Ryo Kato's home page

About me

• The (stable) homotopy groups of spheres
• Picard group of stable homotopy categories
• Bousfield lattice of stable homotopy categories
• Picard graded homotopy groups
• Cohomology groups of generalized Weierstrass Hopf algebroids

Curriculum Vitae

Papers

1. R. Kato and K. Shimomura, A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence,
   to appear in Mathemaical Journal of Okayama University.
2. R. Kato, The E(1)-local Picard graded homotopy groups of the sphere spectrum at the prime two,
   to appear in Hiroshima Mathematical Journal.
3. R. Kato, H. Okajima and K. Shimomura, Notes on an algebraic stable homotopy category,
   to appear in Poroceedings on ``Surveys around Ohkawa's theorem on Bousfield classes''. Springer
4. R. Kato, The TR-groups of the sphere spectrum at the prime two,
   Kochi J. Math. 11 (2016), 59-69. pdf
5. R. Kato, K. Shimomura and Y. Tatehara, Generalized Bousfield lattices and a generalized retract conjecture,
   Publ. Res. Inst. Math. Sci. 50 (2014), no. 3, 497-513.
6. R. Kato and K. Shimomura, The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime,
   Nagoya Math. J. 207 (2012), 951-961.
7. R. Kato and K. Shimomura, Products of Greek letter elements dug up from the third Morava stabilizer algebra,
   Algebr. Geom. Topol. 12 (2012), no.2, 951-961.

Talks

1. BP, E_n and K(n),
   Ryo Kato,
   Workshop on Geometric perspective of toplogical modular forms, The University of Tokyo, Japan, November 2012.
2. On the K-theory of local fields,
   Ryo Kato,
   West coast algebraic topology summer school 2012: Advances in K-theory, Stanford University, California state in USA, July 2012.
3. The stable homotopy groups of spheres and the Adams-Novikov spectral sequence,
   Ryo Kato,
   Young topologists meeting 2011, The Ecole Polytechnique Federale de Lausanne in Lausanne, Switzerland, June 2011.