Abel Awards 2020

2020/03/30 Roa Zubia, Guillermo - Elhuyar Zientzia

• Sariak
• Matematika

This year have received the Abel award two people who have worked with the theory of chaos: Hillel Furstenberg and Gregory Margulis. Margulis also won the Fields medal in 1978. But as a Jew in Russia, and because of the situation of the Jews in that country, they did not give him a visa to go to pick up the prize. Furstenberg is also a Jew, born in Germany during the Nazis, and fled to the United States when the Second World War broke out. He has always been very good mathematician. When Americans saw their signature in an article, they believed that Furstenberg was the pseudonym of a group of mathematicians.

Hillel Furstenberg and Gregory Margulis investigated the same, but each in a different place. Random walks were investigated. Imagine that you go out to the street with a die. And you have to start walking according to the number that shows by throwing the die. With the first, a step toward the north, with the double toward the south, with the triple toward the east and with the four toward the west, for example (forget the fifth and the sixth). If you launch the dice for each step, the path you are going to make will be very chaotic. You will hardly advance correctly. For example, if the die always shows the same number, of course. The paths thus created are random paths. Random, as the angloxasons say, they can be very useful for exploration.

The truth is that in this type of tracks are also patterns. The theory of chaos seeks patterns and a certain order in chaotic systems. Having said this, what did Furstenberg and Margulis do? For they applied mathematics of probability in such a system. We spoke of mathematics and, of course, they did not apply with a given the movement of a person going out to the street, but with a system of multiplication of mathematical matrices. In the end, they calculated how many random means were effective in carrying out these matrices products. And, surprisingly, many of these paths served for this work. It seems to be a very mathematical issue, without interest, but no. In addition to in mathematics, this calculation of random routes is applicable to the thousand system. For example, how to connect a computer network in a company (an Intranet). Which machine must be connected to have an efficient cluster network? Well, the formulas of the theorems of Furstenberg and Margulis help to find an effective configuration.

That is, the Abel prize is a well-deserved prize for Furstenberg and Margulis 2020, which combines the theory of chaos, probability and other branches of mathematics. But the truth is that the crisis of the coronavirus has delayed the delivery of prizes for the year 2021. Both awards will be presented next year at the same event.