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Kate Wenqi Zhu

Postdoctoral Researcher

University of Oxford

Biography

Hi! I’m Kate Wenqi Zhu, a Postdoctoral Researcher at the Mathematical Institute, University of Oxford, working on AI in the Mathematical Foundations of AI under the supervision of Prof. Jared Tanner.

I received my D.Phil. in Mathematics from the University of Oxford in 2026, supervised by Prof. Coralia Cartis. My research sits at the intersection of optimization, numerical analysis, algebraic geometry, and AI-driven mathematical discovery. My core work focuses on high-order tensor methods for nonconvex optimization, including computational complexity analysis, tensor approximation, sum-of-squares techniques, polynomial optimization, and implementable high-order subproblem solvers.

Looking ahead, my research aims to develop AI-integrated systems for large-scale mathematical discovery, combining generative AI with algebraic and optimization theory to uncover mathematical structures beyond the reach of classical solvers.

Before my D.Phil., I completed an M.Sc. in Mathematical Modelling and Scientific Computing at Oxford, ranked first in cohort, as well as a BA and MMath in Mathematics at Oxford. I also gained industry experience at Goldman Sachs and J.P. Morgan before returning to academic research.

Potential Collaborations: If you are interested in optimization, AI for mathematics, or AI-integrated mathematical discovery, feel free to reach out.

Interests

  • AI-Integrated Mathematical Discovery
  • Higher-Order Optimization
  • Tensor Methods / Tensor Approximation
  • Sum-of-Squares Techniques
  • Computational Complexity Analysis
  • Regularization Techniques
  • Tractable Polynomial Optimization

Education & Experience

  • Postdoctoral Researcher, 2026-present
    University of Oxford
  • D.Phil. in Mathematics, 2022-2026
    University of Oxford
  • M.Sc. Mathematical Modelling and Scientific Computing, 2021
    University of Oxford
  • BA & MMath Mathematics, 2010-2014
    University of Oxford
Jun 30, 2026

Congrats! Zhu Mind / Master Mind was conditionally approved for the HKSTP Programme.

Mar 15, 2026

New preprint posted: A Globally Convergent Third-Order Newton Method via Unified Semidefinite Programming Subproblems.

Mar 01, 2026

Invited to give a 1-hour research talk at the University of Bath, UK.

Jan 26, 2026

New preprint posted: Sufficiently Regularized Nonnegative Quartic Polynomials are Sum-of-Squares.

Jan 20, 2026

Our paper Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization appeared in Mathematical Programming Computation.

Jan 15, 2026

Our tensor-based Dinkelbach method paper appeared in Applied Numerical Mathematics: link.

Jan 10, 2026

Our paper Recover Cell Tensor: Diffusion-Equivalent Tensor Completion for Fluorescence Microscopy Imaging was accepted to ICLR 2026.

Jan 01, 2026

Started as a Postdoctoral Researcher at the Mathematical Institute, University of Oxford, working on AI in the Mathematical Foundations of AI with Prof. Jared Tanner.

Dec 01, 2025

Invited to give a 1-hour online research talk at the University of California.

Aug 01, 2025

Organized two minisymposia and gave a talk at ICCOPT 2025, focusing on higher-order optimization and polynomial methods.

Jul 15, 2025

Presented recent work at EUROPT 2025 (Southampton) and the Biennial Numerical Analysis Conference (Glasgow).

Jul 01, 2025

Awarded Leslie Fox Prize for Numerical Analysis Second Prize Awardees 🏆 Link)

Jul 01, 2025

Invited to give a 1-hour research talk at Tsinghua University on higher-order optimization methods.

Jun 30, 2025

Presenting our LLM Sum-of-Square Solvers in ICML AI4Maths Link

Jun 10, 2025

Academic visit and research talks in Shenzhen, including Shenzhen University, CUHK–Shenzhen, and SUSTech.

May 16, 2025

📝 QQR got accepted for Mathematical Programming! Link

May 10, 2025

V+A got accepted to IMA Journal of Numerical Analysis! Link)

Apr 16, 2025

New paper on Global Optimality Characterizations of Third-Order Taylor Polynomials posted to arXiv Link

Jan 16, 2025

A novel tensor-based Dinkelbach-Type method for computing extremal tensor generalized eigenvalues, new Paper posted to arXiv Link

Jan 13, 2025

New Paper accepted to IEEE Transactions on Geoscience and Remote Sensing (TGRS), new application to radar automatic target recognition Link

Jan 03, 2025

📝 New papers submitted and under review. First numeric paper on High-order tensor methods Link !

