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 firstname.lastname@example.org. You can also sign up to our Mailing List to receive regular updates on these events!
Venue: Huxley 130
Time: Wednesday 4pm-5pm
(25/10/17) Markovian Approximation for the Generalized Langevin Equation
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.
(03/10/17) Kidneys and Map Colouring: an exploration of graph theory
(03/10/17) An Introduction to Spatial Network
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]
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)
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.