Xiang Xiang Wang

I am a Postdoctoral Research Associate in the Department of Mathematics at the University of Georgia, working with Prof. Guo-Wei Wei. I previously spent a year in Prof. Wei’s group as a Research Associate at Michigan State University. My research focuses on mathematical AI for data science, developing mathematical and computational tools — drawing on differential geometry, topology, and matrix analysis — to make sense of complex, high-dimensional data in biology and imaging, from single-cell genomics to viral classification. I completed my Ph.D. in Mathematics at the University of Nevada, Reno.

News

• [Sep 2026] Received the 2026 Phi Kappa Phi Love of Learning Award.
• [May 2026] Featured in Nevada Today: Math alumna advances mathematical methods at Michigan State University

Research Interests

• Topological and Geometric Data Analysis
• Grassmannian and Riemannian Geometry
• Matrix and Quaternion Matrix Analysis
• Mathematical AI and Data Science
• Machine Learning for Biological and Imaging Data

Research Experience

• Postdoc Research Associate, University of Georgia, 2026-present (Advisor: Guo-Wei Wei) — I develop mathematical AI methods for data science by integrating geometric and topological representations with machine learning. My research uses Grassmannian geometry and topological data analysis to capture structure in high-dimensional biological data. Recent projects include GrassTop for viral classification and phylogenetic analysis and data-adaptive Grassmann manifold representations for spatial transcriptomics alignment.
• Research Associate, Michigan State University, 2025-2026 (Advisor: Guo-Wei Wei) — Developed geometric, topological, and spectral methods for biological and imaging data analysis, including Grassmann manifold models and sheaf-based methods.
• Ph.D. Student in Mathematics, University of Nevada, Reno, 2021-2025 (Advisor: Tin-Yau Tam) — Investigated Grassmannian geometry and quaternion matrix methods for data representation, with applications to image and video analysis.
• Statistical Analyst, Provost Office of University of Nevada, Reno, June 2023-August 2023 — Designed data processing workflows for the Co-Requisite Assessment Program.
• Master’s Student in Statistics, Shanghai University, 2017-2020 (Advisor: Qing-Wen Wang) — Researched quaternion matrices and eigenvalue problems, developed a fast algorithm for computing eigenvalues of large-scale quaternion matrices.

Funded Grants

• Co-Principal Investigator, Self-Assembly of Tunable Molecular Memristors with Long-Range Order for Resilient and Energy-Efficient Neuromorphic Computing. U.S. Department of Energy, Office of Science, Basic Energy Sciences, through Pacific Northwest National Laboratory. $360,000, June 15, 2026–January 14, 2029. PNNL Award No. PNNL0000883191; DOE FWP 84274. PI: Guo-Wei Wei.

Education

• 2021-2025: Ph.D. in Mathematics, Department of Mathematics and Statistics, University of Nevada, Reno. GPA: 4 (out of 4)
• 2017-2020: M.Sc. in Statistics, Shanghai University. Average Score: 90.25 (out of 100)
• 2013-2017: B.Sc. in Information and Computing Science, North China University of Water Resources and Electric Power. Consistently ranked first in my major each semester

Awards

• Love of Learning Award, The Honor Society of Phi Kappa Phi, 2026.
• College of Science Outstanding Graduate Assistant Award, University of Nevada, Reno. 2025
• Graduate Student Association (GSA) Travel Award, University of Nevada, Reno, 2022. ($500)
• Graduate Student Association (GSA) Research Grant Award, University of Nevada, Reno, 2021. ($1,000)
• Graduate Dean’s Merit Scholarship, University of Nevada, Reno, 2021. ($10,000)
• College Graduate Excellence Award of Shanghai City, China, 2020.
• Excellent Student Award of Shanghai University, China, 2018.
• Third Prize in “Huawei Cup”, the 15th China Post-Graduate Mathematical Contest in Modeling, Shanghai University, China, 2018.
• Outstanding Graduate Award of Henan Province, China, 2017.
• “Three Good Students” Award of General Higher Education in Henan Province, 2016.
• National Scholarship, China, 2015. (CNY 8,000)
• Second Prize in the Sixth National College Mathematics Competition, China, 2014.

