Doctor of Science

No

Algebraic geometry, Arithmetic geometry

00years06months

Research Activities:
I study arithmetic geometry. The algebraic K-theory and the regulator map are the main topic of my study. These objects are closely related to the L-function of an algebraic variety. My aim is to find an elementary description of elements of the algebraic K-theory and to calculate the image of these elements by the regulator map.

Teaching Activities:
I provide several lectures of mathematics for freshmen and sophomores, and provide lectures of algebra and topology in the department of mathematics. I also gives lectures of topology for students of graduate course of mathematics.

Research Interests

• A research on t-core partitions
  keyword : t-core partitions, quadratic forms
  2016.04～2019.03.
• A research on higher arithmetic Riemann-Roch theorem
  keyword : Chern character, Arakelov geometry, analytic torsion
  2014.04.
• A research on higher arithmetic Chern character
  keyword : Chern character, Arakelov geometry, algebraic cycles
  2010.04～2014.03.
• Research on the regulator map by using algebraic cycles
  keyword : algebraic cycles, regulator map
  2007.03～2016.03Goncharov conjectured that one can construct elements of K-theory by using functional equations satisfied by polylogarithm functions. In this research, I am tackling this problem using integrals along algebraic cycles. To be more precise, I would like to achieve the following: Firstly, I prove that the integrals along algebraic cycles describe the regulator maps. Next I compose algebraic cycles on algebraic varieties from the polylog cycles defined by Bloch. In doing so, functional equations satisfied by polylogarithm functions play an important role. Finally, I obtain some new results on regulator maps by calculating the integrals of certain differential forms along these algebraic cycles..
• Higher K-theory in Arakelov geometry, the regulator map of number fields
  keyword : algebraic K-theory, Arakelov geometry
  2002.04～2007.03I have constructed an analogue of algebraic K-theory in Arakelov geometry, and showed that it possesses the product structure. Moreover, I have found an another proof of the Zagier conjecture about the regulator map for an algebraic number field. Now I am interested in the regulator map for an arbitrary algebraic variety..

Academic Activities

Educational Activities