the kardar-parisi-zhang (kpz) equation is the stochastic partial differential equation that models interface growth. in the talk i will present the construction of a stationary measure for the kpz equation on a bounded interval with general inhomogeneous neumann boundary conditions. along the way, we will encounter classical orthogonal polynomials, the asymmetric simple exclusion process, and precise asymptotics of q-gamma functions.
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this construction is a joint work with ivan corwin.

classical algorithms typically provide "one size fits all" performance, and do not leverage properties or patterns in their inputs. a recent line of work aims to address this issue by developing algorithms that use machine learning predictions to improve their performance. in this talk i will present two examples of this type, in the context of streaming and sampling algorithms. in particular, i will show how to use machine learning predictions to improve the performance of (a) low-memory streaming algorithms for frequency estimation (iclr’19), and (b) sampling algorithms for estimating the support size of a distribution (iclr’21). both algorithms use an ml-based predictor that, given a data item, estimates the number of times the item occurs in the input data set.
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the talk will cover material from papers co-authored with t eden, cy hsu, d katabi, s narayanan, r rubinfeld, s silwal, t wagner and a vakilian.