|Official Title||Associate Professor|
|Affiliation||Natural Sciences, Science and Engineering|
|Profile||I am interested in the structure of the stable homotopy category of spectra, and I have been working on it using some gadgets like Adams or Adams-Novikov spectral sequence. Of course, the relevant computations are very hard as much as ``Tour de France''.
Recently, I have been trying to obtain information about the stable homotopy groups of spheres using cohomology theories that are not complex orientable. Typical examples of such theories are the topological modular forms and real Johonson-Wilson-theory, which is obtained by taking the homotopy fixed points of the spectrum representing the complex Johnson-Wilson theory. For example, it has already been shown abroad that this theory can be used to solve the problem of embedding projective spaces into Euclidean spaces. I believe that ER theory may be applied to other specific problems, such as determining the LS category of a space. In addition, I am currently working on a spectrum classification problem using quasi-equivalence related to ER theory.
|Research Field(Keyword & Summary)||
|Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS)||https://nrid.nii.ac.jp/en/nrid/1000080343739/|
|Recruitment of research assistant(s)||No|
|Affiliated academic society (Membership type)||The Mathematical Society of Japan|
|Education Field (Undergraduate level)||calculus, multivariable calculus, linear algebra, set theory, basic topology|
|Education Field (Graduate level)||homotopy theory, algebraic topology|