19th Colloque Wright - The Art of Maths

Videos from the 19th Colloque Wright - The Art of Maths (Geneva 2-6 November 2020) Public talks.

Etienne Ghys

(2 NOVEMBER 2020)

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Chaos: unpredictable but understandable

Etienne Ghys Research Director at CNRS, Professor at the École normale supérieure in Lyon Permanent Secretary of the Academy of Science of France It is unusual for a mathematical idea to spread through society. But this is the case with chaos theory, popularized by the butterfly effect, imagined by the American meteorologist Edward Lorenz, who in 1972 asked the famous question: “Does the flapping of a butterfly’s wings in Brazil trigger a tornado in Texas?” The idea in this picture is that a small cause can have big consequences. But can chaos theory be summed up in such a simplistic way? Can a scientific theory be satisfied with negative statements? Are mathematicians responsible for the inadequate transmission of this theory? This lecture will attempt to address these questions and, in particular, to describe the positive side of the theory. Because there is a positive side. Chaos sometimes creates a kind of order. Chaotic systems may be unpredictable, but they are far from incomprehensible.

Laure Saint-Raymond

(3 NOVEMBER 2020)

Disorder, chance and large numbers

Laure Saint-Raymond Professor at the École normale supérieure in Lyon Bôcher Memorial Prize in 2020 Disorder increases irreversibly. This statement does not necessarily apply at any given time to a child’s bedroom or to the way the world works. Rather, it is the statement of the second principle of thermodynamics, expressed by the physicist Sadi Carnot in 1824. It is a principle that can be experienced every day. When milk is poured into water, for example, the two liquids mix and do not remain separated from each other. Playing balls in a bag will not spontaneously line up according to their colour but will mix randomly. While it is easy to mix two gases together, it is almost impossible to separate them once they have been brought together. This talk takes a look at a simple mathematical model that explains why we can observe spontaneous mixing but not the opposite phenomenon. Spoiler alert: the key to understanding this temporal irreversibility lies in probability theory and more precisely in the law of large numbers.

Martin Hairer

(4 NOVEMBER 2020)

A mathematical journey From the infinitely small to the infinitely large

Martin Hairer Professor of mathematics at Imperial College London Fields Medal in 2014 The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty different scales of size. As we move from one to the other, the laws of nature can sometimes behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton’s classical mechanics, not to mention other intermediate theories. Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics. The aim of this talk is to explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models, despite their superficially playful character, can sometimes lead to certain quantitative predictions.

Alain Connes

(5 NOVEMBER 2020)

The music of shapes

Alain Connes Professor at the Collège de France, at the Institut des hautes études scientifiques at the University of Paris-Saclay and at Ohio State University, Columbus Fields medal in 1982 Quantum physics, especially matrix mechanics, has had a profound influence on mathematical notions of geometric space. This lecture will explain this link by dealing, among other things, with «spectra» and «the music of shapes». Indeed, if the geometrical characteristics of an instrument, for example, determine the sounds it can produce, then conversely, knowledge of the scale and chords produced by an object is sufficient to reconstruct its shape. This property makes it possible to characterize geometrical shapes from invariants that do not refer to a coordinate system. The resulting new geometry, illustrating the mathematical link between visual and auditory perception, has a wealth of applications in physics, in particular for gravitation and quantum physics. This lecture will also be an opportunity to discuss the meaning of the notions of variability and the emergence of time.

Stanislav Smirnov

(6 NOVEMBER 2020)

Mathematics : art or science?

Mathematics is an amazing and mysterious science. Ever since the time of Plato, philosophers argue whether mathematical objects are imaginary, or whether they come from the real world, while mathematicians mostly prove theorems without even asking about their link to reality. On the other hand, the Pharaohs of Egypt and the Kings of Babylon had already grasped the practical power of mathematics, and of course the technological advances of the past two centuries are built on successful applications of our science. Where does mathematics come from? Why is the “imaginary” science so useful in real life? How mathematicians choose problems to work on, and why do they find their science so fascinating? We will not be able to answer all these questions in our talk, but we will try to give a glimpse of how mathematicians work.