**Pankaj Vishe**

University of York, UK

August 14, 2014

**Effective Ratner equidistribution result for $mathrm{SL}(2, mathbb R)ltimes mathbb R^{2k} $ and appl**:
Let $G=mathrm{SL}(2,mathbb R)ltimes mathbb R^{2k}$ and let $Gamma$ be a congruence subgroup of $mathrm{SL}(2,mathbb Z)ltimesmathbb Z^{2k}$. We give an effective equidistribution result for a family of 1-dimensional unipotent orbits in $Gammaackslash G$. The proof involves Specral methods and bounds for exponential sums. We apply this result to obtain an effective Oppenheim type result for a class of indefinate irrational quadratic forms. This is based on a joint work with Andreas Strombergsson.