Faculty Profiles - SONG JUAE

Information

写真a

SONG JUAE

Organization

Faculty of Mathematics Division of Algebra and Geometry Assistant Professor
Graduate School of Mathematics Department of Mathematics（Concurrent）
School of Sciences Department of Mathematics（Concurrent）

Contact information

Homepage

https://sites.google.com/site/songjuaeshomepage/%E3%83%9B%E3%83%BC%E3%83%A0?authuser=0

External link

Research Areas

Natural Science / Algebra

Degree

博士（理学）（ 2022.3 Tokyo Metropolitan University ）
修士（理学）（ 2019.3 Tokyo Metropolitan University ）

Research History

Faculty of Mathematics Division of Algebra and Geometry Assistant Professor

2025.4 - Present
Kyoto University 大学院理学研究院 Specially Appointed Assistant Professor

2023.10 - 2025.3

Education

Tokyo Metropolitan University

2019.4 - 2022.3

　 More details

Country：Japan
Tokyo Metropolitan University

2017.4 - 2019.3

　 More details

Country：Japan

Research Interests・Research Keywords

Research theme： Construction of algebro-geometric foundation for tropical geometry

Keyword：トロピカル幾何学 / トロピカル有理関数半体 / 半環 / 合同 / トロピカル多様体

Research period： 2025.4 - Present

Awards

「研究奨励A」賞

2022 一般財団法人成和記念財団
「研究奨励B」賞

2019 一般財団法人成和記念財団

Papers

Congruences on tropical rational function semifields and tropical curves Reviewed International journal

Communications in Algebra 2026.2

　More details

Language：English Publishing type：Research paper (scientific journal)
Semiring isomorphisms between rational function semifields of tropical curves Reviewed

JuAe Song

Journal of Pure and Applied Algebra 228 ( 9 ) 107683 - 107683 2024.9 （ ISSN:0022-4049 ）

　More details

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier BV

DOI： 10.1016/j.jpaa.2024.107683
Galois correspondence for Galois coverings of tropical curves Reviewed

Song JuAe

Journal of Algebra and Its Applications 2023.10 （ ISSN:0219-4988 eISSN:1793-6829 ）

　More details

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：World Scientific Pub Co Pte Ltd

We define Galois coverings of tropical curves for which a Galois correspondence and a universal mapping property hold.

DOI： 10.1142/s0219498825500446
Upper bounds of orders of automorphism groups of leafless metric graphs Reviewed

Yusuke Nakamura, JuAe Song

AKCE International Journal of Graphs and Combinatorics 21 ( 1 ) 71 - 76 2023.9 （ ISSN:0972-8600 eISSN:2543-3474 ）

　More details

Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Informa UK Limited

DOI： 10.1080/09728600.2023.2251042
Rational function semifields of tropical curves are finitely generated over the tropical semifield Reviewed

Song JuAe

International Journal of Algebra and Computation 32 ( 08 ) 1575 - 1594 2022.11 （ ISSN:0218-1967 eISSN:1793-6500 ）

　More details

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：World Scientific Pub Co Pte Ltd

We prove that the rational function semifield of a tropical curve is finitely generated as a semifield over the tropical semifield [Formula: see text] by giving a specific finite generating set. Also, we show that for a finite harmonic morphism between tropical curves [Formula: see text], the rational function semifield of [Formula: see text] is finitely generated as a [Formula: see text]-algebra, where [Formula: see text] stands for the pull-back of the rational function semifield of [Formula: see text] by [Formula: see text].

DOI： 10.1142/s0218196722500710
Galois quotients of tropical curves and invariant linear systems Reviewed

JuAe SONG

Hokkaido Mathematical Journal 51 ( 3 ) 2022.10 （ ISSN:0385-4035 ）

　More details

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Department of Mathematics, Hokkaido University

DOI： 10.14492/hokmj/2020-406
Generators of invariant linear system on tropical curves for finite isometry group Reviewed

Song JuAe

Hokkaido Mathematical Journal 50 ( 1 ) 55 - 76 2021.2

　More details

Authorship：Lead author,　Last author,　Corresponding author Language：English Publishing type：Research paper (scientific journal)

DOI： 10.14492/hokmj/2018-879

▼display all

Books

特異点とMcKay対応・トロピカル幾何学とその応用

（Role：Contributor第7章）

近代科学社 2026.2

Presentations

Tropical curves with parallel rays Invited

第10回代数幾何学研究集会－宇部－ 2026.1

　More details

Event date： 2026.1

Language：English Presentation type：Oral presentation (invited, special)
一次元有理関数半体 Invited

