Toshiya Yurikusa's Homepage

Research experience

Apr. 2025 - Present: Specially Appointed Assistant Professor, Osaka Metropolitan University, Japan

Feb. 2023 - Mar. 2025: Visiting Scholar, Tohoku University, Japan

Feb. 2023 - Feb. 2025: JSPS Overseas Research Fellowships, University of Versailles Saint-Quentin, France

Oct. 2022 - Feb. 2023: Part-time Lecturer, Yamagata University, Japan

Apr. 2022 - Sep. 2022: Part-time Lecturer, Tohoku University, Japan

Oct. 2021 - Mar. 2022: Part-time Lecturer, Yamagata University, Japan

Apr. 2020 - Feb. 2023: JSPS Research Fellow (PD), Tohoku University, Japan

Oct. 2019 - Mar. 2020: JSPS Research Fellow (PD), Nagoya University, Japan

Nov. 2019 - Feb. 2020: Visiting Scholar, University of Paris 11, France (supported by JSPS Overseas Challenge Program for Young Researchers)

Apr. 2017 - Sep. 2019: JSPS Research Fellow (DC1), Nagoya University, Japan

Teaching experience

Apr. 2025 - Present: Calculus 1B, Osaka Metropolitan University, Japan

Oct. 2022 - Feb. 2023: Mathematics C (Linear algebra), Yamagata University, Japan

Apr. 2022 - Sep. 2022: Overview of mathematical statistics, Tohoku University, Japan

Apr. 2022 - Sep. 2022: Mathematical statistics, Tohoku University, Japan

Oct. 2021 - Mar. 2022: Mathematics C (Linear algebra), Yamagata University, Japan

Education

Sep. 27, 2019: Doctor of Philosophy (Mathematical Science), Nagoya University, Japan

Mar. 27, 2017: Master of Mathematical Science, Nagoya University, Japan

Mar. 25, 2015: Bachelor of Science, Nagoya University, Japan

Grants

Apr. 2021 - Mar. 2026: Grant-in-Aid for Early-Career Scientists (21K13761)

Apr. 2020 - Mar. 2023: JSPS Research Fellowshps for Young Scientists (20J00410)

Nov. 2019 - Feb. 2020: JSPS Overseas Challenge Program for Young Researchers

Apr. 2017 - Mar. 2020: JSPS Research Fellowshps for Young Scientists (17J04270)

Awards

Mar. 2017: Mathematical Sciences Thesis Award, Nagoya University

Publications

Toshiya Yurikusa. Denominator vectors and dimension vectors from triangulated surfaces. Journal of Algebra, 641:620--647, 2024.

Peigen Cao, Yasuaki Gyoda, and Toshiya Yurikusa. Bongartz completion via c-vectors. International Mathematics Research Notices, 2023(15):13099--13135, 2023.

Toshitaka Aoki and Toshiya Yurikusa. Complete gentle and special biserial algebras are g-tame. Journal of Algebraic Combinatorics, 57:1103--1137, 2023.

Pierre-Guy Plamondon and Toshiya Yurikusa. Tame algebras have dense g-vector fans. International Mathematics Research Notices, 2023(4):2701--2747, 2023. with an appendix by Bernhard Keller.

Toshiya Yurikusa. Acyclic cluster algebras with dense g-vector fans. In McKay Correspondence, Mutation and Related Topics, volume 88, pages 437--459. Mathematical Society of Japan, 2023.

Yasuaki Gyoda and Toshiya Yurikusa. F-matrices of cluster algebras from triangulated surfaces. Annals of Combinatorics, 24(4):649--695, 2020.

Toshiya Yurikusa. Density of g-vector cones from triangulated surfaces. International Mathematics Research Notices, 2020(21):8081--8119, 2020.

Toshiya Yurikusa. Combinatorial cluster expansion formulas from triangulated surfaces. The Electronic Journal of Combinatorics, 26(2):P2--33, 2019.

Toshiya Yurikusa. Cluster expansion formulas in type A. Algebras and Representation Theory, 22(1):1--19, 2019.

Toshiya Yurikusa. Wide subcategories are semistable. Documenta Mathematica, 23:35--47, 2018.

Talks

gベクトル扇の稠密性とその応用, OCAMI colloquium, Osaka Metropolitan University, Japan, June 2, 2025.

Dimension vectors of τ-rigid modules and intersection numbers on triangulated surfaces, MSJ Spring Meeting 2025, Waseda University, Japan, March 21, 2025.

Algebras with dense g-fans, Autumn School & Conference: New developments in representation theory of algebras, Okinawa Institute of Science and Technology (OIST), Japan, November 28, 2024.

Denominator and dimension vectors from intersection numbers, Tohoku Cluster Seminar, online, November 6, 2023.

Algebras with dense g-vector fans, Silting in Representation Theory, Singularities, and Noncommutative Geometry (Gong show), Hotel Hacienda Los Laureles, Mexico, September 12, 2023.

Denominator and dimension vectors from intersection numbers, Séminaire AG, UVSQ, France, May 9, 2023.

Acyclic cluster algebras with dense g-vector fans, MSJ Autumn Meeting 2022, Hokkaido University, Japan, September 13, 2022.

