JAMS

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The JAMS is a weekly seminar with talks given by junior researchers on a topic in all areas in Mathematics. It is a great opportunity to share research, get feedback from other students and to become more confident in presenting work. We also provide drinks and snacks!

This year, there are two different types of talks:

Classic JAMS: Short talks, somewhat specialised and more focused on new results. A great opportunity to get know what fellow PhD students’ research is about.

Introductory JAMS: Longer talks, but more accessible and educational. These are meant to introduce you to the basic ideas of active research fields, and give you a broader picture of modern Applied Mathematics.

If you are interested in giving a talk (of either type) or have further questions, please email us at imperialsiam@gmail.com. You can also sign up to our Mailing List to receive regular updates on these events!

Venue: Huxley 130
Time: Wednesday 4pm-5pm

Upcoming Seminars

 

(13/12/17) Euler Equations: A Coincidence or Genius
Erwin Luesink & So Takao
Abstract

There are at least two equations in mathematics known as the “Euler equations”. In particular, one describes the motion of a free rigid body and another describes the motion of an ideal fluid. In this talk, we are going to show that the equations for both the free rigid body and ideal fluids have the same geometric interpretation as “a geodesic flow on a Lie group equipped with a left or right invariant Riemannian metric” and therefore in retrospect, it is somewhat a remarkable coincidence that they are both called the “Euler equations”

 

Past Seminars

(03/10/17) Kidneys and Map Colouring: an exploration of graph theory
Melissa Lee
Abstract

In this talk, I will introduce graph theory as one of the many topics in pure mathematics. I’ll talk about how a nice stroll through Russia gave rise to the first examples of graphs, and how graphs have been used in recent years to solve some interesting and important problems with both abstract and real world applications.

(03/10/17) An Introduction to Spatial Network
Matt Garrod
Abstract

Networks are everywhere! A network can be used to describe anything which consists of a series of a discrete objects (nodes) and connections or links between them (edges). Examples include: social networks, the internet, transport networks such as the London underground, ecosystems and numerous other examples. Many of these networks are embedded in space, meaning that nodes which share similar locations are more likely to be connected. I will discuss how we can model these networks and touch on some of the recent research I have been doing on the statistical properties of these networks.

(11/10/17) Python for data processing and scientific computing 
José Luis Ricón [Slides] [Zip File]
Abstract


In this talk, I will introduce the Python ecosystem for mathematics, science, and engineering, highlighting packages such as pandas or matplotlib. No prior knowledge of Python is assumed – but experienced programmers will learn new tricks as well!

(18/10/17) Limit order book modelling with hybrid marked point processes (Joint work with Mikko S. Pakkanen)
Maxime Morariu-Patrichi
Abstract

First, I will present the original motivation of my research, which is limit order book modelling. Most of trading now happens on electronic markets through a limit order book mechanism. In short, the limit order book is the collection of outstanding buy and sell orders for a given stock. Economically, it conveys information on the current supply of and demand for the security. I will show an animation of a limit order book that is based on real data. Second, inspired by the limit order book modelling problem, I will introduce a new class of marked point processes, that we name hybrid. A hybrid marked point point process models the arrival in time of random events and the time evolution of the state of a system. I will discuss a key example that we call state-dependent Hawkes processes and explain how it compares to the existing literature, and, in particular, to classical Hawkes processes and continuous-time Markov chains. Third, hybrid marked point processes are defined in a self-referential manner and, thus, it is not clear a priori that they exist, i.e., that they are well-defined mathematical objects. We address this existence problem by studying a well-known Poisson-driven stochastic differential equation. The existing strong existence and uniqueness results rely on a Lipschitz condition that hybrid marked point processes may fail to satisfy. This motivates us to propose a natural pathwise construction that instead requires only a sublinearity condition. Using a domination argument, we are able to verify that this construction yields indeed a solution. As we restrict ourselves to non-explosive marked point processes, we also manage to prove uniqueness without any specific assumptions.

