News: Mar 24, 2017
This year’s grants from Wallenberg Foundation’s investment in mathematics go to 13 mathematicians, including David Witt Nyström who receive a grant for recruiting a postdoctor and Dmitrii Zhelezov who receive a grant for a postdoctoral position at a foreign university.
Since 2014, the Knut and Alice Wallenberg Foundation and the Royal Swedish Academy of Sciences have supported mathematical research in Sweden through an extensive mathematics program. Its aim is that Sweden will regain an internationally leading position in the area. New mathematics is necessary for increasing areas of use in both research and industry. The funding does not target a particular area of mathematics, but will support basic research.
David Witt Nyström will receive funding to recruit an international researcher for a postdoctoral position at the Department of Mathematics, Chalmers University of Technology and the University of Gothenburg, Sweden. The proposed researcher Ya Dang will defend his doctoral thesis in May and is a Ph.D. student to Professor Jean-Pierre Demailly, Institute Fourier in Grenoble, who is a world leading researcher in Kähler geometry and who has had collaborations with the Complex Analysis group of the department earlier.
Algebraic geometry, which has its roots in classical antiquity, is one of the oldest and most extensive branches of mathematics. New theories within its domain continue to arise, creating new methods for solving as yet unproven problems. Due to the wealth of new ideas, existing fields of mathematical research have been divided into smaller branches, such as complex geometry, which is at the heart of the current project. Algebraic geometry studies sets consisting of solutions to polynomial equations. Such solution sets can take the form of circles, ellipses, spheres, and other geometric objects. For example, two points can be associated with a one-dimensional family of circles crossing both points. This is an example of a linear series, which is an important field of study in algebraic geometry.
In the beginning of the 1990s, a Russian-American mathematician, Andrei Okounkov, introduced a way of associating each linear series with a convex body, called an Okounkov body. In 2006 he received the most prestigious award in mathematics, the Field’s medal, which is awarded to eminent mathematicians under forty years old. These convex Okounkov bodies have been successfully used to explain the properties of linear systems. The theory of linear systems is also connected to Kähler geometry, which is a meeting place for complex geometry, differential geometry, and symplectic geometry. It is assumed that the well-known and fundamental results regarding linear series can be generalized to a broader Kähler setting. Such generalizations would have significant consequences for Kähler geometry. Even though it remains to be seen which generalizations are possible, interesting open problems abound.
Dmitrii Zhelezov will receive funding for a postdoctoral position at a foreign university and funding for two years after returning to Sweden. He will hold a postdoctoral position with Professor Endre Szemerédi at Alfréd Rényi Institute of Mathematics in Budapest, Hungary. Dmitrii Zhelezov received his Ph.D. in Mathematics from Chalmers University of Technology in 2016 with the thesis ”Additively and multiplicatively structured sets” and was employed at the Department of Mathematical Sciences until August 2016.
The aim of the project is to study arithmetic combinatorics, a branch of number theory. In contrast to other branches of mathematics, combinatorics focuses on specific problems, which are easy to formulate but notoriously difficult to solve, even when sometimes no mathematical apparatus beyond high school level is necessary for the solution. One of the most famous problems in number theory is the Goldbach conjecture, which states that every even integer greater than two can be expressed as a sum of two prime numbers. In 1742, German mathematician Christian Goldbach formulated the conjecture in a letter to a Swiss mathematician, Leonard Euler, by then already recognized as a genius. Euler’s response confirmed that he thought it was true but he couldn’t prove it. Nor has anyone else been able to do so, in the almost 300 years since. The difficulty in proving the conjecture stems from the fact that it refers to addition, whereas prime numbers are defined through multiplication – an integer is prime if it can be divided only by 1 and by itself. However, not much is known about how prime numbers should be linked to addition.
A set of sums consists of the sums of all pairs of elements in a given set. The Goldbach conjecture asks whether the set of sums of prime numbers contains all even numbers greater than two. Initially, easy to handle questions about sets of sums can be studied. Subsequently, more advanced new tools and sophisticated methods, which had been developed for other problems, can be applied. Sets of sums have many other applications as well. The methods and concepts of abstract number theory have been successfully applied to modern cryptography. They are used to process our credit card payments as well as when we surf the internet.
Photo: Setta Aspström
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In case of doubt or confusion, the Swedish version of this press release takes precedence.