L1

What do fiber polymers and ice sheets have in common? They both flow with a directionally dependent - anisotropic - viscosity. This behaviour occurs in other geophysical flows, such as the Earth's mantle, where a material's microstructure affects its large-scale flow. In ice, the alignment of crystal orientations can cause the viscosity to vary by an order of magnitude, consequently having a strong impact on the flow of ice sheets and glaciers. However, the effect of anisotropy on large-scale flow is not well understood, due to a lack of understanding of a) the best physical approximations to model crystal orientations, and b) how crystal orientations affect rheology. In this work, we aim to address both these questions by linking rheology to crystal orientation predictions, and testing a range of models against observations from the Greenland ice sheet. The results show assuming all grains experience approximately the same stress provides realistic predictions, and we suggest a set of equations and parameters which can be used in large-scale models of ice sheets. 

Neural network architectures play a key role in determining which functions are fit to training data and the resulting generalization properties of learned predictors. For instance, imagine training an overparameterized neural network to interpolate a set of training samples using weight decay; the network architecture will influence which interpolating function is learned. 

In this talk, I will describe new insights into the role of network depth in machine learning using the notion of representation costs – i.e., how much it “costs” for a neural network to represent some function f. Understanding representation costs helps reveal the role of network depth in machine learning. First, we will see that there is a family of functions that can be learned with depth-3 networks when the number of samples is polynomial in the input dimension d, but which cannot be learned with depth-2 networks unless the number of samples is exponential in d. Furthermore, no functions can easily be learned with depth-2 networks while being difficult to learn with depth-3 networks. 

Together, these results mean deeper networks have an unambiguous advantage over shallower networks in terms of sample complexity. Second, I will show that adding linear layers to a ReLU network yields a representation cost that favors functions with latent low-dimension structure, such as single- and multi-index models. Together, these results highlight the role of network depth from a function space perspective and yield new tools for understanding neural network generalization. 

Conferences and networking are important parts of academic life, particularly early in your academic career.  But how do you make the most out of conferences?  And what are the does and don'ts of networking?  Learn about the answers to these questions and more in this panel discussion by postdocs from across the Mathematical Institute.

Join us for a session with Keith Macksoud, Executive Director at global recruitment consultant Options Group in London and who previously has > 20 years’ experience in Prime Brokerage Sales at Morgan Stanley, Citi, and Deutsche Bank.  Keith will discuss the recruitment process for financial institutions, and how to increase your chances of a successful application. 

Keith will detail his finance background in Prime Brokerage and provide students with an exclusive look behind the scenes of executive search and strategic consulting firm Options Group. We will look at what Options Group does, how executive search firms work and the Firm’s 30-year track record of placing individuals at many of the industries’ largest and most successful global investment banks, investment managers and other financial services-related organisations. 

About Options Group

Options Group is a leading global executive search and strategic consulting firm specializing in financial services including capital markets, global markets, alternative investments, hedge funds, and private banking/wealth management.

https://www.optionsgroup.com/

What makes a good talk? This year, graduate students and postdocs will give a series talks on how to give talks! There may even be a small prize for the audience’s favourite.

If you’d like to have a go at informing, entertaining, or just have an axe to grind about a particularly bad talk you had to sit through, we’d love to hear from you (you can email Ric Wade or ask any of the organizers).
 

Speaker: James Taylor
Title: D-Modules and p-adic Representations

Abstract: The representation theory of finite groups is a beautiful and well-understood subject. However, when one considers more complicated groups things become more interesting, and to classify their representations is often a much harder problem. In this talk, I will introduce the classical theory, the particular groups I am interested in, and explain how one might hope to understand their representations through the use of D-modules - the algebraic incarnation of differential equations.

Speaker: Anthony Webster
Title: An Introduction to Epidemiology and Causal Inference

Abstract: This talk will introduce epidemiology and causal inference from the perspective of a statistician and former theoretical physicist. Despite their studies being underpinned by deep and often complex mathematics, epidemiologists are generally more concerned by seemingly mundane information about the relationships between potential risk factors and disease. Because of this, I will argue that a good epidemiologist with minimal statistical knowledge, will often do better than a highly trained statistician. I will also argue that causal assumptions are a necessary part of epidemiology, should be made more explicitly, and allow a much wider range of causal inferences to be explored. In the process, I will introduce ideas from epidemiology and causal inference such as Mendelian Randomisation and the "do calculus", methodological approaches that will increasingly underpin data-driven population research.