(25/10/17) Markovian Approximation for the Generalized Langevin Equation
Kalle Timperi
Abstract

The aim of my PhD project is to develop more efficient and accurate numerical algo- rithms for analysing and simulating the generalized Langevin equation (GLE), a stochastic integro-differential equation which has recently gained popularity as a more realistic model for several phenom- ena in different contexts, including anomalous dif- fusion in biological flu- ids, microrheology, heat transport within nano-scale devices, and nuclear quantum effects. In climate modeling the GLE arises through the Mori-Zwanzig formalism as the equation describing the coarse-grained reduced- order model of an initially high-order model. The advantage of the GLE over the conventional Langevin equation is that it allows for the incorpo- ration of temporally non-local drag forces through an integration kernel in the diffusion term. This also poses new challenges for both the analyti- cal and numerical treatment of the dynamics de- scribed by the equation. Also, the applicability of existing numerical schemes in practical contexts requires careful analysis of the measurement and modeling errors associated with these techniques.

(25/10/17) Link of Singularities
Mirko Mauri
Abstract

The link of a complex isolated singularities is the odd-dimensional real manifold cut out by a sphere of radius arbitrarily small centred at that point. It plays a significant role in the description of the topology of a neighbourhood of the singularity. Unluckily, even basic invariants, like its fundamental group, are not fully understood.

In this expository talk I will provide some motivational examples without particular algebro-geometric prerequisites.

You can find a funny 3-minute introduction to the subject at https://www.youtube.com/watch?v=TpB9pa3j0l0.

(01/11/17) Wet Thermodynamics Of The Atmosphere — A “Condensed” Summary
Tom Bendall
Abstract

The goal of my talk is to show how the introduction of moisture changes the behaviour and governing equations of the atmosphere. I will start by summarising the thermodynamics of a dry atmosphere (one in the absence of water), before giving a more complicated description with gaseous and liquid water.

(01/11/17)Building your own finite element solver in Firedrake
Thomas Gibson
Abstract

In this talk, we present a new contribution to the automation and abstraction of the finite element method, the Firedrake Project at Imperial College London. The result is a more complete separation of concerns which eases the incorporation of separate contributions from computer scientists, numerical analysts and application specialists alike. We will discuss how Firedrake can be employed in designing sophisticated solvers and dynamical cores for problems in computational science.

(08/11/17) Field Theories for Stochastic Processes with Applications to Biology
Johannes Pausch
Abstract

Field Theories have been extremely successful in describing the world from quantum to galactic scales, from single particles to particle ensembles, and from from equilibrium to non-equilibrium. In this talk, I am going to present a flavour of statistical field theory that deals with stochastic processes which often are interpreted as reaction-diffusion processes. However, the realm of these stochastic processes goes way beyond standard reaction-diffusion processes. Our framework can deal with continuous, discrete and hybrid spaces, moving boundaries, memory, to name but a few. For illustration, we are going to look at an example from cell-biology: microtubule growth.

(15/11/17) Eddy-Induced Oceanic Lagrangian Transport
Josie Park
Abstract

Eddies (small scale structures) are essential in the distribution and transport of oceanic tracers, i.e heat, salt or biochemical tracers. The gulf stream is a perfect example of this as it transports warm salty waters across the North Atlantic, while further acting as a partial barrier to transport across its core. General ocean circulation models (GCMs) lack the necessary resolution to resolve these small scale effects and so therefore they must be approximated. I will be discussing the importance of Eddy Induced Transport in the Oceans, failings of the current approach used to approximate it, and possible alternative approaches.

(15/11/17) A Parameterisations of turbulent eddies in oceanic general circulation models
Mike Haigh
Abstract

Many large-scale oceanic phenomena, e.g. the Gulf Stream, are driven by turbulent eddies which themselves exist on lengthscales on the order of 100km (mesoscale). The fact that such small-scale turbulent structures drive the large-scale ocean circulation gives rise to one of the greatest problems in geophysical fluid dynamics. The equations governing geophysical fluid flow are too complex to solve analytically, and we must therefore employ numerical models which solve the governing equations on a discrete grid. However, in order to numerically resolve the important turbulent flows, we typically require grid-scales on the order of 1km. Doing this is often computationally unfeasible, and we must therefore solve the governing equations on a coarse grid which is unable to capture the effects of small-scale flows. The solution is to define a parameterisation to be included in a coarse-grid model, which accounts for the effects of the turbulent eddies on the large-scale flow. I will describe the numerous methods that have been invoked to define eddy parameterisations, and outline my own research in this area

(22/11/17) Optimal market making across different asset classes
Douglas Machado Vieira
Abstract

In financial markets, a market maker is a market participant that continuously provide both buy and sell quotes for a single or multiple assets. This agent is crucial for maintaining the liquidity of the markets in which they participate. The profit of the market maker comes from the spread between these quotes. Tight spread implies more attractive prices and, hence, a flow of trades, at the cost of less profit per round-trip transaction. On the other hand, given that supply and demand change over time, the market maker has to dynamically control their quotes, otherwise they risk accumulating excessively high positive or negative positions in the traded asset, exposing them to market risk. In this talk, I will introduce the problem of optimal quotes for a market making strategy using optimal stochastic control theory. Then, I will expose the latest advancements in the literature and what challenges are involved when extending the models towards different asset classes.

