Berlin-Oxford Summer School in Mathematics of Random Systems 2024
The Berlin-Oxford Summer School in Mathematics of Random Systems 2024 is jointly organised by the the Berlin-Oxford IRTG group and the EPSRC CDT in Mathematics of Random Systems. The Summer School will be held at St Hilda's College and the Mathematical Institute in Oxford. In addition to the lecture courses, there will additional invited talks by guest lecturers and presentations by selected PhD students.
Event Timetable
The full Summer School timetable is available here.
Monday, 9th September
Registration and Lectures from 10:00 to 17:20 @ Rooftop Garden Suite, St Hilda’s College
Tuesday, 10th September
Lectures from 09:30 to 16:40 @ 14-16 Norham Gardens, OX2 6QB (previously the Cherwell Center)
Wednesday 11th September
Lectures from 09:30 to 16:20 @ Rooftop Garden Suite, St Hilda’s College
Local walk from 16:20 for approximately an hour
Conference dinner at 19:00 @ St Hilda's Dining Hall
Thursday 12th September
Lectures from 09:30 to 15:00 @ Riverside Pavilion, St Hilda’s College
Punting Trip/Botanic Garden visit at 16:00 @ Magdalen Bridge Boathouse
Friday 13th September
Lectures and closing talk from 09:30 to 12:50 @ L4, Mathematical Institute, Andrew Wiles Building, Oxford
St Giles' Fair
The Annual St. Giles' Fair is taking place on Monday and Tuesday, 9-10 September 2024. You can find the notice from Oxford city council here, and further details about the fair here.
Invited Lecturers
Organising Committee
Peter Bank (Technische Universitaet Berlin)
Ben Hambly (University of Oxford)
Venues: St Hilda's College and Mathematical Institute, Oxford
Lecture Courses
Professor Huyen Pham (Paris) - Machine learning and stochastic control
This course will present some recent developments on the interplay between control and machine learning. More precisely, we shall address the following topics:
Part I: Neural networks-based algorithms for PDEs and stochastic control.
Deep learning based on the approximation capability of neural networks and efficiency of gradient descent optimizers has shown remarkable success in recent years for solving high dimensional partial differential equations (PDEs) arising notably in stochastic optimal control. We present the different methods that have been developed in the literature relying either on deterministic or probabilistic approaches: - Deep Galerkin, Physics informed Neural networks - Deep BSDEs and Deep Backward dynamic programming.
Part II: Deep reinforcement learning.
The second part of the lecture is concerned with the resolution of stochastic control in a model-free setting, i.e. when the environment and model coefficients are unknown, and optimal strategies are learnt from samples observation of state and reward by trial and error. This is the principle of reinforcement learning (RL), a classical topic in machine learning, and which has attracted an increasing interest in the stochastic analysis/control community. We shall review the basics of RL theory, and present the latest developments on policy gradients, actor/critic and q-learning methods in continuous time.
Part III: Generative modeling for time series via optimal transport approach.
We present novel generative models based on diffusion processes and optimal transport approach for simulating new samples of times series data distribution.
Professor Ellen Powell (Durham) - The Gaussian Free Field
One simple way to think of the Gaussian Free Field (GFF) is that it is the most natural and tractable model for a random function defined on either a discrete graph (each vertex of the graph is assigned a random real-valued height, and the distribution favours configurations where neighbouring vertices have similar heights) or on a subdomain of Euclidean space. The goal of these lectures is to give an elementary, self-contained introduction to both of these models, and highlight some of their main properties. We will start with a gentle introduction to the discrete GFF, and discuss its various resampling properties and decompositions. We will then move on to the continuum GFF, which can be obtained as an appropriate limit of the discrete GFF when it is defined on a sequence of increasingly fine graphs. We will explain what sort of random object (i.e, generalised function) it actually is, and how to make sense of various properties that generalise those of the discrete GFF.
Reference:
Wendelin Werner, Ellen Powell: Lecture notes on the Gaussian Free Field
