AbstractConsider the action of GL_d(Z) on the d-dimensional torus R^d/Z^d. Given a probability measure on GL_d(Z) and a point on the torus, a random walk is defined. In this talk, I will report some recent progress about the equidistribution of such random walks. More precisely, I will talk about quantitative results under the assumption that the acting group has semisimple Zariski closure. Thi...
AbstractMeromorphic 1-forms on the Riemann sphere with prescribed orders of singularities form strata endowed with period coordinates. Fixing residues at the poles defined a fibration of any stratum to the vector space of configurations of residues. For strata of 1-forms with only one zero, the isoresidual fibration is a cover of the space of configurations of residues ramified over an arrangem...