Professor Isaksen publishes research article in PNAS
In October 2020, WSU mathematics Professor Daniel Isaksen and his collaborators Guozhen Wang (at Fudan University, in Shanghai, China) and Zhouli Xu (at University of California, San Diego) published their research article "Stable homotopy groups of spheres" in the journal Proceedings of the National Academy of Sciences (PNAS). PNAS is a very prestigious journal which publishes papers reporting new advances in the physical, social, and biological sciences. Since the scope of PNAS is so broad, covering so many different subjects, the journal makes an effort to be very selective, and to only publish papers whose results will be of serious interest to a very wide scientific audience. PNAS publishes very few articles in pure mathematics, and it is a significant honor to have an article accepted there.
Professor Isaksen's article in PNAS is about the new results obtained by the new methods he developed in collaboration with Wang and Xu for the sake of calculation of 2-primary stable homotopy groups of spheres. Roughly speaking, these calculations give deep data about the classification of geometric spaces built by "sewing" or "gluing" together two spheres of very large dimension. That same data is used as the input for solving many other geometric classification problems in high dimensions, involving spaces much too complicated to be built from just two spheres. A brief and approachable (for a mathematical audience) survey of the problem and known results is contained in the Isaksen-Wang-Xu paper, which you can read here: PNAS
This is a significant advance on one of the hardest central problems in algebraic topology, and WSU is proud of Professor Isaksen's accomplishment.