# 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)

### Sir Vaughan F.R. Jones, outstanding mathematician and incoming member of the Abel committee, has passed away

(11.09.2020) More### The Norwegian Academy of Science and Letters calls for nominations of candidates for the Abel Prize 2021

(03.07.2020) More### The Honouring of the 2020 Abel Prize Laureates

All events in connection to the Abel Prize Week in May are cancelled due to the Corona pandemic. The 2020 Abel Prize Laureates Hillel Furstenberg and Gregory Margulis will be honoured, together with the Abel Prize Laureate(s) of 2021 during next year’s Abel Prize Ceremony, May 25 2021.

### Furstenberg and Margulis to share the Abel Prize

The Abel Prize for 2020 goes to Hillel Furstenberg, Hebrew University of Jerusalem, Israel and Gregory Margulis, Yale University, New Haven, CT, USA, for “pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics.”

(13.03.2020) More### President of the Academy announces Abel Prize winner

The President of the Norwegian Academy of Science and Letters, Hans Petter Graver will announce the winner of the 2020 on March 18. The Academy's choice of laureate is based on the Abel Committee's recommendation.

**The event will be in an all-digital format and streamed live from this location**