(22/11/17) Optimal market making across different asset classes
Douglas Machado Vieira
Abstract

In financial markets, a market maker is a market participant that continuously provide both buy and sell quotes for a single or multiple assets. This agent is crucial for maintaining the liquidity of the markets in which they participate. The profit of the market maker comes from the spread between these quotes. Tight spread implies more attractive prices and, hence, a flow of trades, at the cost of less profit per round-trip transaction. On the other hand, given that supply and demand change over time, the market maker has to dynamically control their quotes, otherwise they risk accumulating excessively high positive or negative positions in the traded asset, exposing them to market risk. In this talk, I will introduce the problem of optimal quotes for a market making strategy using optimal stochastic control theory. Then, I will expose the latest advancements in the literature and what challenges are involved when extending the models towards different asset classes.

(29/11/17) Particle Filtering for Stochastic Navier-Stokes equations
Francesc Pons Llopis
Abstract

We consider the problem of Filtering for stochastic partial differential equations. We focus on the case with 2-D irrotational stochastic Navier-Stokes equations defined on a torus as signal, and incomplete (finite dimensional) Eulerian observations. Particle Filter methods offer a mathematically rigorous approximations with known convergence rate to optimal filter solution. However, this method is too computationally expensive to be of any practical use in high dimensions (curse of dimensionality). We study different modifications of the traditional Bootstrap Particle Filter algorithm which can help overcome these limitations. Those modifications are importance sampling and/or a combination of tempering steps and MCMC moves. Numerical results show that those modifications render important improvements compared to traditional particle filter.

(29/11/17) The Mathematics of Pastries
Andreas Bock
Abstract

This talk aims to give an overview of shape analysis i.e. it means to compare two shapes or images mathematically. Appealing to intuition, the audience will sample various different flavours of mathematics such as Riemannian geometry, functional analysis and fluid mechanics. Shape analysis is an exciting and relatively new area so above all we strive to keep the exposition accessible to individuals with any kind of mathematical background.

 

(06/12/17) Graph theory from a geometrical perspective
Alexis Arnaudon
Abstract

In this talk, I will introduce basic concepts of graph theory from the perspective of differential geometry by thinking of a graph as a ‘discretized manifold’. Although this interpretation breaks down as soon as the structure of the graph is not regular, many tools from differential geometry still survive. I will show several useful examples of these constructions in the context of community detection algorithms.

(06/12/17) A journey from kinetic transport models to fractional-diffusion-advection equations
Pedro Aceves
Abstract

n recent years the concept of superdiffusion has been found to be a useful tool to describe many phenomenon appearing in nature. In particular, it has been recently discovered that the bacteria E. coli may exhibit a superdiffusive behavior under certain circumstances. E. coli is a microorganism that swims towards regions of higher chemoatractants, and away from unfavorable environments. This type of behavior is known as chemotaxis. The movement of E. coli is characterized by a series of run-and-tumble events, which can be modeled via a velocity-jump process. Hence, a possible way to describe it is through kinetic transport equations. Due to the fact that E. coli was found to have a superdiffusive behavior, the Keller-Segel model, which is commonly used to describe the movement of E. coli, fails in describing the behavior of it under this setting. In this talk we shall introduce some kinetic models with a given chemoatractant concentration, and perform the rigorous passage to the macroscopic limit, obtaining fractionaldiffusion-advection equations. The coefficients of the latter equations depend on the microscopic quantities governing the movement of the agents.

 

Spring 2017: [Archive] Autumn 2016: [Archive]

Spring 2016: [Schedule] [Archive] Autumn 2015: [Schedule] [Archive]

Spring 2015: [Schedule] [Archive] Autumn 2014: [Schedule] [Archive]