Main Classes Taken

• Topology
• Numerical Analysis and Approximation
• Abstract and Real Analysis
• Complex Function Theory
• Seminar in Teaching Mathematics and Statistics
• Numerical Linear Algebra
• Set Theory and Hilbert Spaces
• Multilinear Algera

Teaching

• Teaching Assistant, Michigan State University — MTH 133 Calculus II, Spring 2026
• Instructor, Michigan State University — Mathematics-Assisted AI and AI-Inspired Mathematics, Fall 2025 (Delivered four lectures on advanced topics including manifold theory and quaternionic Grassmannians as part of a multi-instructor course)
• Instructor of Record, University of Nevada, Reno — Math 127 Precalculus II, Winter 2023, Summer 2023, Spring 2024
• Instructor of Record, University of Nevada, Reno — Math 126E Precalculus I Expanded, Fall 2023
• Instructor of Record, University of Nevada, Reno — Math 176 Introductory Calculus for Business and Social Sciences, Summer 2023, Fall 2024, Spring 2025, Summer 2025
• Teaching Assistant, University of Nevada, Reno — Math 126 Precalculus I, Fall 2022, Spring 2023
• Teaching Assistant, University of Nevada, Reno — Math 176 Introductory Calculus for Business and Social Sciences, Spring 2022
• Grader, University of Nevada, Reno — Theory of Positive Integers, Fall 2021, Fall 2023

Publications

Preprints and Manuscripts

• X.X. Wang, G.W. Wei, GrassTop: Grassmannian k-mer Topology for Viral Classification and Phylogenetic Analysis. Submitted to Theory in Biosciences, 2026. Preprint available on arXiv:2609.13341.
• X.X. Wang, S. Cottrell, G.W. Wei, Data-Adaptive Grassmann Manifold Representations for Spatial Transcriptomics Alignment. Submitted to SIAM Journal on Applied Mathematics, 2026. Preprint available on arXiv:2609.12805.
• S. Cottrell, X.X. Wang, G.W. Wei, A Review of Geometric, Topological, and Spectral Approaches in Single-Cell Data Analysis. Submitted to Current Opinion in Systems Biology, 2026.
• T.Y. Tam, X.X. Wang, Geometric Means and Their Properties of Grassmannians. Preprint available on arXiv:2412.15161, 2025.

Published and Accepted

• X.X. Wang, G.W. Wei, A Hierarchical Sheaf Spectral Embedding Framework for Single-Cell RNA-seq Analysis, SIAM Journal on Life Sciences, accepted for publication, 2026. arXiv:2603.26858.
• X.X. Wang, G.W. Wei, Multi-dimensional Persistent Sheaf Laplacians for Image Analysis, Foundations of Data Science, Early Access, 2026. DOI: 10.3934/fods.2026024.
• X.X. Wang, S. Cottrell, G.-W. Wei, Multiscale Grassmann Manifolds for Single-Cell RNA-seq Data Analysis, Machine Learning: Science and Technology, 7 (2026), 3 (20 pages).
• Z. Wang, D. Li, G. Wang, M. Zia, X. Wei, X.X. Wang, J. Jiang, Chaotic Dynamics-Regulated Topological Learning for Patient-Specific Preictal State Identification. Accepted for publication at Machine Learning: Science and Technology, 2026.
• X.X. Wang, T.-Y. Tam, Quaternion Grassmannians for Color Image Set Recognition, Journal of Mathematical Imaging and Vision, 68 (2026), 13 (16 pages).
• Z.H. He, Y.Z. Xu, Q.W. Wang, X.X. Wang, Solving a system of quaternion matrix equations by using PSVD for multiple matrices with applications, Journal of Computational and Applied Mathematics, (2025), 117072 (18 pages).
• Z.H. He, T.T. Liu, X.X. Wang, Eigenvalues of Quaternion Tensors: Properties, Algorithms and Applications, Advances in Applied Clifford Algebras, 35 (2025), 4 (23 pages).
• Z.H. He, W.L. Qin, J. Tian, X.X. Wang, Y. Zhang, A new Sylvester-type quaternion matrix equation model for color image data transmission, Computational and Applied Mathematics, 43 (2024), 227 (30 pages).
• Z.H. He, X.X. Wang, Y.F. Zhao, Eigenvalues of Quaternion Tensors with Applications to Color Video Processing, Journal of Scientific Computing, 94 (2023), 1 (15 pages).
• Z.H. He, C. Navasca, X.X. Wang, Decomposition for a quaternion tensor triplet with applications, Advances in Applied Clifford Algebras, 32 (2022), 9 (19 pages).
• Z.H. He, W.L. Qin, X.X. Wang, Some applications of a decomposition for five quaternion matrices in control system and color image processing, Computational and Applied Mathematics, 40 (2021), 205 (29 pages).
• S.W. Yu, Z.H. He, T.C. Qi, X.X. Wang, The equivalence canonical form of five quaternion matrices with applications to imaging and Sylvester-type equations, Journal of Computational and Applied Mathematics, 393 (2021), 113494 (20 pages).
• Z.H. He, C. Chen, X.X. Wang, A simultaneous decomposition for three quaternion tensors with applications in color video signal processing, Analysis and Applications, 19 (3) (2020) 529-549.
• Q.W. Wang, X.X. Wang, Arnoldi method for large quaternion right eigenvalue problem, Journal of Scientific Computing, 82 (2020), 58 (20 pages).
• G.H. Peng, X.X. Wang, Y.Z. Zhang, Multidimensional scaling analysis based on attribute reduction of bivariate mutual information, International Mathematical Forum, 12 (3) (2017) 111-118 (9 pages).

