Postdoctoral fellowship to Sune Precht Reeh
PhD student at the Department of Mathematical Sciences, Sune Precht Reeh, has received a postdoctoral fellowship at 1.7 million DKK from the Danish Council for Independent Research. The grant is to be used on a two-year study in the United States, primarily at Massachusetts Institute of Technology (MIT).
The Danish Council for Independent Research / Natural Sciences this time awards 12 postdoc grants to research talents in Denmark to a total sum of approximately DKK 19 million DKK, with the aim of providing younger researchers the best possible conditions for producing outstanding research results at a high international level.
Sune's project title is “Fusion systems and Burnside rings in equivariant stable homotopy theory”. He says about the project:
"I will continue my work with fusion systems and Burnside rings. Unlike earlier, where I mainly worked algebraically, I will utilize the expertise that is at MIT and Harvard in equivariant stable homotopy theory to explore the topological aspects of my research."
Before heading to Boston, Sune will participate in the Algebraic Topology program at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California. There will be several high quality conferences as well as top scientists visiting MSRI for the entire program. Sune has been offered to visit as a Program Associate.
At MIT Sune’s main host will be Professor Haynes Miller, who Sune himself calls "my mathematical grandfather " - as it is his PhD-supervisor's supervisor. Sune hopes to meet many other researchers from the Boston area. The project budget includes funds to participate in topology conferences in the U.S. and to visit other researchers.
Sune Precht Reeh is completing his doctoral studies at the Department of Mathematical Sciences, University of Copenhagen, and is a member of the Centre for Symmetry and Deformation. In addition to his research Sune has been involved with mathematics interested high school students, especially through the Danish Youth Association of Science, where he has been co-organizer of their Math Summer Camps.
A study of symmetries and spectra
In his project description Sune elaborate on the research ahead:
"A group action studies an object from its symmetries. For example, there are 24 ways in which a 6-sided dice can be rotated. The group of rotations is said to "act" on the dice. The same group can act on several different objects: the same 24 rotations will also give symmetries of an 8-sided dice. The Burnside ring of a group is studying what happens when multiple actions of the same group are combined.
“In a fusion system you study the sub-structure of a group that has to do with a chosen primes p. How much can you say about a group from its p-structure? And if two groups have the same p-structure, what do they have in common?
“In stable homotopy theory you examine the properties of objects that are stable when the dimension of the object is increased again and again towards infinity. Such stable objects are called spectra. Any group of symmetries also has an associated spectrum, and the "Segal conjecture" (that is proven to be true) gives a strong connection between a group's spectrum and the Burnside ring.
“The proposed project will shed light on the relationships between fusion systems and spectra."