All Questions

I recently came across to the following action of $\text{SL}(2,\Bbb Z)$ on the space $\Bbb R^n\times\Bbb R^n$ defined as $$ \begin{pmatrix} a & b \\ c & d \end{pmatrix}\cdot \big(v,\,w\big)\...

I have a research-level but not necessarily new question about certain equidistribution problems. If $\phi \in L^2(S^2)$ then we could define the Weyl sums: $$ \int \phi \, \mu_d = \frac{1}{|\mathcal{...

Here are two setup where the notion of "mildly mixing" comes up: for representations and for group acting by measure preserving transformations (see definitions below). Since a natural class of ...

So is there a complexification or 'real'ization of the mapping class group or can it be realised as a lattice in some lie group. like $PSL(2, \mathbb Z)$ in $PSL(2, \mathbb R)$. for g=1 this certainly ...