Presentations

Oral Presentations

• X.X. Wang, Grassmannian Methods for Single-Cell RNA-seq Data, The 27th Conference of the International Linear Algebra Society (ILAS 2026), Virginia, May 18-22, 2026.
• X.X. Wang, Grassmannian Methods for Visual and Single-Cell Data, Joint Mathematics Meetings (JMM 2026), Washington, January 4-7, 2026.
• X.X. Wang, Color Image and Video Recognition Based on Quaternionic Grassmannians, 2025 SIAM Great Lakes Section Annual Meeting, Chicago, September 27-28, 2025.
• X.X. Wang, Quaternion Grassmannians for Color Image Set Recognition, Joint Mathematics Meetings (JMM 2025), Seattle, January 8-11, 2025.
• X.X. Wang, Some Properties of Geodesic Triangles in Grassmannians, The 2024 Workshop Matrices and Operators (MAO 2024), Reno, USA, June 14-17, 2024.
• X.X. Wang, Some Inequalities of Geometric Means in Grassmannians, Joint Mathematics Meetings (JMM 2024), San Francisco, January 3-6, 2024.
• X.X. Wang, Geometric means and their properties of Grassmannians, The 10th International Conference on Matrix Analysis and Applications (ICMAA), KunMing, China, August 15-18, 2023.
• X.X. Wang, Geometric means and their properties of Grassmannians, International Workshop on Matrix Analysis and Its Applications, Quynhon, Vietnam, July 7-8, 2023.
• X.X. Wang, Arnoldi method for right eigenvalue problem of the large-scale quaternion matrices, Joint Mathematics Meetings (JMM 2023), Boston, January 4-7, 2023.
• X.X. Wang, Arnoldi method for right eigenvalue problem of the large-scale quaternion matrices, Joint Mathematics Meetings (JMM 2022), Seattle, January 5-8, 2022, postponed due to COVID-19 and held virtually, April 6-9, 2022.

Poster Presentations

• X.X. Wang, Some Inequalities of Geometric Means in Grassmannians, 6th Annual GSA Poster Symposium, November 1, 2023. [Poster]

Leadership & Collaboration

• Organizer, AMS Special Session “Mathematical and Computational Methods for Biological Structures and Data,” Spring Southeastern Sectional Meeting, Birmingham, AL, March 21, 2027 (upcoming).
• Co-organizer, special session at the Joint Mathematics Meetings (JMM 2027), upcoming.
• Organizer, MS34 “Mathematical and Computational Methods for High-Dimensional Biological Data,” SIAM Texas-Louisiana Sectional Meeting, Dallas, October 30–November 1, 2026 (upcoming).
• Co-organizer, Special Session on Matrix Analysis and Its Applications, Joint Mathematics Meetings (JMM 2026), Washington, DC, January 2026.
• Chaired sessions at major conferences (JMM 2025, MAO 2024).

