# Mathematical billiards and chaos

### Abel Lectures 2014 at the University of Oslo, Norway

The Abel Laureate Yakov Sinai will give his prize lecture at the University of Oslo on 21 May. This will be followed by two Abel Lectures by Gregory Margulis and Konstantin Khanin. Domokos Szász will give the popular science lecture titeled "Mathematical billiards and chaos". See lecture summaries below.

10.00

Yakov Sinai: Now everything has been started? The origin of deterministic chaos

The theory of deterministic chaos studies statistical properties of solutions of non-linear equations and has many applications.The appearence of these properties is connected with intrinsic instability of dynamics.

11:05

Gergory Margulis: Kolmogorov-Sinai entropy and homogeneous dynamics

Homogeneous dynamics is another name for flows on homogeneous spaces. It was realized during last the 30--40 years that such dynamics have many applications to certain problems in number theory and Diophantine approximation. In my talk I will describe some of these applications and briefly explain the role of Kolmogorov-Sinai entropy in the proof of corresponding results from homogeneous dynamics.

12:45**Konstantin Khanin: Between mathematics and physics**

Over the past few decades we have witnessed an unparalleled process of unification between mathematics and physics. In this talk we shall discuss some of Sinai's seminal results which hugely contributed to this process. Sinai's contributions were based on outstanding new ideas in such core areas of mathematical physics as statistical mechanics, spectral theory of Schrödinger operators, renormalization theory, and turbulence.

14:15

Domokos Szász: Mathematical billiards and chaos

Can random behavior arise in purely deterministic systems? By way of responding to that question the theory of hyperbolic dynamical systems made a spectacular progress in the 1960's. Phenomenologically, being chaotic can be seen as being sensitive to initial conditions, something borne out in nature by the difficulty of forecasting weather or earthquakes, . . . (Sci-fi has dubbed this as the 'butterfly effect'.) To produce a mathematical model of chaotic motion Sinai, in the 60's, introduced scattering billiards, i. e. those with convex obstacles (like flippers in bingo halls). He also showed that the simplest' Sinai billiard was ergodic. This opened the way to answering a 1872 hypothesis of the great Austrian physicist Boltzmann, a hypothesis that, in the 1930's, also led to the birth of ergodic theory. Beyond their mathematical beauty and fruitful interconnections with many branches of mathematics, chaotic billiards are most appropriate models where laws of statistical physics can be verified. A celebrated example is Einstein's 1905 diffusion equation.

I intend to explain - for a general audience - some of Sinai's groundbreaking ideas and their implications for chaotic billiards. No particular background knowledge will be assumed.

### Practical information

21 May, 10:00 - 15.15

University of Oslo, Georg Sverdrup's House, Auditorium 1

The lectures are open, but the free lunch requires registration at abelprisen@dnva.no

### See detailed program(PDF)

### Abel in Oxford" with lecture by Sir Andrew Wiles

It has become a tradition that the Abel Committee after its final meeting hosts an Abel seminar. This year the committee meeting at London Mathematical Society was followed by "Abel in Oxford" with Abel Laureate Andrew Wiles as the main speaker. Martin Bridson, head of the Mathematical Institute, University of Oxford and Camilla Serck-Hanssen, Vice President of the Norwegian Academy of Science and Letters gave introductory talks.

(02.02.2018) More### Yves Meyer received the Abel Prize from H.M. King Harald

H.M. King Harald presented the Abel Prize to Yves Meyer of the École normale supérieure Paris-Saclay, France at an award ceremony in Oslo on 23 May. He receives the prize for his pivotal role in the development of the mathematical theory of wavelets, says John Rognes, chair of the Abel committee. Among the prominent guests attending the award ceremony was the French ambassador to Norway, Jean-François Dobelle and the Norwegian Minister of Education and Research, Torbjřrn Rře Isaksen.

(26.05.2017) More### Three days of celebration for Abel Laureate Yves Meyer

His Majesty King Harald will present the Abel Prize to Yves Meyer at an award ceremony in Oslo on 23 May. He receives the prize "for his pivotal role in the development of the mathematical theory of wavelets", to quote the Abel committee. Yves Meyer, of the École normale supérieure Paris-Saclay, was the visionary leader in the modern development of this theory, at the intersection of mathematics, information technology and computational science.

(12.05.2017) More### The Abel lectures 2017

Abel Laureate Yves Meyer gave his prize lecture at the University of Oslo on the 24th of May, with following Abel lectures by Stéphane Mallat, Ingrid Daubechies og Emmanuel Jean Candčs. Watch the lectures here.

(08.05.2017) More### Congratulations from AMS President

"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Yves Meyer, recipient of the 2017 Abel Prize. Professor Meyer has been a visionary in a broad range of fields, including number theory and differential equations. His fundamental work in the theory of wavelets has transformed the world of signal processing and has led to a myriad of practical applications." -- AMS President Kenneth A. Ribet (University of California, Berkeley)

Photo: Jim Brook

(02.04.2017) More