Wei-Hsuan Yu 俞韋亘

About me

I work in discrete geometry, coding theory, and algebraic combinatorics. My research focuses on configurations with few distances, equiangular lines, spherical designs, and bounds for classical and quantum codes. I use algebraic, combinatorial, and optimization methods, including semidefinite programming.

I joined National Central University in 2018. Previously, I held positions at ICERM, Brown University, and Michigan State University. I received my Ph.D. in Mathematics from the University of Maryland, College Park, in 2014, advised by Alexander Barg and John J. Benedetto.

Recent updates

• June 2026: “Sharing tea on a graph,” joint work with J. Pascal Gollin, Kevin Hendrey, Hao Huang, Tony Huynh, Bojan Mohar, Sang-il Oum, Ningyuan Yang, and Xuding Zhu, was accepted by Combinatorial Theory. Preprint

• May 2026: New preprint with Chun-Yen Shen and Tuyen Trung Truong: “On the structure and generic non-Cartesianity of polynomials in product spaces.” Preprint

• Summer 2026: Invited presentations at the National University of Singapore, HKUST, Shandong University in Qingdao, and Xidian University in Xi’an. See Talks for details.

Research

My research studies how algebraic structure and geometric constraints determine the size and form of finite configurations. Central examples include sets with few distances, equiangular lines, spherical designs, and error-correcting codes.

Few-distance sets and equiangular lines

I study upper bounds, constructions, and structural properties of point sets with few pairwise distances and systems of equiangular lines. This work combines polynomial methods, spectral techniques, forbidden-subgraph arguments, and semidefinite programming.

Together with Alexey Glazyrin, I developed a method using zonal spherical functions that determines the maximum size of spherical two-distance sets in dimensions at least seven, apart from possible exceptional dimensions of the form (2k + 1)² − 3. Advances in Mathematics, 2018

Selected papers:

• A. Glazyrin and W.-H. Yu, “Upper bounds for s-distance sets and equiangular lines,” Advances in Mathematics (2018). arXiv

• M. Cao, J. Koolen, Y.-C. Lin, and W.-H. Yu, “Lemmens-Seidel conjecture and forbidden subgraph,” Journal of Combinatorial Theory, Series A (2022).

• F.-Y. Liu and W.-H. Yu, “Semidefinite programming bounds for spherical three-distance sets,” Electronic Journal of Combinatorics (2024). DOI

Classical and quantum coding theory

I develop bounds for codes through algebraic combinatorics and optimization. Topics include binary codes with prescribed distance sets, split Terwilliger algebras, and entanglement-assisted quantum codes.

With collaborators, I determined the maximum size of binary two-distance codes for every length at least six, and obtained exact results for several families of constant-weight codes with two, three, or four distances. Combinatorial Theory, 2024

Selected papers:

• A. Barg, A. Glazyrin, W.-J. Kao, C.-Y. Lai, P.-C. Tseng, and W.-H. Yu, “On the size of maximal binary codes with 2, 3, and 4 distances,” Combinatorial Theory (2024). DOI

• P.-C. Tseng, C.-Y. Lai, and W.-H. Yu, “Semidefinite programming bounds for binary codes from a split Terwilliger algebra,” Designs, Codes and Cryptography (2023). DOI

• C.-Y. Lai, P.-C. Tseng, and W.-H. Yu, “Semidefinite programming bounds on the size of entanglement-assisted codeword stabilized quantum codes,” IEEE Transactions on Information Theory (2024). DOI

Designs, algebraic combinatorics, and applications

I study spherical designs, tight frames, coherent configurations, and weighing matrices. Collaborative projects also connect these structures and optimization methods with time-frequency analysis and quantum state tomography.

With collaborators, I developed a nonconvex Riemannian gradient method for quantum state tomography, with a convergence contraction factor independent of the target state's condition number and nearly optimal reconstruction error bounds. Physical Review Letters, 2024

Selected papers:

• M. Araya, M. Harada, H. Kharaghani, S. Suda, and W.-H. Yu, “Unbiased weighing matrices of weight 9,” Designs, Codes and Cryptography (2025). DOI

• E. Bannai, E. Bannai, C.-Y. Lee, Z. Xiang, and W.-H. Yu, “On the two-distance embedding in real Euclidean space of coherent configuration of type (2,2;3),” Discrete Mathematics (2025). DOI

• M. Sourisseau, Y. G. Wang, H.-T. Wu, and W.-H. Yu, “Improved concentration of frequency and time (ConceFT) by novel complex spherical designs,” Applied and Computational Harmonic Analysis (2021).

