14:00 Francesco Pedullà, Imperial College London
An asymptotic upper bound on renormalisation constants with regularity structures
When studying the properties of renormalised solutions to singular SPDEs, a helpful tool can be relatively precise descriptions of the asymptotic behaviour of the renormalisation constants that appear in the equation as the ultraviolet cut-off is removed. The aim of this talk is to present a simple inductive argument to obtain asymptotic upper bounds on the renormalisation constants arising in the theory of regularity structure. These bounds are expected to be sharp except in the presence of logarithmically divergent counter-terms and essentially only assume the stochastic estimates used to solve the equation.
As an application, we extend the result of Hairer, Ryser and Weber on the triviality of the solution to the dynamical Phi42 equation without renormalisation to the full sub-critical regime. This is achieved by combining our asymptotic bounds and a novel extension of the existing solution theory for singular SPDEs provided in the regularity structures literature, which is aimed at allowing for a wider class of initial conditions.
This is joint work with Rhys Steele.
14:25 Nikkita Ngalande, Oxford University
Network-Based Analysis of Economic Shocks: A Multi-Year Input-Output Approach
15:00 Dr Samuel Johnston, King's College London
The Brownian marble
The Brownian web is a stochastic process that makes sense of initiating coalescing Brownian motions from every point of spacetime. In this talk, we will be interested in a random subset of the Brownian web which we call the Brownian marble. The Brownian marble is a self-similar fractal-like set with `bubbles' that emerge between the coalescing Brownian motions. The parameter controlling the shape of the bubbles undergoes a phase transition, which is related to the idea of `coming down from infinity' for coalescent processes. In making sense of the Brownian marble we appeal to various ideas and objects, such as the dual Brownian web, Bessel processes, and interlacing identities.
This talk is based on joint work with Andreas Kyprianou, Tim Rogers and Emmanuel Schertzer.
16:00 Prof Xin Guo, University of California, Berkeley
Signature-based statistical methodology for forecast problem
There are well documented challenges for most forecast problems with time series data, including issues of non-stationarity, nonlinearity, and data fragmentation. Meanwhile, modern deep learning models struggle with the interpretability issue and in principle require a substantial number of data for training. In this talk, we will propose a simple signature-based adaptive Lasso approach which has been developed and implemented successfully in Amazon that addresses all these challenges and shows strong potentials for a wide range of applications.
Time permits, we will discuss a few related theoretical results.
17:00 Prof Michael Magee, Durham University
