*The Della Pietra Lecture Series is pleased to present Dr. Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick, England, and popular-science and science-fiction writer.*

**Special Presentation for Students, **Wednesday September 25, 2019, at **11:00am**, Simons Center Della Pietra Family Auditorium

**Title: **Cows, Mice, and Sonic Hedgehogs

**Abstract:** Painters, poets, and writers have long been captivated by the extraordinary beauty of animals in the wild. Who could fail to be moved by the power and elegance of a Siberian tiger, the ponderous enormity of an elephant, the haughty pose of a giraffe, or the pop-art stripes of a zebra? Yet each of these animals began life as a single cell, a fusion of sperm and egg. How do you cram an elephant into a cell? When the structure of DNA was discovered, the answer seemed simple. You don’t. What you cram into an elephant egg is the *information* required to make an elephant. However, the cells still have to be assembled in the right way. How does this happen?

An intriguing answer came from the imagination of a great mathematician, Alan Turing. Turing is famous for his wartime code-breaking and his fundamental contributions to computer science and artificial intelligence. It is less well known that he was also a pioneer of mathematical biology.

In 1952 Turing proposed a mechanism for the creation of animal markings. He suggested that these patterns appear in two stages. While the animal is still an embryo, biological molecules react with each other, and diffuse across its surface. The result is a ‘pre-pattern’ of chemicals, which later turns into the observed pattern by triggering the production of pigment proteins. The heart of his theory is a system of mathematical ‘reaction-diffusion’ equations, which give rise to many patterns, includeing stripes, spots, and many more complex markings. They are remarkably similar to the patterns seen on innumerable animals, tropical fish, and seashells, and are often extraordinarily beautiful.

Initial interest in Turing’s theory died down, but it has undergone a serious revival in recent years, mainly as a result of new biological discoveries. The talk will describe the theory, and these new results. It will be non-technical and highly illustrated, with plenty of examples.

**General Public Lecture, **Thursday September 26, 2019 at **5:45 pm**, Simons Center Della Pietra Family Auditorium **(Reception at 5:00pm)**

**Title:** The Math of Visual Illusions.

**Abstract:** Puzzling things happen in human perception when ambiguous or incomplete information is presented to the eyes.** **Rivalry occurs when two different images, presented one to each eye, lead to alternating percepts, possibly of neither image separately. Illusions, or multistable figures, occur when a single image can be perceived in several ways. The Necker cube is the most famous example. Impossible objects arise when a single image is has locally consistent but globally inconsistent geometry. Famous examples are the Penrose triangle and etchings by Maurits Escher.

These phenomena provide clues about the workings of the visual system. We describe recent research modeling how the brain can make decisions. A neural network is designed to interpret incoming sensory data in terms of previously learned patterns. Rivalry occurs when different interpretations are confused, and illusions arise when the same data have several interpretations. Impossible objects are sometimes associated with switching between different interpretations of an ambiguous figure.

The lecture will be non-technical and highly illustrated, with plenty of examples.

**Dr. Stewart will deliver a third technical lecture for faculty and advanced graduate students as part of the ****SCGP Weekly Colloquium**** on Tuesday September 24 at 1:00pm.**

*All of these lectures have been made possible by a generous donation from the Della Pietra family. The Della Pietra Lecture Series aims to bring world-renowned scientists to the Simons Center for Geometry and Physics to enhance the intellectual activity of the Center and also bring greater awareness of recent and impactful discoveries in Physics and Mathematics to the Long Island community.*

For more information visit our website or call 631-632-2800.

**Ian Stewart** FRS is Emeritus Professor of Mathematics at the University of Warwick and a leading populariser of mathematics. He is author or coauthor of over 200 research papers on pattern formation, chaos, network dynamics, and biomathematics. He has been a Fellow of the Royal Society since 2001, and recently served on Council, its governing body, for three years. He has five honorary doctorates and is an honorary wizard of Unseen University on Terry Pratchett’s fictional Discworld.

He has published more than 120 books including *Why Beauty is Truth*, *Professor Stewart’s Cabinet of Mathematical* *Curiosities, Calculating the Cosmos, Significant Figures, *and the four-volume series *The Science of Discworld *with Terry Pratchett and Jack Cohen. He has also written the science fiction novels *Wheelers *and *Heaven *with Jack Cohen, and *The Living Labyrinth* and *Rock Star* with Tim Poston.

He wrote the Mathematical Recreations column for *Scientific American *from 1990 to 2001. His 90 television appearances include the 1997 Royal Institution Christmas Lectures for the BBC. In one lecture he brought a live tiger into the lecture room, and in another he vanished in a puff of smoke after demonstrating time travel using a wormhole. He has made over 450 radio broadcasts, most of them about mathematics for the general public, and has delivered hundreds of public lectures on mathematics, including the Queen’s Lecture in Berlin. He was Gresham Professor of Geometry at Gresham College, London from 1994 to 1998, delivering six public lectures each year.

His awards include the Royal Society’s Faraday Medal, the Gold Medal of the Institute of Mathematics and Its Applications, the Zeeman Medal (IMA and London Mathematical Society), the Lewis Thomas Prize (Rockefeller University), the Euler Book Prize (Mathematical Association of America), and the Bloody Stupid Johnson Award (Discworld Convention).