• M.-C. Hsu, E.-J. Kuo, W.-H. Yu, J.-F. Cai, and M.-H. Hsieh, “Quantum state tomography via non-convex Riemannian gradient descent,” Physical Review Letters (2024). DOI

Averaging dynamics on graphs

With collaborators, I proved a sharp distance-dependent bound for tea-sharing dynamics on graphs, answering a question of Nina Gantert. Sharing tea on a graph, accepted by Combinatorial Theory.

Publications

Accepted

• J. Pascal Gollin, Kevin Hendrey, Hao Huang, Tony Huynh, Bojan Mohar, Sang-il Oum, Ningyuan Yang, W.-H. Yu, and Xuding Zhu, “Sharing tea on a graph,” Combinatorial Theory, accepted June 2026. arXiv:2405.15353.

Published articles and book chapters

1. M. Araya, M. Harada, H. Kharaghani, S. Suda, and W.-H. Yu, “Unbiased weighing matrices of weight 9,” Designs, Codes and Cryptography 93(10) (2025), 4235-4273. DOI: 10.1007/s10623-025-01676-y. arXiv:2501.15444. 〔中文簡介・中英投影片・四格漫畫〕 

2. C.-Y. Lee, W.-H. Yu, Y.-N. Peng, and C.-J. Lai, “On character table of Clifford groups,” Journal of Mathematical Physics 66(2) (2025), 022201. DOI: 10.1063/5.0204167. 〔中文簡介・中英投影片・四格漫畫〕 

3. E. Bannai, E. Bannai, C.-Y. Lee, Z. Xiang, and W.-H. Yu, “On the two-distance embedding in real Euclidean space of coherent configuration of type (2,2;3),” Discrete Mathematics 348(4) (2025), 114378. DOI: 10.1016/j.disc.2024.114378. 〔中文簡介・中英投影片・四格漫畫〕 

4. E. Bannai, E. Bannai, C.-Y. Lee, H. Tanaka, and W.-H. Yu, “The real equiangular tight frames obtained from rank 3 graphs,” Electronic Journal of Graph Theory and Applications 12(2) (2024), 329-341. DOI: 10.5614/ejgta.2024.12.2.12. 〔中文簡介・中英投影片・四格漫畫〕 

5. J.-R. Yu, Y.-T. Wu, Y.-J. Sung, T.-S. Chiueh, W.-H. Yu, F.-N. Hwang, Z.-Q. Wu, Z. Anwar, W.-Y. Lin, and H.-Y. Wang, “Improving interpretation consistency of serum capillary electrophoresis by development of quantitative graphic indexes,” International Journal of Molecular Sciences 25(22) (2024), 12240. DOI: 10.3390/ijms252212240. 〔中文簡介・中英投影片・四格漫畫〕 

6. M.-C. Hsu, E.-J. Kuo, W.-H. Yu, J.-F. Cai, and M.-H. Hsieh, “Quantum state tomography via non-convex Riemannian gradient descent,” Physical Review Letters 132 (2024), 240804. DOI: 10.1103/PhysRevLett.132.240804. 〔中文簡介・中英投影片・四格漫畫〕 

7. C.-Y. Lai, P.-C. Tseng, and W.-H. Yu, “Semidefinite programming bounds on the size of entanglement-assisted codeword stabilized quantum codes,” IEEE Transactions on Information Theory 70(11) (2024), 7867-7881. DOI: 10.1109/TIT.2024.3433550. 〔中文簡介・中英投影片・四格漫畫〕 

8. A. Barg, A. Glazyrin, W.-J. Kao, C.-Y. Lai, P.-C. Tseng, and W.-H. Yu, “On the size of maximal binary codes with 2, 3, and 4 distances,” Combinatorial Theory 4(1) (2024), #7. DOI: 10.5070/C64163844. 〔中文簡介・中英投影片・四格漫畫〕 

9. F.-Y. Liu and W.-H. Yu, “Semidefinite programming bounds for spherical three-distance sets,” Electronic Journal of Combinatorics 31(4) (2024), P4.11. DOI: 10.37236/11979. 〔中文簡介・中英投影片・四格漫畫〕 

10. P.-C. Tseng, C.-Y. Lai, and W.-H. Yu, “Semidefinite programming bounds for binary codes from a split Terwilliger algebra,” Designs, Codes and Cryptography 91(10) (2023), 3241-3262. DOI: 10.1007/s10623-023-01250-4. 〔中文簡介・中英投影片・四格漫畫〕 

