Yukihiro UCHIDA - My portal - researchmap

Profile Information

Affiliation: Associate Professor, Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University

Degree: Ph.D. (Mathematical Science)(Mar, 2008, Nagoya University)

Researcher number: 90533258
J-GLOBAL ID: 201401030901633570
researchmap Member ID: B000238016

External link: https://y-uchida.fpark.tmu.ac.jp/index_e.html

Research Areas

1

Natural sciences / Algebra /

Research History

8

Apr, 2020 - Present

Associate Professor, Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University
Apr, 2018 - Mar, 2020

Associate Professor, Department of Mathematical Sciences, Graduate School of Science, Tokyo Metropolitan University
Apr, 2012 - Mar, 2018

Associate Professor, Department of Mathematics and Information Sciences, Graduate School of Science and Engineering, Tokyo Metropolitan University
Apr, 2009 - Mar, 2012

Research Fellow of the Japan Society for the Promotion of Science (PD), Graduate School of Science, Kyoto University
Oct, 2008 - Mar, 2009

GCOE Program-Specific Research Fellow, Graduate School of Science, Kyoto University
Apr, 2008 - Sep, 2008

Research Fellow of the Japan Society for the Promotion of Science (PD), Graduate School of Mathematics, Nagoya University
Apr, 2007 - Mar, 2008

Research Fellow of the Japan Society for the Promotion of Science (DC2), Graduate School of Mathematics, Nagoya University
Jul, 2006 - Mar, 2007

Research Assistant, Graduate School of Mathematics, Nagoya University

Education

3

Apr, 2006 - Mar, 2008

Doctoral Program, Graduate School of Mathematics, Nagoya University
Apr, 2004 - Mar, 2006

Master's Program, Graduate School of Mathematics, Nagoya University
Apr, 2000 - Mar, 2004

Department of Mathematics, School of Science, Nagoya University

Committee Memberships

3

Apr, 2013 - Present

Secretary, Activity Group on Algorithmic Number Theory and Its Applications, The Japan Society for Industrial and Applied Mathematics
Apr, 2024 - Mar, 2025

Representative Member, The Japan Society for Industrial and Applied Mathematics
Apr, 2021 - Mar, 2024

Editor, Tokyo Journal of Mathematics

Awards

1

Sep, 2017

Best Paper Award 2017 (Survey), The Japan Society for Industrial and Applied Mathematics

Yukihiro UCHIDA

Papers

13

The local-global property for bitangents of plane quartics

Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, Takashi Taniguchi, Yukihiro Uchida

JSIAM Lett., 12 41-44, 2020 Peer-reviewed
Algebro-geometric aspects of the Christoffel-Darboux kernels for classical orthogonal polynomials

Masanori Sawa, Yukihiro Uchida

Trans. Amer. Math. Soc., 373(2) 1243-1264, 2020 Peer-reviewed
Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations

Masanori Sawa, Yukihiro Uchida

J. Math. Soc. Japan, 71(3) 831-860, 2019 Peer-reviewed
Counting points on hyperelliptic curves of genus 2 with real models

Yukihiro Uchida

JSIAM Lett., 11 1-4, 2019 Peer-reviewed
Computing the Mordell-Weil Groups of Hyperelliptic Jacobians

Yukihiro UCHIDA

Transactions of the Japan Society for Industrial and Applied Mathematics, 25(3) 229-253, 2015 Peer-reviewed
A small secret exponent attack on cryptosystems using Dickson polynomials

Akihiko Onishi, Yukihiro Uchida, Shigenori Uchiyama

JSIAM Lett., 7 41-43, 2015 Peer-reviewed
The elliptic curve Diffie-Hellman problem and an equivalent hard problem for elliptic divisibility sequences

Junichi Yarimizu, Yukihiro Uchida, Shigenori Uchiyama

JSIAM Lett., 6 5-7, 2014 Peer-reviewed
The Tate-Lichtenbaum Pairing on a Hyperelliptic Curve via Hyperelliptic Nets.

Yukihiro Uchida, Shigenori Uchiyama

Pairing-Based Cryptography - Pairing 2012 - 5th International Conference, Cologne, Germany, May 16-18, 2012, Revised Selected Papers, 2011 218-233, 2012 Peer-reviewed
Valuations of Somos 4 sequences and canonical local heights on elliptic curves

Yukihiro Uchida

Math. Proc. Cambridge Philos. Soc., 150(3) 385-397, 2011 Peer-reviewed
Canonical local heights and multiplication formulas for the Jacobians of curves of genus 2

Yukihiro Uchida

Acta Arith., 149(2) 111-130, 2011 Peer-reviewed
Division polynomials and canonical local heights on hyperelliptic Jacobians

Yukihiro Uchida

Manuscripta Math., 134(3-4) 273-308, 2011 Peer-reviewed
The difference between the ordinary height and the canonical height on elliptic curves

Yukihiro Uchida

J. Number Theory, 128(2) 263-279, 2008 Peer-reviewed
On the difference between the ordinary height and the canonical height on elliptic curves

Yukihiro Uchida

Proc. Japan Acad. Ser. A Math. Sci., 82(3) 56-60, 2006 Peer-reviewed

Misc.

