Tuesday, November 13, 2018
11/13/2018 - 4:00pm
The problem of computational super-resolution asks to recover “high-resolution features” of a signal from inaccurate and low-resolution data, using some kind of a-priori model as a regularization. I will describe several situations for which sharp bounds for stable reconstruction are known, depending on signal complexity, noise/uncertainty level, and available data bandwidth. I will also discuss optimal recovery algorithms, and some open questions.
11/13/2018 - 4:15pm
I will discuss several results on abstract homomorphisms between the groups of rational points of algebraic groups. The main focus will be on a conjecture of Borel and Tits formulated in their landmark 1973 paper. Our results settle this conjecture in several cases; the proofs make use of the notion of an algebraic ring. I will mention several applications to character varieties of finitely generated groups and representations of some non-arithmetic groups.