11. Y. Wang, R. S. Womersley, H.-T. Wu, and W.-H. Yu, “Numerical computation of triangular complex spherical designs with small mesh ratio,” Journal of Computational and Applied Mathematics 421 (2023), 114796. DOI: 10.1016/j.cam.2022.114796. 〔中文簡介・中英投影片・四格漫畫〕 

12. P.-H. Lu, C.-C. Chiang, W.-H. Yu, M.-C. Yu, and F.-N. Hwang, “Machine learning-based technique for the severity classification of sublingual varices according to traditional Chinese medicine,” Computational and Mathematical Methods in Medicine (2022). 〔中文簡介・中英投影片・四格漫畫〕. DOI: 10.1155/2022/3545712 

13. P.-H. Lu, Y.-Y. Chen, F.-M. Tsai, Y.-L. Liao, H.-F. Huang, W.-H. Yu, and C.-Y. Kuo, “Combined acupoints for the treatment of patients with obesity: an association rule analysis,” Evidence-Based Complementary and Alternative Medicine (2022). 〔中文簡介・中英投影片・四格漫畫〕 

14. M. Cao, J. Koolen, Y.-C. Lin, and W.-H. Yu, “Lemmens-Seidel conjecture and forbidden subgraph,” Journal of Combinatorial Theory, Series A 185 (2022). 〔中文簡介・中英投影片・四格漫畫〕 

15. Zhiqiang Xu, Zili Xu, and W.-H. Yu, “Bounds on antipodal spherical designs with few angles,” Electronic Journal of Combinatorics  28(3) (2021), P3.39. DOI: 10.37236/9891. 〔中文簡介・中英投影片・四格漫畫〕 

16. M. Sourisseau, Y. G. Wang, H.-T. Wu, and W.-H. Yu, “Improved concentration of frequency and time (ConceFT) by novel complex spherical designs,” Applied and Computational Harmonic Analysis 54 (2021), 137-144. arXiv:1907.13493. 〔中文簡介・四格漫畫〕 

17. E. Bannai, E. Bannai, Z. Xiang, W.-H. Yu, and Y. Zhu, “Classification of spherical two-distance set and {4,2,1} designs,” Taiwanese Journal of Mathematics 25(1) (2021), 1-22. 〔中文簡介・中英投影片・四格漫畫〕 

18. L. Hou, B. Hou, S. Gao, and W.-H. Yu, “New code upper bounds for the folded n-cube,” Journal of Combinatorial Theory, Series A  172 (2020). arXiv:1801.06971. 〔中文簡介・中英投影片・四格漫畫〕 

19. Y.-C. Roger Lin and W.-H. Yu, “Saturated configuration and new large construction of equiangular lines,” Linear Algebra and its Applications 588 (2020), 272-281. arXiv:1801.04502. 〔中文簡介・中英投影片・四格漫畫〕 

20. Y.-C. Roger Lin and W.-H. Yu, “Equiangular lines and the Lemmens-Seidel conjecture,” Discrete Mathematics 343(2) (2020), 111667. DOI: 10.1016/j.disc.2019.111667. 〔中文簡介・中英投影片・四格漫畫〕 

21. M. Haver, K. Lee, W. McDermott, A. Wilson, W.-H. Yu, and A. Zeleke, “Closed forms of recursive polynomials and applications,” Ars  〔中文簡介・中英投影片・四格漫畫〕 Combinatoria 142 (2019), 175-195.

22. A. Glazyrin and W.-H. Yu, “Upper bounds for s-distance sets and equiangular lines,” Advances in Mathematics 330 (2018), 810-833. arXiv:1611.09479. 〔中文簡介・中英投影片・四格漫畫〕 

23. Y. Zhu, E. Bannai, E. Bannai, K.-T. Kim, and W.-H. Yu, “On spherical designs of harmonic index T,” Electronic Journal of Combinatorics 24(2) (2017), P2.14. arXiv:1507.05373. 〔中文簡介・中英投影片・四格漫畫〕 

24. W.-H. Yu, “New bounds for equiangular lines and spherical two-distance sets,” SIAM Journal on Discrete Mathematics 31(2) (2017), 908-917. arXiv:1609.01036. 〔中文簡介・中英投影片・四格漫畫〕 

25. T. Okuda and W.-H. Yu, “A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4,” European Journal of Combinatorics 53 (2016), 96-103. arXiv:1409.6995. 〔中文簡介・中英投影片・四格漫畫〕 

26. A. Barg, K. Okoudjou, A. Glazyrin, and W.-H. Yu, “Finite two-distance tight frames,” Linear Algebra and its Applications 474 (2015), 163-175. arXiv:1402.3521. 〔中文簡介・中英投影片・四格漫畫〕 

