraic stacks

We give the basic definitions of group actions on (algebraic) stacks, and prove the existence of fixed points and quotients as (algebraic) stacks.

Twisted Symmetric Group Actions

We will show the raitonality of some twisted symmetric group actions.

栈上群作用的建模（特别是Lubin-Tate作用）

Modeling Group Actions on Stacks (Especially the Lubin-Tate Action)

本文综述了研究投射有限群在形式模栈上作用的两种方法——几何建模与双塔法，并以Lubin-Tate作用为例展示其应用。

A remark on braid group actions on coherent sheaves

A construction of braid group actions on coherent sheaves using mixed Hodge modules and some well known constructions from geometric representation theory is given.

Regularization of birational actions of FW groups

We prove that every birational action of a group with Property FW can be regularized.

Stochastic Properties of Dynamical Systems Arising from (quantum) Spaces and Actions of Groups

We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic properties.

Galois action on knots I: Action of the absolute Galois group

Our aim of this and subsequent papers is to enlighten (a part of, presumably) arithmetic structures of knots. This paper introduces a notion of profinite knots which extends topological knots and shows its various basic properties. Particularly an action of the absolute Galois group of the rational number field on profinite knots is rigorously established, which is attained by our extending the action of Drinfeld's Grothendieck-Teichmüller group on profinite braid groups into on profinite knots.