Kyushu University Academic Staff Educational and Research Activities Database
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Yuichiro Takeda Last modified date:2019.06.20

Associate Professor / Mathematics: Mathematics
Department of Mathematics
Faculty of Mathematics


Graduate School
Undergraduate School


E-Mail
Academic Degree
Doctor of Science
Country of degree conferring institution (Overseas)
No
Field of Specialization
Algebraic geometry, Arithmetic geometry
Total Priod of education and research career in the foreign country
00years00months
Outline Activities
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
Research Interests
  • A research on t-core partitions
    keyword : t-core partitions, quadratic forms
    2016.04.
  • 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
Papers
1. José Ignacio Burgos Gil, Elisenda Feliu and Yuichiro Takeda, On Goncharov’s Regulator and Higher Arithmetic Chow Groups, International Mathematics Research Notices, 10.1093/imrn/rnq066, 2010.04.
2. Yuichiro Takeda, Higher Algebraic K-theory, Publ. Math. RIMS, 2005.07.
3. Yuichiro Takeda, Complexes of exact hermitian cubes and the Zagier conjecture, Mathematische Annalen, 10.1007/s00208-003-0474-1, 328, 1-2, 87-119, 2003.12.
Educational
Educational Activities
I give lectures of differential calculus and linear algebra. I also give lectures of algebra and geometry in the department of mathematics and the graduate school of mathematics. I supervise some graduate students.