27. A. Barg and W.-H. Yu, “New bounds for equiangular lines,” in Discrete Geometry and Algebraic Combinatorics, A. Barg and O. Musin (eds.), Contemporary Mathematics 625, AMS (2014), 111-121. arXiv:1311.3219. 〔中文簡介・中英投影片・四格漫畫〕 

28. A. Barg and W.-H. Yu, “New upper bounds for spherical two-distance sets,” Experimental Mathematics 22(2) (2013), 187-194. arXiv:1204.5268. 〔中文簡介・中英投影片・四格漫畫〕 

Conference proceedings

1. P.-C. Tseng, C.-Y. Lai, and W.-H. Yu, “Upper bounds on the size of entanglement-assisted codeword stabilized codes using semidefinite programming,” 2024 IEEE International Symposium on Information Theory (ISIT). DOI: 10.1109/ISIT57864.2024.10619303.

2. P.-C. Tseng, C.-Y. Lai, and W.-H. Yu, “Improved semidefinite programming bounds for binary codes by split distance enumerations,” 2022 IEEE International Symposium on Information Theory (ISIT). DOI: 10.1109/ISIT50566.2022.9834515.

Preprints and Submitted Manuscripts

1. Chun-Yen Shen, Tuyen Trung Truong, and W.-H. Yu, “On the structure and generic non-Cartesianity of polynomials in product spaces.” arXiv:2605.22320 (submitted 21 May 2026).

2. W.-C. Chen and W.-H. Yu, “Bounds on two-distance sets in Euclidean space and unit sphere.” arXiv:2509.00858.

3. L.-R. Bao and W.-H. Yu, “Constructions of large m-distance sets on triangular lattice.” arXiv:2509.00880.

4. S. Suda, Zili Xu, and W.-H. Yu, “Existence and nonexistence of spherical 5-designs of minimal type.” arXiv:2508.18685.

5. Sihuang Hu, Hexiang Huang, and W.-H. Yu, “Hegedus’ conjecture and tighter upper bounds for equidistant codes in Hamming spaces.” arXiv:2504.07036.

6. S. Das, V. Djaljapayan, Y.-C. Roger Lin, and W.-H. Yu, “Stability for hyperplane covers.” arXiv:2306.07574.

7. C. Cleveland, C.-Y. Lee, S.-F. Tsai, W.-H. Yu, and H.-W. Lee, “Graphlet and orbit computation on heterogeneous graphs.” arXiv:2304.14268.

8. W.-J. Kao, S. Suda, and W.-H. Yu, “Semidefinite programming bounds for complex spherical codes.” arXiv:2204.04108.

9. W.-J. Kao and W.-H. Yu, “Four-point semidefinite bound for equiangular lines.” arXiv:2203.05828.

10. C.-J. Yeh and W.-H. Yu, “Improvement of generalization of Larman-Rogers-Seidel’s theorem.” arXiv:2106.09582.

Talks

Selected invited presentations, 2024–2026

2026

• 3 August: Innovations and Challenges in Extremal Combinatorics, Institute for Mathematical Sciences, National University of Singapore, Singapore.

• 12–26 July: Graphs and Groups, Tessellations and Transformations (G2T2), Hong Kong University of Science and Technology, Hong Kong.

• 22–26 June: Qingdao Workshop on Coding Theory and Related Topics, Shandong University (Qingdao Campus), Qingdao.

• 18–21 June: 2026 Xidian IMS Conference on Combinatorics and Related Areas, Xi’an.

2025

• August: 13th Cross-Strait Combinatorics Conference, Zhejiang University, Hangzhou.

• June: Qingdao Workshop on Lattices and Codes, Shandong.

• May: RIMS Workshop, New Developments in Combinatorics and Information Science, Kyoto.

• March: NUS Combinatorics Seminar, Singapore.

2024

• December: RIMS Conference on “Finite Group Theory, Algebraic Combinatorics, and Vertex Algebras.”

• August: Combinatorics Seminar, Shandong University at Qingdao.

• 18–20 June: 40th Symposium on Algebraic Combinatorics, University of Yamanashi, Kofu.

Students

Ph.D. students

• 李金彥 (Chin-Yen Lee) — Ph.D., 2025 (2020–2025). Dissertation: “Embedding the n-Qubit Projective Clifford Group into a Symmetric Group.” [Thesis record]

• 江嘉恩 — Current; co-advised with Yen-Chi Lin, National Taiwan Normal University.

