Combining chaos theory and geometry, the mathematician received the prestigious Abel Prize

Dennis Sullivan was awarded the 2022 Abel Prize, one of the most prestigious prizes in mathematics, for his contributions to the fields of topology and dynamical systems.

According to a statement from the Norwegian Academy of Sciences and Letters (DNVA), American mathematician Dennis Sullivan has been awarded the 2022 Abel Prize for his groundbreaking contributions to the field of topology thanks to his contributions to the field of topology. combines algebra, geometry and dynamics.

Mathematician Dennis Sullivan.

Topology is the study of the properties of objects and spaces that do not change when they are deformed. These objects can be visualized as a form of "rubber geometry", because even though objects are stretched into different shapes like rubber pads, their bond cannot be broken. .

For example, a square can be deformed into a circle without "breaking", but a donut structure (with another circle inside) cannot. Thus, a square can be viewed as topologically equivalent to a circle.

Sullivan, is currently a professor of mathematics at Stony Brook University in New York (USA). He began studying topology as a graduate student at Princeton University in the early 1960s.

His 1966 doctoral thesis, entitled "Triangulation Homotopy Equivalences," helped revolutionize the study of manifolds, or spaces that "look flat" when viewed from any point on their surface but have a complex overall structure (like the surface of a sphere).

Dennis Sullivan speaks on a blackboard at Stony Brook University in New York, USA.

In the following decades, Sullivan went on to receive a scholarship to the University of Warwick in the UK; University of California, Berkeley; and MIT. According to DNVA, he has gradually changed the way that mathematicians think about algebraic topology and geometry by introducing new ideas and constructing a new set of "vocabularies".

In 1970 he wrote a collection of unpublished, but widely circulated, and widely regarded notes that directly influenced the classification of manifolds and problems. focus in algebraic topology.

In the late 1970s, Sullivan began to work on problems in dynamic systems, including the study of a moving point in geometric space and as a fundamental part of chaos theory (also known as chaos theory). Carry).

His work combined dynamical systems and algebraic topology in ways that had never been done before. In 1985, Sullivan proved a 60-year-old hypothesis that points moving through a complex dynamical system in a fractal pattern would eventually return to their starting point instead of "wandering" endlessly. .

With his theories, Sullivan repeatedly changed the understanding of topology by introducing new concepts, proving landmark theorems, refuting old hypotheses, and formulating new theories. new problems, thereby pushing this field to new heights.

The Abel Prize is an award given annually by the King of Norway to outstanding mathematicians. The award ceremony took place in the hall of the Faculty of Law at the University of Oslo, where the Nobel Peace Prize ceremony took place from 1947 to 1989. The Abel Prize Committee also established the Abel Conference, which is administered by the Society. Norwegian Mathematics.