Bongartz completion via c-vectors, MSJ Spring Meeting 2022, online, March 28, 2022.

Bongartz completion via c-vectors, Infinite Analysis 21 (IA21) Workshop Around Cluster Algebras, online, September 29, 2021.

Cluster algebras with dense g-vector fans, MSJ Autumn Meeting 2021, online, September 15, 2021.

Surface model of complete gentle algebras and g-vector fans, Topological Studies around Riemann Surfaces, online, August 17, 2021.

Ingalls-Thomas対応の一般化とgベクトル扇, Tohoku University Geometry Seminar, online, March 23, 2021.

Tame algebras have dense g-vector fans, MSJ Spring Meeting 2021, online, March 15, 2021.

Tame algebras have dense g-vector fans, The 17th Mathematics Conference for Young Researchers, online, March 4, 2021.

曲面団代数における分母ベクトルと次元ベクトル, Tohoku Branch of the Mathematical Society of Japan 2020, online, February 20, 2021.

Dimension vectors and denominator vectors in cluster algebras from surfaces, Mathsci Freshman Seminar 2021, online, February 13, 2021.

Denseness of g-vector fans for tame algebras, Kyoto Representation Theory Seminar, online, January 7, 2021.

Complete special biserial algebras are g-tame, MSJ Autumn Meeting 2020, online, September 23, 2020.

Cluster algebras with dense g-vector fans, Cluster algebras 2020, online, August 25, 2020.

Tame algebras have dense g-vector fans, South Osaka Algebra Seminar, online, July 3, 2020.

Denseness of g-vector cones from marked surfaces, S\'eminaire d'Alg\`ebre, Institut Henri Poincar\'e, Paris, France, December 2, 2019.

Morita theorem, examples, Summer School on DG theory and Derived Categories, Nagoya University, Japan, September 26, 2019.

Density of g-vector cones from triangulated surfaces, MSJ Autumn Meeting 2019, Kanazawa University, Japan, September 17, 2019.

f-vectors of cluster algebras from triangulated surfaces, COmbinatorics Summer school 2019 (COS 2019), Kaikyo View Shimonoseki, Japan, September 4, 2019.

Density of g-vector cones from triangulated surfaces, The Eighth China - Japan - Korea International Symposium on Ring Theory, Nagoya University, Japan, August 26, 2019.

Ingalls-Thomas bijections, Algebraic Lie Theory and Representation Theory 2019 (ALTReT 2019), Yamaki Ryokan, Japan, May 24, 2019.

Wide subcategories are semistable, MSJ Spring Meeting 2019, Tokyo Institute of Technology, Japan, March 17, 2019.

Density of g-vector cones from triangulated surfaces, The 24th Conference on Algebra for Young Researchers, Tokyo University, Japan, February 21, 2019.

Combinatorial cluster expansion formulas from triangulated surfaces, MSJ Autumn Meeting 2018, Okayama University, Japan, September 24, 2018.

A generalization of Ingalls-Thomas bijections, The 27th Yamatokoriyama Seminar, National Institute of Technology, Japan, September 12, 2018.

Combinatorial cluster expansion formulas from triangulated surfaces, 18th International Conference on Representations of Algebras (ICRA 2018), Czech technical university in Prague, Czech, August 15, 2018.

Combinatorial cluster expansion formulas from triangulated surfaces, Algebraic Lie Theory and Representation Theory 2018 (ALTReT 2018), Sophia University Karuizawa Seminar House, Japan, May 27, 2018.

Wide/Semistable subcategories and wall-chamber structure, The 23rd Conference on Algebra for Young Researchers, Osaka University, Japan, March 7, 2018.

団代数と角の完全マッチング, Osaka Combinatorics Seminar, Osaka City University, Japan, November 25, 2017.

Wide subcategories are semistable, The 50th Symposium on Ring Theory and Representation Theory, Yamanashi University, Japan, October 8, 2017.

Wide subcategories are semistable, South Osaka Algebra Seminar, Osaka Prefecture University, Japan, September 22, 2017.

Cluster expansion formulas from triangulated surfaces, COmbinatorics Summer school 2017 (COS 2017), Ryokan Irifuneso, Japan, September 7, 2017.

Quivers with potential from surface triangulations, BIREP Summer School on Gentle Algebras, Bad Driburg, Germany, August 17, 2017.

Poster presentation

Dense g-vector fans for tame algebras, McKay correspondence, Mutation and related topics, online, July 24, 2020.

Density of g-vector cones from triangulated surfaces, Cluster Algebras 2019 (CA19), Research Institute for Mathematical Sciences (RIMS), Japan, June 20, 2019.

Wide subcategories are semistable, The 50th Symposium on Ring Theory and Representation Theory, Yamanashi University, Japan, October 8, 2017.

Organizations

Tohoku Cluster Seminar, Tohoku University, April 2023-Present.

Preprojective algebras and Calabi-Yau algebras, Online, March 2022.

The 25th Conference on Algebra for Young Researchers, Report only, March 2020.

Ring Theory and Representation Theory Seminar in 2019, Nagoya University, February-December 2019.

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