Master’s students

• 廖振綺 (Zhen-Qi Liao) — M.S., 2026. Thesis: “Applying Semidefinite Programming to Strongly Regular Graphs.” [Official conference handbook] Recipient of the 33rd Young Combinatorics Workshop Master’s Thesis Award — Honorable Mention (第33屆組合數學新苗研討會碩士論文獎－佳作). [Official award list]

• 葉政叡 — M.S., July 2023. Thesis: “多項式方法於等角直線叢上的半正定規劃上界” (Polynomial Method in Semidefinite Programming Bounds for Equiangular Lines). [Thesis record]

• 謝欣妤 — M.S., January 2023. Thesis: “等角直線叢的研究” (A Study on Equiangular Lines). [Thesis record]

• 瓦宇力 (Wahyu) — M.S., January 2022; from Indonesia. Thesis: “An Observation on 7-distance Set in Euclidean Plane.” [Thesis record]

• 林軒宇 — M.S., October 2020. Thesis: “歐式空間二距離集合之探討” (A study of two-distance set in Euclidean space). [Thesis record]

• 陳佑銘 — M.S., July 2020. Thesis: “A Study On Kissing Number Problem.” [Thesis record]

• 劉豐源 — M.S., August 2019; co-supervised by Che-Rung Lee in the Institute of Computer Science, National Tsing Hua University. Thesis: “使用半正定規劃解決球面三距離集合問題” (Semidefinite Programming Bounds For Spherical Three-Distance Sets). [Thesis record] Recipient of the 2019 Outstanding Young Combinatorics Thesis Award (組合新苗優秀論文獎).

Undergraduate mentoring

I served as a mentor in the Summer Undergraduate Research Institute in Experimental Mathematics (SURIEM), Lyman Briggs College, Michigan State University, in May–July 2016 and May–July 2017.

• Sichen Chu — Semidefinite programming bounds for spherical three-distance sets.

• Jordan Giebas and Zachary Rosenthal — Numerical constructions of spherical t-designs.

Teaching

My teaching areas include optimization, coding theory, graph theory, discrete mathematics, linear algebra, and calculus.

About

Academic appointments

• August 2021–present: Associate Professor, National Central University.

• August 2018–July 2021: Assistant Professor, National Central University.

• September 2017–May 2018: Postdoctoral Institute Fellow, ICERM, Brown University. Mentor: Henry Cohn, Microsoft Research and MIT.

• August 2014–May 2017: Fixed-term Assistant Professor, Michigan State University.

Education

• May 2014: Ph.D. in Mathematics, University of Maryland, College Park. Advisor: Alexander Barg; co-advisor: John J. Benedetto.

• June 2004: M.S. in Mathematics, National Taiwan Normal University. Advisor: Yen-Chi Lin.

• June 2002: B.S. in Mathematics, National Tsing Hua University.

Honors and awards

• 2020: NCTS Young Theoretical Scientist (國家理論科學研究中心年輕理論學者獎).

• 2020–2024: MOST Outstanding Young Scholar Research Project (科技部優秀年輕學者研究計畫), a four-year award.

• 2018–2021, 2023, 2025: National Central University Outstanding Research Awards (中央大學傑出研究獎勵).

• Ministry of Education Government Scholarship for Overseas Study in Mathematics (95年度教育部公費留學數學學門獲獎者).

Research grants

• 2024–2026: Optimal classical and quantum codes. Taiwan NSTC Grant 113-2115-M-008-007-MY2.

• 2020–2024: Optimal spherical codes and designs. Taiwan MOST Grant 109-2628-M-008-002-MY4; Outstanding Young Scholar Research Project.

• 2018–2020: Various methods on equiangular lines. Taiwan MOST Grant 107-2115-M-008-010-MY2.

Academic and professional service

Journal refereeing: Journal of Combinatorial Theory, Series A; European Journal of Combinatorics; SIAM Journal on Discrete Mathematics; Applied and Computational Harmonic Analysis; IEEE Transactions on Information Theory.

Professional service: Member, Mathematical Olympiad Committee, Taiwan (中華民國數學奧林匹亞委員會), academic years 110–114.

University service: Undergraduate and graduate advising at National Central University; service on the Calculus Teaching Committee, advising committees, Library Management Committee, and Department Alumni Committee. Career mentor and faculty advisor to the mathematics student association; convener of the advising committee in academic year 112.

Additional Materials

Research materials

• Conjecture Prize

• Attachment for “The real equiangular tight frames obtained from rank 3 graphs”

Earlier talks and materials

• WPI slides, 2015

• Anhui University slides, 2016

• Beijing slides, 2018

• Shanghai materials, 2018

Last updated: September 2026.

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