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.

Description: "Diffusion scaling of a limit-order book model"

Description: David Kelly (NYU)

Fast-slow systems with chaotic noise.

Abstract:
It has long been observed that multi-scale systems, particularly those in climatology, exhibit behavior typical of stochastic models, most notably in the unpredictability and statistical variability of events. This is often in spite of the fact that the underlying physical model is completely deterministic. One possible explanation for this stochastic behavior is deterministic chaotic effects. In fact, it has been well established that the statistical properties of chaotic systems can be well approximated by stochastic differential equations. In this talk, we focus on fast-slow ODEs, where the fast, chaotic variables are fed into the slow variables to yield a diffusion approximation. In particular we focus on the case where the chaotic noise is multidimensional and multiplicative. The tools from rough path theory prove useful in this difficult setting.