Title: Random gluing polygons.



Abstract.
We consider an oriented closed surface obtained by 
randomly glued $n$ polygons along their sides.
The total number of sides are supposed to be 
an even number $N$ and the resulting surface can be encoded by a random permutation 
$\gamma$ of $[N]$. We show that $\gamma$ is distributed asymptotically (as $N\to\infty$) 
uniformly among either even or odd permutations depending on parities of $N$ and $n$.
Then we 
study the distribution of the genus of the surface obtained and show that asymptotically
it is 
normal Gaussian distribution with mean $(N/2-n-\log N)/2$ and variance $(\log N)/4$.
This is a 
joint work with Boris Pittel.