Our annual student organised event, showcasing three diverse talks from esteemed colleagues across the UK and Atlantic. Join us for a virtual drinks reception afterwards!
Valerio Lucarini (University of Reading) – “A new mathematical framework for Atmospheric Blocking Events”
We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events, which are associated with low frequency, large scale waves in the atmosphere. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with conditions of anomalously high instability of the atmosphere. Additionally, the lifetime of a blocking is positively correlated with the intensity of such an anomaly, against intuition. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking, while a relative increase of predictability is found in the mature phase, while the opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. We associate blockings to a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor of the system. The UPOs differ substantially in terms of instability, which explains the diversity of the atmosphere in terms predictability. The UPOs associated to blockings are indeed anomalously unstable, which leads to them being rarely visited. The onset of a blocking takes place when the trajectory of the system hops into the neighbourhood of one of these special UPOs. The decay takes place when the trajectory hops back to the neighbourhood of usual, less unstable UPOs associated with zonal flow. This justifies the classical Markov chains-based analysis of transitions between weather regimes. The existence of UPOs differing in the dimensionality of their unstable manifold indicates a very strong violation of hyperbolicity in the model, which leads to a lack of structural stability. We propose that this is could be a generic feature of atmospheric models and might be a fundamental cause behind difficulties in representing blockings for the current climate and uncertainties in predicting how their statistics will change as a result of climate change.
2.30pm – 3.15pm:
Yonatan Berman (London Mathematical Laboratory) – “The Ergodicity Problem in Economics”
The ergodicity problem queries the equality or inequality of time averages and expectation values. I will trace its curious history, beginning with the origins of formal probability theory in the context of gambling and economic problems in the 17th century. This is long before ergodicity was a word or a known concept, which led to an implicit assumption of ergodicity in the foundations of economic theory. Over the past decade we have asked what happens to foundational problems in economic theory if we export what is known about the ergodicity problem in physics and mathematics back to economics. Many problems can be resolved. Following an overview of our theoretical and conceptual progress, I will report on a recent experiment that strongly supports our view that human economic behavior is better described as optimizing time-average growth rates of wealth than as optimizing expectation values of wealth or utility of wealth.
3.30pm – 4.15pm:
Morgan Craig (University of Montreal) – “Exploiting heterogeneity to personalize oncolytic virus immunotherapy”
Cancer is an intrinsically heterogeneous disease distinguished by disparate outcomes based on cancer types, patient-specific characteristics, and treatment modalities. The classic approach to most cancer treatments is to administer cyclic chemotherapy at the maximal tolerable dose to reduce the tumour burden. Unfortunately, this is also generally accompanied by a host of secondary toxicity events, as cytotoxic chemotherapy also destroys healthy cells, primarily white blood cells. Instead, cancer immunotherapies aim to leverage the body’s own immune defence mechanisms against the tumour. Oncolytic viruses (OVs) are a type of immunotherapy that preferentially target cancerous cells, infecting and destroying them and simultaneously bolstering immune responses. Certain OVs are already clinically-available, however a barrier to their development is the heterogenous response to treatment observed in trials. It is therefore crucial to characterize heterogeneity within and around the tumour, and to quantify the effects that neighbouring tumour and immune cells have on therapeutic success. Here I will discuss quantitative approaches my lab uses to provide a way to test and optimize OV protocols before they are used in patients, ultimately reducing bottlenecks along the drug development pipeline, rationalizing therapeutic scheduling, and improving patient outcomes.
Virtual wine reception