# 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)

### Record turnout for Atiyah’s Abel Lecture at ICM in Rio

1250 mathematicians from all over the world filled the big conference hall in Rio de Janeiro on Monday the 6^{th} of August to listen to Sir Michael Atiyah’s Abel Lecture, “The Future of Mathematical Physics: New ideas in old bottles”.

### Sir Michael Atiyah gives Abel lecture at ICM in Rio

Sir Michael Atiyah who receiced the Abel Prize in 2004, shared with Isadore Singer, will give the Abel Lecture at ICM in Rio on the 6th of August. He has titled the lecture: "The Future of Mathematical Physics: new ideas in old bottles". Atiyah will be introduced by Jacob Palis, former president of the International Mathematical Union and a member of the Abel Committee.

(26.07.2018) More### Robert P. Langlands received the Abel Prize from H.M. King Harald

In the University Aula in Oslo, surrounded by Munch's paintings and a diverse mathematical audience, Robert P. Langlands was today, May 22, awarded the Abel Prize for 2018 by H.M. King Harald. Langlands received the award of 6 million NOK “for his visionary program connecting representation theory to number theory.” The Langlands program is frequently described as a grand unified theory of mathematics.

(22.05.2018) More### The Abel lectures 2018

Abel Laureate Robert Langlands gave his prize lecture titled "*On the geometric theory" *at the University of Oslo on the 23th of May. John Rognes, chair of the Abel committee, introduced Langlands to an almost full auditorium. Langlands' lecture was followed by two others talks, by Jim Arthur and Edward Frenkel. Watch the lectures live

### Would you like to attend the 2018 Abel Prize award ceremony?

The Abel Prize award ceremony takes place at 22 may 2018, 14:00 in the University Aula in Oslo, Norway. His Majesty King Harald V will present the prize to this year’s laureate, Robert P. Langlands. The ceremony is open, but requires registration. For registration, click here.

(11.04.2018) More