# Hebrew University topology and geometry seminar

January 6, 2016

1100-1235

Ross building, Seminar Room 70A

## Egor Shelukhin

*Institute for Advanced Study, Princeton
*

##
The $L^{p}$ diameter of the group of area-preserving diffeomorphisms of $S^{2}$

**Abstract:**
We use a geometric idea to give an analytic estimate for the word-length in the pure braid group of $S^{2}$. This yields that the $L^{1}$-norm (and hence each $L^{p}$-norm,
including $L^{2}$) on the group of area-preserving diffeomorphisms of $S^{2}$ is unbounded.
This solves an open question arising from the work of Shnirelman and Eliashberg-Ratiu. Joint work in progress with Michael Brandenbursky.