Per Alexandersson received his Ph.D. in mathematics at Stockholm University in 2013. He will hold a postdoctoral position in Professor James Haglund’s research group at the University of Pennsylvania in Philadelphia, USA.
The research project to be undertaken together with Professor Haglund consists of two related problems in the representation theory and the theory of symmetric functions, i.e. functions, which do not change under permutations of their variables. Irreducible characters are the key objects studied in the theory of representations. They can be thought of as the primary indivisible elements from which larger objects are built. One can think of an analogy with prime numbers, which constitute indivisible factors of all whole numbers.
The study of the important concept of a bi-graded ring stands at the center of the first problem. Some of the key questions involve the properties of the ring. Some researchers think that by studying the geometric properties of the so-called hyper-plane arrangements one can find the sizes of the ring’s components. However, the problem is still open. Several eminent mathematicians are active in this area of research.
The second problem consists of the study of the coefficients of certain symmetric polynomials. Their applications spread over several fields of mathematics including representation theory, harmonic analysis, and combinatorics. In addition to their significance in pure mathematics, symmetric functions and the representation theory have found many applications. For example, they are used in quantum physics, and in image compression.
Photo Gaudeamus/ Stockholm University