Discipline of Mathematical Sciences Colloquium 2024

2 April 2024
2:10 to 3:00 pm

Professor Shane G. Henderson

Cornell University

COVID-19 Modeling to Keep Cornell University Open Throughout the Pandemic

Unlike most universities, Cornell University reopened its Ithaca campus for in-person instruction in the Fall of 2020 during the COVID period and did so safely through the use of pooled testing. This decision and many others were guided by our mathematical modeling group. I'll discuss some of the questions we explored, the models we built, the data that informed our models, how we dealt with several central data issues including tremendous uncertainty in parameter choices for models, and how our outsized influence on Cornell COVID policy came about in the first place.

Professor Shane G. Henderson holds the Charles W. Lake, Jr. Chair in Productivity in the School of Operations Research and Information Engineering (ORIE) at Cornell University. His research interests include discrete-event simulation, simulation optimization, emergency services planning and transportation. He is the editor in chief of the open-access journal Stochastic Systems. He is an INFORMS Fellow and a co-recipient of the INFORMS Wagner Prize for his work on bike-sharing programs. He has served as Director of the School of ORIE, as Chair of the INFORMS Applied Probability Society, and as simulation area editor for Operations Research. He has previously held positions in the Department of Industrial and Operations Engineering at the University of Michigan and the Department of Engineering Science at the University of Auckland.

31 May 2024
2:00 to 3:00 pm

Lisette de Pillis

Harvey Mudd College, Claremont, California

Professor of Mathematics and Norman F. Sprague Professor of Life Sciences

Mathematical Modelling of Biological Systems - From Rabbits to Cancer

Mathematical models hold the keys to understanding some of the most interesting and complex phenomena in the natural world. In this talk, we will see examples of how to harness insights from known physical scenarios and the power of mathematical modeling to answer new questions that may at first appear intractable. Can the concept of an overflowing bathtub help us understand the dynamics of an epidemic? Can the interactions between a rabbit and a lynx give insight into how immune cells fight cancer? By making a few simplifying assumptions, we can draw parallels between natural systems that may appear radically different on the surface to unlock new levels of understanding in the world around us.

23 August 2024
2:10 to 3:00 pm

Dr Susan Wei

University of Melbourne

Towards a Mathematical Foundation of Deep Learning

This talk will explore the ongoing efforts to construct a robust mathematical foundation for deep learning. We will start with a concise introduction to deep learning and its fundamental principles. Key challenges and open questions will be highlighted, focusing on how three simple ingredients—data, network architecture, and training dynamics—conspire to produce remarkable behaviours. We will also examine the potential of singular learning theory, emphasising its utility in deriving theory-driven hypotheses that enhance our understanding of deep learning. This presentation aims to engage both mathematicians and data science practitioners, offering insights into the evolving theoretical frameworks that underpin deep learning.

Leah Edelstein-Keshet

(Emeritus professor)
Dept of Mathematics,
University of British Columbia

Local and nonlocal models for the formation of robust cell clusters

In developmental biology, clusters of cells are known to stay in a group while migrating to some target site. But what keeps those cells together? Similar questions have been posed for swarms of insects, flocks of birds, and/or collective behaviour of agents. I will focus on continuum models for cell density. Both long-ranged (interaction at a distance) and local effective forces have been considered, leading to integro-PDEs and their local PDE approximations. I will describe recent work with Andreas Buttenschoen and Shona Sinclair on Morse potentials, derivation of such potentials from an underlying chemotaxis mechanism (dating back to Alex Mogilner, 1995), and predictions for what combination of attractant and repellent is consistent with robust clusters.

18 October 2024
2:10 to 3:00 pm

Mathematical inevitability

I am a category theorist, and in this talk I hope to give you a flavour of the kinds of problems that category theorists are concerned with.

In particular, I want to look at what might be termed “mathematical inevitability". This relates to the view of mathematics as a kind of discourse between coming up with brilliant new ideas, and working out the consequences of those ideas. For instance, the integers with their addition might be considered a brilliant idea; but now the question arises whether multiplication is a new brilliant idea on top of that, or simply a natural consequence of addition.

Mathematical inevitability is about showing that things which appear to be brilliant ideas of their own are actually natural consequences of something more basic; expressing the sense in which they are natural consequences often leads into the domain of category theory. I hope to illustrate this with a range of examples which touch on areas such as algebra, logic, probability, operator algebra and programming language semantics.