Monday, January 27, 2020
Time  Items 

All day 

4:00pm 
01/27/2020  4:00pm Ratner’s celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one can deduce an effective equidistribution result by mixing methods, an idea that goes back to Margulis’ thesis. When the homogeneous space is noncompact, one needs to impose further “diophantine conditions” over the base point, quantifying some recurrence rates, in order to get a quantified equidistribution result.
In the talk I will discuss certain diophantine conditions, and in particular I will show how a new Margulis’ type inequality for translates of horospherical orbits helps verify such conditions, leading to a quantified equidistribution result for a large class of points, akin to the results of A. Strombergsson dealing with SL2 case. In particular we deduce a fully effective quantitative equidistribution statement for horospherical trajectories of lattices defined over number fields, without pertaining to Roth’s/strong subspace theorem. If time permits, I will discuss relations of this result to the recent work about effective linearization by LindenstraussMargulisMohammadiShah. Location:
DL431
01/27/2020  4:30pm Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbb{C}$, G be the corresponding simply connected algebraic group and $\mathbb{O}\subset \mathfrak{g}^*$ be a nilpotent coadjoint orbit. In this talk, I will prove that the set of Gequivariant formal graded quantizations of $\mathbb{O}$ is an affine space. This talk is based on arXiv:1810.11531. Location:
LOM 214