4

Periods modulo $p$ of integer sequences associated with division polynomials of genus $2$ curves

Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, Takashi Taniguchi, Yukihiro Uchida

arXiv, Oct 2, 2023
On the rationality of classical orthogonal polynomials, quadrature formulas and geometric designs

Masanori Sawa, Yukihiro Uchida

Sugaku, 75(3) 295-314, Jul, 2023 Peer-reviewedInvited
A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps

Hiro-o Tokunaga, Yukihiro Uchida

arXiv, Aug, 2018
From cryptography to number theory : some algorithms on algebraic curves (Analytic Number Theory : Number Theory through Approximation and Asymptotics)

UCHIYAMA Shigenori, UCHIDA Yukihiro

RIMS Kokyuroku, 1874 32-44, Jan, 2014

Presentations

67

On explicit construction of rational interval designs

Teruyuki Mishima, Masanori Sawa, Yukihiro Uchida, Xiao-Nan Lu

MSJ Autumn Meeting 2024, Sep, 2024
On explicit construction of rational interval designs

Yukihiro Uchida

Niigata Algebra Seminar, Jun, 2024 Invited
Explicit construction of rational interval design and Hilbert–Kamke problem

Teruyuki Mishima, Masanori Sawa, Yukihiro Uchida, Xiao-Nan Lu

MSJ Spring Meeting 2024, Mar, 2024
有理的interval designの明示的構成法とHilbert-Kamke問題

三島輝之, 澤正憲, 内田幸寛, Xiao-Nan Lu

2023年度応用数学合同研究集会, Dec, 2023
The problem of the existence of centrally symmetric rational designs

Teruyuki Mishima, Masanori Sawa, Yukihiro Uchida

MSJ Autumn Meeting 2023, Sep, 2023
Periodicity of Somos sequences related to curves of genus 2

内田幸寛

京大数論合同セミナー, May, 2023 Invited
Periodicity of Somos sequences related to curves of genus 2

Yukihiro Uchida

Number Theory in Tokyo, Mar, 2023 Invited
矩形求積公式の有理性に関する不定方程式と準直交多項式

内田幸寛

第2回神戸整数論ミニワークショップ, Jan, 2021 Invited
矩形求積公式の有理性と不定方程式

内田幸寛

第17回数理科学コロキウム, Nov, 2020
quadrature公式の有理性について

澤正憲, 内田幸寛

日本応用数理学会2020年研究部会連合発表会, Mar, 2020
平面4次曲線の双接線に関する局所大域性

伊藤哲史, 石塚裕大, 内田幸寛, 大下達也, 谷口隆

日本応用数理学会2019年研究部会連合発表会, Mar, 2019
古典準直交多項式の判別式の明示公式とその応用

澤正憲, 内田幸寛

日本数学会2018年度秋季総合分科会, Sep, 2018
実モデルを持つ種数2の超楕円曲線の位数計算

内田幸寛

日本応用数理学会2017年度年会, Sep, 2017
高さとArakelov理論，それらのGalois表現の計算への応用

内田幸寛

2017年度第25回整数論サマースクール「楕円曲線とモジュラー形式の計算」, Aug, 2017 Invited
種数2の超楕円曲線の位数計算と等分多項式

内田幸寛

代数幾何学と暗号数理の展開, Feb, 2017 Invited
ある不定方程式系の解と準エルミート多項式の零点の有理性について

内田幸寛

第12回代数曲面ワークショップ, Feb, 2016 Invited
楕円曲線を用いたMulti-Secret Sharingについて

池田崇, 内田幸寛, 内山成憲

日本応用数理学会2015年度年会, Sep, 2015
超楕円 Jacobi 多様体上の標準高さの計算について

内田幸寛

Workshop on Computational Number Theory with Implementations 2015, Feb, 2015 Invited
Jacobi多様体上の標準高さに関するアルゴリズム

内田幸寛

数学ソフトウェアとフリードキュメントXIX, Sep, 2014 Invited
Dickson 多項式を用いた暗号方式に対する秘密鍵が小さい場合の攻撃法

尾西昭彦, 内田幸寛, 内山成憲

日本応用数理学会2014年度年会, Sep, 2014

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Professional Memberships

2

Research Projects

7

数論統計の手法によるディオファントス幾何学の研究とその応用

科学研究費助成事業, 挑戦的研究(萌芽), 日本学術振興会, Jun, 2024 - Mar, 2027

谷口隆, 伊藤哲史, 石塚裕大, 大下達也, 内田幸寛
Study on the arithmetic of algebraic curves and its applications using computers

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2020 - Mar, 2025
Discrete integrable systems and Diophantine problems

Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Research (Exploratory), Grant-in-Aid for Challenging Research (Exploratory), Japan Society for the Promotion of Science, Jul, 2021 - Mar, 2024
Arithmetic and the Abel Jacobi map on elliptic surfaces and their applications

Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research, Grant-in-Aid for Challenging Exploratory Research, Japan Society for the Promotion of Science, Apr, 2013 - Mar, 2017

Hiroo Tokunaga, Shigenori Uchiyama, Yukihiro Uchida, Shinzo Bannai, Taketo Shirane, Benoît Guerville-Ballé, Khulan Tumenbayar
A study of algorithms on the arithmetic of algebraic curves and Abelian varieties

Grants-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, 2013 - 2016

UCHIDA Yukihiro
高さ関数を用いた代数多様体の有理点に関する研究

科学研究費補助金(特別研究員奨励費), 特別研究員奨励費, 日本学術振興会, 2009 - 2011

内田幸寛
代数曲線の有理点・整数点を求めるアルゴリズムに関する研究

科学研究費補助金(特別研究員奨励費), 特別研究員奨励費, 日本学術振興会, 2007 - 2008

内田幸寛