Tuesday, January 21, 2020
01/21/2020 - 4:00pm
We show that under certain conditions, random walks on a d-dim torus by affine expanding maps have a unique stationary measure. We then use this result to show that given an IFS of contracting similarity maps of the real line with a uniform contraction ratio 1/D, where D is some integer > 1, under some suitable condition, almost every point in the attractor of the given IFS (w.r.t. a natural measure) is normal to base D.
01/21/2020 - 4:15pm
Abstract: Every smooth proper algebraic variety over a $p$-adic field is expected to have semistable model after passing to a finite extension. This conjecture is open in general, but its analogue for Galois representations, the $p$-adic monodromy theorem, is known. In this talk, we will explain a generalization of this theorem to etale local systems on a rigid analytic variety.