数理・情報系研究集会 @ 熊本 2025.11

　More details

Event date： 2025.11

Language：Japanese
Rational function semifields of dimension one Invited

Math & Computer セミナー 2025.11

　More details

Event date： 2025.11

Language：English
トロピカル曲線とその有理関数半体の双対性 Invited

談話会 2025.10

　More details

Event date： 2025.10

Language：Japanese
Finite generation of rational function semifields Invited

名古屋代数幾何学セミナー 2025.7

　More details

Event date： 2025.7
Finite generation of rational function semifields Invited

九大代数学セミナー・代数幾何学セミナー 2025.4

　More details

Event date： 2025.4

Language：English
トロピカル曲線の幾何と代数 Invited

トロピカル幾何学とその応用 2025.3

　More details

Event date： 2025.3
An algebraic characterization of rational function semifields of tropical curves Invited

宋珠愛

Non-archimedean and tropical geometry from complex and algebraic geometry and dynamics 2025.1

　More details

Event date： 2025.1

Language：English Presentation type：Oral presentation (general)
Tropical rational function semifields and congruences Invited

宋珠愛

新潟若手代数・幾何シンポジウム 2024.11

　More details

Event date： 2024.11

Language：English Presentation type：Oral presentation (general)
A geometric interpretation of Krull dimensions of $\boldsymbol{T}-algebras Invited

宋珠愛

Kinosaki Algebraic Geometry Symposium 2024 2024.10

　More details

Event date： 2024.10

Language：English Presentation type：Oral presentation (general)
Geometry and algebra of metric graphs

宋珠愛

２０２４軽井沢グラフと解析研究集会 2024.10

　More details

Event date： 2024.10

Language：English Presentation type：Oral presentation (general)
A geometric interpretation of Krull dimensions of $\boldsymbol{T}-algebras

宋珠愛

Workshop on Tropical Geometry, Singularity theory, and Algebraic Geometry 2024.9

　More details

Event date： 2024.9

Language：English Presentation type：Oral presentation (general)
Geometry over finitely generated semifields over the tropical semifield Invited

宋珠愛

佐賀創発数理セミナー 2024.7

　More details

Event date： 2024.7

Language：English Presentation type：Oral presentation (invited, special)
Tropical rational function semifields and congruences Invited

宋珠愛

談話会 2024.6

　More details

Event date： 2024.6

Language：English Presentation type：Oral presentation (invited, special)
Duality of tropical geometry and algebra

宋珠愛

第 17 回数論女性の集まり 2024.6

　More details

Event date： 2024.6

Language：English Presentation type：Oral presentation (general)
Tropical rational function semifields and congruences Invited

Song JuAe

MSセミナー 2024.5

　More details

Event date： 2024.5

Language：English Presentation type：Oral presentation (invited, special)
A brief introduction to tropical geometry and my results Invited

宋珠愛

数論合同セミナー 2024.4

　More details

Event date： 2024.4

Language：English Presentation type：Oral presentation (invited, special)
A characterization of rational function semifields of tropical curves Invited

宋珠愛

Algebraic Geometry, Topology, Combinatorics and Related Topics 2024 2024.3

　More details

Event date： 2024.3

Language：English Presentation type：Oral presentation (invited, special)
A characterization of rational function semifields of tropical curves

宋珠愛

第6回トロピカル幾何ワークショップ 2024.3

　More details

Event date： 2024.3

Language：English Presentation type：Oral presentation (general)
生存戦略：理想と現実のすり合わせ Invited

宋珠愛

女子学部生サマーキャンプ企画検討会 2024.3

　More details

Event date： 2024.3

Language：Japanese Presentation type：Oral presentation (invited, special)
Finitely generated congruences on tropical rational function semifields defined by subsets of tropical tori Invited

宋珠愛

Workshop on Nonarchimedean geometry and related fields 2024.1

　More details

Event date： 2024.1 - 2024.2

Language：English Presentation type：Oral presentation (invited, special)
Finitely generated congruences on tropical rational function semifields defined by subsets of tropical tori Invited

宋珠愛

晴ればれ岡山代数幾何学シンポジウム 2024.1

　More details

Event date： 2024.1

Language：English Presentation type：Oral presentation (invited, special)
Congruences on tropical rational function semifields and tropical curves

宋珠愛

第27回代数学若手研究会 2023.3

　More details

Event date： 2023.3

Language：English Presentation type：Oral presentation (general)
\boldsymbol{T}-algebra homomorphisms between rational function semifields of tropical curves