Dec 21, 2024

I am excited to join RisingWISE Training & Development for STEM early career women researchers

Nov 15, 2024

📝 CQR got accepted for Mathematical Programming CQR!

Jul 22, 2024

🎓 Honoured to be invited to the Chinese Academy of Sciences to give a talk and research visit. Heading to Beijing.

Jun 25, 2024

I will be visiting the Chinese Academy of Sciences in Beijing, China for a research collaboration.

Apr 21, 2024

🌟 Thrilled to receive an invitation to the Jane Street Graduate Research Fellowship Research Workshop with a Travel Grant to travel to the States. *

Apr 03, 2024

📝 1 paper submitted and under review, Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models

Mar 21, 2024

📝 1 paper Newsvendor conditional value-at-risk minimisation: A feature-based approach under adaptive data selection got accepted by EJOR.

Dec 25, 2023

📝 Two papers submitted and under review. Go CQR and QQR!

Jul 01, 2023

Invited for Mini symposia in the Optimization 2023 Conference at the University of Aveiro, Portugal.

Jun 22, 2023

Honoured to present my research at the Biennial Numerical Analysis Meeting at the University of Strathclyde, Glasgow, Scotland.

Jun 01, 2023

I had an amazing time presenting at the SIAM Conference on Optimization in Seattle, U.S.

Apr 15, 2023

Research visit to the CIMDA Centre for Intelligent Multidimensional Data Analysis in Hong Kong, China.

Dec 01, 2022

📝 🏅 NeurIPS Workshop Spotlight Talk Award for “The Benefits of Higher-Order Optimization in Machine Learning Workshop.” link

Sep 03, 2022

Presented in the IMA Conference on the Mathematical Challenges of Big Data in Oxford, UK.

Jul 01, 2022

Presented my research at the IMA Conference on Numerical Linear Algebra and Optimization in Birmingham, UK. My first presentation in conference!

Nov 28, 2021

💼 Awarded Full DPhil Studentship, funded by INNOHK and CIMDA Centre partnership to support my PhD research, starting my PhD Journey!

Sep 30, 2021

🥇 M.Sc. Prize for Excellence for graduating top 1 in the cohort in M.Sc. degree in Mathematical Modelling and Scientific Computing from.

Sep 05, 2021

🏅 Catherine Hughes Fund Internship Award from Somerville College, Oxford for research excellence.

May 15, 2021

📚 DTP Studentship and Industrial CASE Studentship funded by UKRI-BBSRC and Syngenta Group awarded*

Jan 01, 2011

📝 🏆 Archibald Jackson Prize and St. Hugh’s College Scholarship awarded for academic distinction at Oxford (2011-2014).

  1. Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization

    Adaptive high-order tensor methods require practical strategies for solving and selecting higher-order subproblem minimizers. This work develops implementable p = 3 variants with adaptive interpolation updates and prerejection mechanisms that improve numerical efficiency.

  2. Tensor-Based Dinkelbach Method for Computing Generalized Tensor Eigenvalues and Its Applications

    This paper develops a tensor-based Dinkelbach-type method for generalized tensor eigenvalue problems, with applications to nonlinear and multilinear spectral computations.

  3. Recover Cell Tensor: Diffusion-Equivalent Tensor Completion for Fluorescence Microscopy Imaging

    This work studies diffusion-equivalent tensor completion for fluorescence microscopy imaging and appears at ICLR 2026.

  4. Cubic-Quartic Regularization Models for Solving Polynomial Subproblems in Third-Order Tensor Methods

    This paper proposes the CQR framework for minimizing nonconvex cubic multivariate polynomials with quartic regularization, deriving optimality characterizations and efficient root-finding procedures for practical high-order tensor methods.

  5. Second-Order Methods for Quartically-Regularised Cubic Polynomials, with Applications to High-Order Tensor Methods

    This paper introduces QQR, a second-order method for minimizing nonconvex quartically regularized cubic polynomials through tractable quadratic-quartic local models.

  6. SoS1: O1 and R1-Like Reasoning LLMs are Sum-of-Square Solvers

    This work connects reasoning LLMs with sum-of-squares solving, contributing to AI-integrated mathematical discovery and automated mathematical reasoning.