## Calendar Entry

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*May 30, 2017 - May 30, 2017*

*18:00 - 19:00*

### Details

**6pm, 30 May 2017**

Newhaven Lecture Theatre

ICMS, 15 South College Street

Edinburgh, EH8 9AA

Tickets are free but should be reserved in advance via Eventbrite.

**A public lecture byTerry Lyons, Oxford**

Newton, around 1665-7 developed his theory of fluxions which gave us the tools of calculus and differential equations. They provide mathematical models for interacting systems, predict the elliptical orbits of planets, and with their extension to partial differential equations provide the models engineers use to understand much of our physical world. However, the theory is an infinitesimal one that relies on smoothness and is not adapted to the complex oscillatory streams that can arise when there is randomness.

Itô (from 1944 on) broadened the calculus to deal with the models incorporating Brownian type systems that had been introduced by Wiener, Thiele, Einstein and Bachelier some half a century earlier. Stochastic differential equations were also to change the world. Man on the moon, telecommunications, finance, photo-chemistry, … are all deeply impacted.

Rough path theory, and Regularity structures are a next step. They provide a new way to describe complex data streams; it is a description that is top down rather than bottom up and links basic analysis and algebra in unexpected ways. It allows a new calculus of rough differential equations that can capture interactions between vastly extended types of streams.

The ramifications span pure and applied perspectives.

Many models in Physics have been given rigorous mathematical meaning (by Hairer et al.) for the first time. Very current contributions to data science have also grown out of this theory. The state of the art in labelling human actions from visual data, or in recognising finger gestures on the screen of a mobile phone as (Chinese) handwriting are good examples. An app using rough path technology has been downloaded to the android over a million times and used for billions of decisions.

Doors open at 17:30. The talk will be followed by an informal reception to which all ticket holders are invited.