宋珠愛

第５回トロピカル幾何ワークショップ 2023.2

　More details

Event date： 2023.2

Language：English Presentation type：Oral presentation (general)
What information on tropical curves do chip firings have? Invited

宋珠愛

第 28 回関東若手幾何セミナー 2022.12

　More details

Event date： 2022.12

Language：English Presentation type：Oral presentation (invited, special)
Rational function semifields of tropical curves Invited

宋珠愛

Workshop on mirror symmetry and related topics, Kyoto 2022 2022.12

　More details

Event date： 2022.12

Language：English Presentation type：Oral presentation (invited, special)
On \boldsymbol{T}-algebra homomorphisms between rational function semifields of tropical curves

宋珠愛

城崎代数幾何学シンポジウム 2022 2022.10

　More details

Event date： 2022.10

Language：English
Chip firings and rational function semifields of tropical curves Invited

宋珠愛

Workshop on Combinatorial topics in Shinshu 2022 2022.7

　More details

Event date： 2022.7

Language：English Presentation type：Oral presentation (invited, special)
Rational function semifields of tropical curves are finitely generated over the tropical semifield

宋珠愛

第26回代数学若手研究会 2022.3

　More details

Event date： 2022.3

Language：English Presentation type：Oral presentation (general)
Rational function semifields of tropical curves are finitely generated over the tropical semifield

宋珠愛

The 18th Mathematics Conference for Young Researchers 2022.3

　More details

Event date： 2022.3

Language：English Presentation type：Oral presentation (general)
Semiring isomorphisms between rational function semifields of tropical curves induce isomorphisms between tropical curves

宋珠愛

第5回数理新人セミナー 2022.2

　More details

Event date： 2022.2

Language：English Presentation type：Oral presentation (general)
Semiring isomorphisms between rational function semifields of tropical curves induce isomorphisms between tropical curves

宋珠愛

第４回トロピカル幾何ワークショップ 2022.2

　More details

Event date： 2022.2

Language：English Presentation type：Oral presentation (general)

▼display all

MISC

現代数学への誘い—トロピカル幾何学入門

現代数学 2025.7
京都大学ガロア祭／問題と解説

数学セミナー 2024.12

Research Projects

トロピカル幾何の代数幾何的土台の構成

Grant number：25K17230 2025.4 - 2029.3

若手研究

　 More details

Authorship：Principal investigator Grant type：Scientific research funding

誕生から二十年ほどと歴史の浅いトロピカル幾何学に、内在的な言葉で代数幾何学的土台を築くための研究である。トロピカル化という、古典的な代数幾何学とトロピカル幾何学を繋ぐ操作ありきで研究されてきたトロピカル幾何学を、トロピカル化との整合性は保ちつつ、より独立した一つの理論に昇華させることを目指す。具体的には、代数的対象と幾何的対象とをうまく対応付け、さらにその幾何的対象も座標空間内のものと抽象的に考えるものの二種類を対応付けることで、この理論が個々のどのような文脈の問題にも柔軟に適用可能になるようにする。

Class subject

幾何学Ⅱ・演習

2025.10 - 2026.3 Second semester
幾何学Ⅰ・演習

2025.4 - 2025.9 First semester
微分積分学Ｂ講義

2024.10 - 2025.3
微分積分学Ⅱ（Ｂ）

2024.10 - 2025.3 Second semester
微分積分学A演義

2024.4 - 2024.9
線形代数Ｂ演義

2023.10 - 2024.3
線形代数Ⅰｂ

2023.4 - 2023.9
代数学特別講義Ⅰ

2023.4 - 2023.9
幾何学特別講義Ⅰ

2023.4 - 2023.9
離散数学

2022.10 - 2023.3
離散数学（演習含む）

2022.10 - 2023.3
代数学特別講義Ⅱ

2022.10 - 2023.3
代数学特別講義Ⅰ

2022.4 - 2022.9

▼display all

FD Participation

2025.4 Role：Participation Title：令和７年度　第１回全学FD（新任教員FDの研修）The 1st All-University FD (training for new faculty members) in FY2025

Organizer：University-wide

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

2025 北海道大学理学部 Classification:Intensive course Domestic/International Classification:Japan
2024 奈良女子大学 Classification:Part-time lecturer
2023 東京都立大学 Classification:Part-time lecturer
2023 城西大学 Classification:Part-time lecturer
2022 城西大学 Classification:Part-time lecturer

Travel Abroad

2019.12 - 2020.3

Staying countory name 1：Germany Staying institution name 1：エバーハルト・カール大学テュービンゲン