Conference Attended

• Organizer, AMS Special Session “Mathematical and Computational Methods for Biological Structures and Data,” Spring Southeastern Sectional Meeting, University of Alabama at Birmingham, Birmingham, AL, March 21, 2027 (upcoming).
• Co-organizer, Special Session, Joint Mathematics Meetings (JMM 2027), Chicago, IL, January 12–15, 2027 (upcoming).
• Organizer, MS34 “Mathematical and Computational Methods for High-Dimensional Biological Data,” SIAM Texas-Louisiana Sectional Meeting, Southern Methodist University, Dallas, TX, October 30–November 1, 2026 (upcoming).
• Workshop on Molecular Biophysical Approaches for Drug Discovery Led by Prof. Duc Nguyen, Michigan State University, March 9–10, 2026.
• 2025 SIAM Great Lakes Section Annual Meeting, Chicago, September 27-28, 2025.
• Volunteer, The Association of Mathematics Teacher Educators (AMTE) 2025 Annual Conference, Grand Sierra Resort, Reno, NV, February 6–8, 2025.
• Chair, Special Session on Matrix Analysis and Its Applications, Joint Mathematics Meetings (JMM 2025), Seattle, January 8-11, 2025.
• Local Organizer, The 2024 Workshop Matrices and Operators (MAO 2024), UNR, June 14-17, 2024.
• Joint Mathematics Meetings (JMM 2024), San Francisco, January 3-6, 2024.
• The 10th International Conference on Matrix Analysis and Applications (ICMAA), KunMing, China, August 15-18, 2023 (Virtual).
• International Workshop on Matrix Analysis and Its Applications, Quynhon, Vietnam, July 7-8, 2023 (Virtual).
• Joint Mathematics Meetings (JMM 2023), Boston, January 4-7, 2023.
• International Conference on Matrix Theory with Applications (ICMTA), Jeju, Korea, December 1-5, 2022 (Virtual).
• Second international workshop on Matrix Theory and Applications, hosted by the Departments of Mathematics: AKFA University-Uzbekistan, Sukkur IBA University-Pakistan, Naresuan University-Thailand and Bukhara State University-Uzbekistan, November 15-17, 2022 (Virtual).
• International Workshop on Matrix Analysis and Its Applications (MAA 2022), Quy Nhon, Viet Nam, June 4, 2022 (Virtual).
• Joint Mathematics Meetings (JMM 2022), Seattle, January 5-8, 2022, postponed due to COVID-19 and held virtually April 6-9, 2022.
• The First NU-SIBAU International Workshop on Matrix Theory and Its Applications, hosted by the Department of Mathematics at Sukkur IBA University, Pakistan and the Department of Mathematics at Naresuan University, Thailand, October 15-17, 2021 (Virtual).
• The 2021 China-Korea International Conference on Matrix Theory with Applications & the 6th International Workshop on Matrix Inequalities and Matrix Equations (IRCTMT-AORC Joint Meeting & MIME 2021), Hainan Normal University, Hainan, China, and Shanghai University, China, November 26-27, 2021 (Virtual).

Pedagogical Training

• Seminar in Teaching Mathematics and Statistics, University of Nevada, Reno, Fall 2022. This course is designed to prepare graduate students for success as teaching assistants in mathematics and statistics.
• 2024 NSHE Corequisite Conference, Western Nevada College, Carson City, USA, April 25-26, 2024. This conference provided a platform for educators to reflect on and celebrate their achievements, strengthen professional relationships, and expand their networks.

Professional Organization Members and University Services

• Member, Phi Kappa Phi Honor Society.
• Member, American Mathematical Society (AMS).
• Member, International Linear Algebra Society (ILAS).
• Organizer, Lecture Series in Mathematical AI and Bioscience (MATH 8970), Department of Mathematics, University of Georgia, Fall 2026; Spring 2027 planned.
• Organizing Committee Member, Biweekly Matrix Seminar, Department of Mathematics and Statistics, University of Nevada, Reno, 2023–present.
• Mentor, Nevada GAIN Program, 2023.
• Journal Reviewer: Linear and Multilinear Algebra, Advances in Operator Theory, zbMath, The Electronic Journal of Linear Algebra, Numerical Algorithms, IEEE Transactions on Signal and Information Processing over Networks, Foundations of Data Science, Qualitative Theory of Dynamical Systems.
• Provided faculty feedback on Mathematics for Economics and Finance (2nd Edition), Cambridge University Press, May 2025 — for potential adoption in undergraduate economics courses.
• Volunteer, Feline Friends Program, Athens Humane Society, Athens, GA, since Fall 2026.

Skills and Interests

• Programming: Python, MATLAB, R, SQL.
• Mathematical and Machine Learning Methods: Topological data analysis, manifold learning, geometric representation learning, computer vision, statistical data analysis.
• Scientific Computing and Research Tools: PyTorch, Jupyter, Git/GitHub, LaTeX, SPSS.
• Other Interests: Snowboard, Hiking, Running.

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