Yuichiro Takeda | Last modified date：2020.01.29 |

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.

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

2016.04～2019.03. - 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**

**Papers**

Educational

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