**Pankaj Vishe**

Durham University, UK

January 16, 2016

**Uniform bounds for Period integrals and sparse equidistribution**:
Let M be a compact quotient of SL(2,R) and let f be a smooth function of
zero average on M. We use spectral methods to get uniform (i.e.
independent of spectral gap) bounds for twisted averages of f along long horocycle orbit segments. We apply this to obtain an equidistribution result for sparse subsets of horocycles on M. This is a joint work with J. Tanis.