Past Forthcoming Seminars

26 January 2018
14:15
Abstract

In contemporary ecology and mathematical biology undergraduate courses, textbooks focus on competition and predation models despite it being accepted that most species on Earth are involved in mutualist relationships. Mutualism is usually discussed more briefly in texts, often from an observational perspective, and obligate mutualism mostly not at all. Part of the reason for this is the lack of a simple math model to successfully explain the observations. Traditionally, particular nonlinearities  are used, which produce a variety of apparently disparate models.

The failure of the traditional linear model to describe coexisting mutualists has been documented from May (1973) through Murray (2001) to Bronstein (2015). Here we argue that this could be because of the use of carrying capacity, and propose the use of a nutrient pool instead, which implies the need for an autotroph (e.g. a plant) that converts nutrients into living resources for higher trophic levels. We show that such a linear model can successfully explain the major features of obligate mutualism when simple expressions for obligated growth are included.

  • Mathematical Geoscience Seminar
26 January 2018
14:00
Abstract

I will discuss a new theoretical approach to information and decisions in signalling systems and relate this to new experimental results about the NF-kappaB signalling system. NF-kappaB is an exemplar system that controls inflammation and in different contexts has varying effects on cell death and cell division. It is commonly claimed that it is information processing hub, taking in signals about the infection and stress status of the tissue environment and as a consequence of the oscillations, transmitting higher amounts of information to the hundreds of genes it controls. My aim is to develop a conceptual and mathematical framework to enable a rigorous quantifiable discussion of information in this context in order to follow Francis Crick's counsel that it is better in biology to follow the flow of information than those of matter or energy. In my approach the value of the information in the signalling system is defined by how well it can be used to make the "correct decisions" when those "decisions" are made by molecular networks. As part of this I will introduce a new mathematical method for the analysis and simulation of large stochastic non-linear oscillating systems. This allows an analytic analysis of the stochastic relationship between input and response and shows that for tightly-coupled systems like those based on current models for signalling systems, clocks, and the cell cycle this relationship is highly constrained and non-generic.

  • Mathematical Biology and Ecology Seminar
26 January 2018
13:00
Abstract


In the 12 months from the middle of June 2016 to the middle of June 2017, a number of events occurred in a relatively short period of time, all of which either had, or had the potential to have,  a considerably volatile impact upon financial markets. The events referred to here are the Brexit  referendum (23 June 2016), the US election (8 November 2016), the 2017 French elections (23 April and 7 May 2017) and the surprise 2017 UK parliamentary election (8 June 2017). 
All of these events - the Brexit referendum and the Trump election in particular - were notable both for their impact upon financial markets after the event and the degree to which the markets failed to anticipate these events. A natural question to ask is whether these could have been predicted, given information freely available in the financial markets beforehand. In this talk, we focus on market expectations for price action around Brexit and the Trump election, based on information available in the traded foreign exchange options market. We also investigate the horizon date of 30 March 2019, when the two year time window that started with the Article 50 notification on 29 March 2017 will terminate.
Mathematically, we construct a mixture model corresponding to two scenarios for the GBPUSD exchange rate after the referendum vote, one scenario for “remain” and one for “leave”. Calibrating this model to four months of market data, from 24 February to 22 June 2016, we find that a “leave” vote was associated with a predicted devaluation of the British pound to approximately 1.37 USD per GBP, a 4.5% devaluation, and quite consistent with the observed post-referendum exchange rate move down from 1.4877 to 1.3622. We find similar predictive power for USDMXN in the case of the 2016 US presidential election. We argue that we can apply the same bimodal mixture model technique to construct two states of the world corresponding to soft Brexit (continued access to the single market) and hard Brexit (failure of negotiations in this regard).
 

  • Mathematical Finance Internal Seminar
25 January 2018
17:00
Mark McCartney
Abstract

James Clerk Maxwell (1831–1879) was, by any measure, a natural philosopher of the first rank who made wide-ranging contributions to science. He also, however, wrote poetry.

In this talk examples of Maxwell’s poetry will be discussed in the context of a biographical sketch. It will be  argued that not only was Maxwell a good poet, but that his poetry enriches our view of his life and its intellectual context.

  • History of Mathematics
25 January 2018
16:00
Martin Huessman
Abstract

In classical optimal transport, the contributions of Benamou–Brenier and 
Mc-Cann regarding the time-dependent version of the problem are 
cornerstones of the field and form the basis for a variety of 
applications in other mathematical areas.

Based on a weak length relaxation we suggest a Benamou-Brenier type 
formulation of martingale optimal transport. We give an explicit 
probabilistic representation of the optimizer for a specific cost 
function leading to a continuous Markov-martingale M with several 
notable properties: In a specific sense it mimics the movement of a 
Brownian particle as closely as possible subject to the marginal 
conditions a time 0 and 1. Similar to McCann’s 
displacement-interpolation, M provides a time-consistent interpolation 
between $\mu$ and $\nu$. For particular choices of the initial and 
terminal law, M recovers archetypical martingales such as Brownian 
motion, geometric Brownian motion, and the Bass martingale. Furthermore, 
it yields a new approach to Kellerer’s theorem.

(based on joint work with J. Backhoff, M. Beiglböck, S. Källblad, and D. 
Trevisan)

  • Mathematical and Computational Finance Seminar
25 January 2018
16:00
Lucia Mocz
Abstract

The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness statements. In this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are able to use these techniques to moreover develop new Colmez-type formulas for the Faltings height.

  • Number Theory Seminar
25 January 2018
16:00
to
17:30
Abstract

How do organisms cope with cellular variability to achieve well-defined morphologies and architectures? We are addressing this question by combining experiments with live plants and analyses of (stochastic) models that integrate cell-cell communication and tissue mechanics. During the talk, I will survey our results concerning plant architecture (phyllotaxis) and organ morphogenesis.

  • Industrial and Applied Mathematics Seminar
25 January 2018
14:00
Bart Vandereycken
Abstract

We present discrete methods for computing low-rank approximations of time-dependent tensors that are the solution of a differential equation. The approximation format can be Tucker, tensor trains, MPS or hierarchical tensors. We will consider two types of discrete integrators: projection methods based on quasi-optimal metric projection, and splitting methods based on inexact solutions of substeps. For both approaches we show numerically and theoretically that their behaviour is superior compared to standard methods applied to the so-called gauged equations. In particular, the error bounds are robust in the presence of small singular values of the tensor’s matricisations. Based on joint work with Emil Kieri, Christian Lubich, and Hanna Walach.

  • Computational Mathematics and Applications Seminar

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