Description: "Treatment Effect Heterogeneity"

Abstract: Applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations, especially variation not explained by observed covariates. We propose a model-free approach for testing for the presence of such unexplained variation. To use this randomization-based approach, we must address the fact that the average treatment effect, generally the object of interest in randomized experiments, actually acts as a nuisance parameter in this setting. We explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance. We also show how this method readily extends to testing for heterogeneity beyond a given model, which can be useful for assessing the sufficiency of a given scientific theory. We finally apply our method to the National Head Start Impact Study, a large-scale randomized evaluation of a Federal preschool program, finding that there is indeed significant unexplained treatment effect variation.

Description: “Forward-backward stochastic differential equations of McKean-Vlasov type and mean field games”

Abstract
http://www.columbia.edu/~hz2244/CUMF/012915.pdf

Description: "Maxima of log-correlated Gaussian fields and of the Riemann Zeta function on the critical line"

Abstract:
A recent conjecture of Fyodorov, Hiary & Keating states that the maxima of the Riemann Zeta function on a bounded interval of the critical line behave similarly to the maxima of a specific class of Gaussian fields, the so-called log-correlated Gaussian fields. These include important examples such as branching Brownian motion and the 2D Gaussian free field. In this talk, we will highlight the connections between the number theory problem and the probabilistic models. We will outline the proof of the conjecture in the case of a randomized model of the Zeta function. We will discuss possible approaches to the problem for the function itself. This is joint work with D. Belius (NYU) and A. Harper (Cambridge).

Description: "Random Subdivisions & Neural Coding"

In the first part, I will talk about random subdivisions obtained from projections of polytopes. These are related to random polytopes and zeros of random tropical polynomials. In the second part, I will discuss results and open problems in neural coding, with emphasis on decoding grid cells.