Yakov Sinai, Professor of Mathematics at Princeton University since 1993, has been awarded the 2014 Abel Prize for his groundbreaking research in dynamical systems, ergodic theory and mathematical physics. A stipend of approximately USD $1,000,000 accompanies the prize, which is often referred to as the “Nobel Prize” of mathematics.
The Abel Prize is named after Niels Henrik Abel, a Norwegian mathematician of the early 19th century who laid the foundation for group theory. “Abelian groups” are named after Abel. The awarding of the Abel Prize to Sinai strikes close to home for one of the present bloggers (DHB), since ergodic theory was his research and dissertation topic while a graduate student at Stanford.
In simplified terms, ergodic theory deals with processes and systems with the property that sampling over time gives statistics identical to averaging over space. Ergodic systems often exhibit intriguing properties such as chaotic behavior, where tiny changes to the system at certain points result in wildly different behavior at subsequent times, yet in a larger sense the system exhibits certain very predictable properties.
As an example of an ergodic system, consider the behavior of gas molecules in a container. One expects that if we follow a single molecule of gas in a container over time, the fraction of the time that it visits a small cube within that container should be the same as the volume of that cube divided by the volume of the container. As another example, familiar to many in sunny climates, pool sweeps that travel in a chaotic pattern around the bottom of a backyard swimming pool are observed to spend roughly the same amount of time in different locations within the pool (although this is not a perfect analogy, since the sweep moves more slowly when it climbs steep sides of the pool).
Sinai has published over 250 research papers, mostly in the arena of ergodic theory and dynamical systems. A number of widely used models and concepts are named after Sinai, including, for instance, the well-known “Kolmogorov-Sinai (K-S) entropy measure. Some other terms named after Sinai include “Sinai’s billiards”, the “Sinai random walk,” “Sinai-Ruelle-Bowen measures,” and “Pirogov-Sinai theory.”
For additional details, see articles in the Economist and Scientific American.