# Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

The talk originates from two studies on the dynamic properties of one-dimensional elastic quasicrystalline solids. The first one refers to a detailed investigation of scaling and self-similarity of the spectrum of an axial waveguide composed of repeated elementary cells designed by adopting the family of generalised Fibonacci substitution rules corresponding to the so-called precious means. For those, an invariant function of the circular frequency, the Kohmoto's invariant, governs self-similarity and scaling of the stop/pass band layout within defined ranges of frequencies at increasing generation index. The Kohmoto's invariant also explains the existence of particular frequencies, named canonical frequencies, associated with closed orbits on the geometrical three-dimensional representation of the invariant. The second part shows the negative refraction properties of a Fibonacci-generated quasicrystalline laminate and how the tuning of this phenomenon can be controlled by selecting the generation index of the sequence.

We consider calculation of VaR/TVaR capital requirements when the underlying economic scenarios are determined by simulatable risk factors. This problem involves computationally expensive nested simulation, since evaluating expected portfolio losses of an outer scenario (aka computing a conditional expectation) requires inner-level Monte Carlo. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR/\TVaR estimators that reduces bias and variance compared to existing methods. Time permitting, I will highlight further related applications of statistical emulation in risk management.

This is joint work with Jimmy Risk (Cal Poly Pomona).

**Oxford Mathematics Public Lectures**

**Can Mathematics Understand the Brain?' - Alain Goriely**

The human brain is the object of the ultimate intellectual egocentrism. It is also a source of endless scientific problems and an organ of such complexity that it is not clear that a mathematical approach is even possible, despite many attempts.

In this talk Alain will use the brain to showcase how applied mathematics thrives on such challenges. Through mathematical modelling, we will see how we can gain insight into how the brain acquires its convoluted shape and what happens during trauma. We will also consider the dramatic but fascinating progression of neuro-degenerative diseases, and, eventually, hope to learn a bit about who we are before it is too late.

Alain Goriely is Professor of Mathematical Modelling, University of Oxford and author of 'Applied Mathematics: A Very Short Introduction.'

March 8th, 5.15 pm-6.15pm, Mathematical Institute, Oxford

**Please email external-relations@maths.ox.ac.uk to register**

Topological data analysis (TDA) is a robust field of mathematical data science specializing in complex, noisy, and high-dimensional data. While the elements of modern TDA have existed since the mid-1980’s, applications over the past decade have seen a dramatic increase in systems analysis, engineering, medicine, and the sciences. Two of the primary challenges in this field regard modeling and computation: what do topological features mean, and are they computable? While these questions remain open for some of the simplest structures considered in TDA — homological persistence modules and their indecomposable submodules — in the past two decades researchers have made great progress in algorithms, modeling, and mathematical foundations through diverse connections with other fields of mathematics. This talk will give a first perspective on the idea of matroid theory as a framework for unifying and relating some of these seemingly disparate connections (e.g. with quiver theory, classification, and algebraic stability), and some questions that the fields of matroid theory and TDA may mutually pose to one another. No expertise in homological persistence or general matroid theory will be assumed, though prior exposure to the definition of a matroid and/or persistence module may be helpful.

Many symptoms of Parkinson’s disease are connected with abnormally high levels of synchrony in neural activity. A successful and established treatment for a drug-resistant form of the disease involves electrical stimulation of brain areas affected by the disease, which has been shown to desynchronize neural activity. Recently, a closed-loop deep brain stimulation has been developed, in which the provided stimulation depends on the amplitude or phase of oscillations that are monitored in patient’s brain. The aim of this work was to develop a mathematical model that can capture experimentally observed effects of closed-loop deep brain stimulation, and suggest how the stimulation should be delivered on the basis of the ongoing activity to best desynchronize the neurons. We studied a simple model, in which individual neurons were described as coupled oscillators. Analysis of the model reveals how the therapeutic effect of the stimulation should depend on the current level of synchrony in the network. Predictions of the model are compared with experimental data.

Through laboratory experiments, we examine the transport, settling and resuspension of sediments as well as the influence of floating particles upon damping wave motion. Salt water is shown to enhance flocculation of clay and hence increase their settling rate. In studies modelling sediment-bearing (hypopycnal) river plumes, experiments show that the particles that eventually settle through uniform-density fluid toward a sloping bottom form a turbidity current. Meanwhile, even though the removal of particles should increase the buoyancy and hence speed of the surface current, in reality the surface current stops. This reveals that the removal of fresh water carried by the viscous boundary layers surrounding the settling particles drains the current even when their concentration by volume is less than 5%. The microscopic effect of boundary layer transport by particles upon the large scale evolution is dramatically evident in the circumstance of a mesopycnal particle-bearing current that advances along the interface of a two-layer fluid. As the fresh water rises and particles fall, the current itself stops and reverses direction. As a final example, the periodic separation and consolidation of particles floating on a surface perturbed by surface waves is shown to damp faster than exponentially to attain a finite-time arrest as a result of efficiently damped flows through interstitial spaces between particles - a phenomenon that may be important for understanding the damping of surface waves by sea ice in the Arctic Ocean (and which is well-known to anyone drinking a pint with a proper head or a margarita with rocks or slush).

Breakthroughs in machine learning have led to impressive results in numerous fields in recent years. I will review some of the best-known results on the computer science side, provide simple ways to think about the associated techniques, discuss possible applications in string theory, and present some applications in string theory where they already exist. One promising direction is using machine learning to generate conjectures that are then proven by humans as theorems. This method, sometimes referred to as intelligible AI, will be exemplified in an enormous ensemble of F-theory geometries that will be featured throughout the talk.