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# Footnotes to Turing (1952): Some Modern Challenges in Pattern Formation

## 28 October 2021 @ 13:00 – 14:00

## Abstract

Motivated by recent work with biologists, I will showcase some mathematical results on Turing instabilities in complex domains. This is scientiﬁcally related to understanding developmental tuning in a variety of settings such as mouse whiskers, human ﬁngerprints, bat teeth, and more generally pattern formation on multiple scales and evolving domains. Some of these problems are natural extensions of classical reaction-diffusion models, amenable to standard linear stability analysis, whereas others require the development of new tools and approaches. These approaches also help close the vast gap between the simple theory of diﬀusion-driven pattern formation, and the messy reality of biological development, though there is still much work to be done in validating even complex theories against the rich dynamics observed in nature. I will emphasize throughout the role that Turing’s 1952 paper had in these developments, and how much of our modern progress (and difficulties) were predicted in this paper. I will close by discussing a range of open questions, many of which fall well beyond the extensions I will discuss, but at least some of which were known to Turing.

### Dr Andrew Krause

I grew up in New Mexico, USA, where I earned undergraduate degrees in Mathematics and Computer Science at the New Mexico Institute of Mining and Technology in 2012, and a Masters degree in Mathematical Analysis in 2014. I then obtained a DPhil (PhD) in Mathematics within the Oxford Centre for Industrial and Applied Mathematics in 2018, and continued as a postdoc in the Wolfson Centre for Mathematical Biology before becoming a Departmental Lecturer in Applied Mathematics jointly between these two groups. I left Oxford in September of this year to join the Department of Mathematical Sciences at Durham University, where I am an Assistant Professor of Applied Mathematics.

**Check back on the day of the event for the Teams link.**

**This will also be streamed in A17, Mathematical Sciences Building for those on campus.**