🎓 Education

Dr. Hao Guo holds a Ph.D. in Pure Mathematics (2018) from the University of Adelaide, Australia, where his thesis focused on Positive Scalar Curvature and Callias-Type Index Theorems for Proper Actions under the supervision of Professors Varghese Mathai and Hang Wang. 📘 He earned his B.Sc. with First Class Honours (2016) from the University of Sydney, completing a thesis on De Rham-Hodge Theory and Witten’s Deformation. 📚 His educational journey reflects strong foundations in differential geometry, index theory, and noncommutative geometry. With training from top Australian institutions and mentorship from internationally respected mathematicians, Dr. Guo has developed both depth and versatility in mathematical thinking, setting the stage for his impactful contributions to geometric analysis and operator algebras. 🧠✏️

💼 Professional Experience

Dr. Guo currently serves as a tenure-track Assistant Professor at the Yau Mathematical Sciences Center, Tsinghua University (2022–present) 🏫, one of Asia’s leading mathematical institutes. Prior roles include ARC Research Associate at the University of Adelaide (2020–2021) and Visiting Assistant Professor at Texas A&M University (2018–2020) 🌐. These positions have enabled him to collaborate across continents, engage in deep theoretical work, and teach a variety of advanced mathematics courses. 👨‍🏫 He has also taken on leadership roles in organizing international conferences and working seminars, reflecting his commitment to academic community-building. His professional path is marked by global experience, cross-disciplinary exposure, and a trajectory toward excellence in both research and education. 🌍📈

🔬 Research Interests

Dr. Guo’s research lies at the intersection of differential geometry, operator algebras, noncommutative geometry, and quantitative K-theory. 🧮 His work focuses on problems related to positive scalar curvature, higher index theory, and coarse geometry. Using advanced analytic and topological tools, he has contributed to the development of equivariant index theorems and functoriality in higher rho invariants. 📐 His recent research explores covering complexity, band width problems, and large-scale geometric invariants. By blending geometric intuition with deep algebraic structures, Dr. Guo addresses some of the most intricate and abstract questions in modern mathematics—pushing forward the boundaries of theoretical research with high impact and originality. 🧠🔍

🏅 Awards and Honors

Dr. Hao Guo has received multiple accolades recognizing both his research and teaching excellence. Most notably, he was awarded the 2024 Ruo Lin Award at Tsinghua University for an outstanding research paper. 🥇 During his Ph.D., he earned the Dean’s Commendation for Doctoral Thesis Excellence (2018) and the Walter & Dorothy Duncan Trust Travel Grant (2017). 🎓 Earlier, he was honored with the B.H. Neumann Prize (2016) for the best student talk at the Annual Meeting of the Australian Mathematical Society. 🏆 His diverse recognitions—from thesis to teaching awards—demonstrate a well-rounded academic profile, blending innovation, communication, and rigor across his career. 💡📜

🧠 Research Skills

Dr. Guo demonstrates expertise in a wide range of mathematical and technical skills. He is proficient in geometric analysis, index theory, and operator algebras, with deep command of tools in noncommutative geometry and K-theory. 🔢 He is also skilled in computational platforms such as Mathematica, MATLAB, Python, and LaTeX—essential for both analytical computation and formal mathematical writing. 💻 In addition, Dr. Guo has excellent academic writing and presentation abilities, having delivered over 30 invited talks and lectures at major international conferences and seminars. 📊 His collaborative approach and methodological rigor make him a highly effective contributor to both independent and team-based research environments. 🤝📈

Publications Top Note 📝

• Title: Quantitative K-Theory, Positive Scalar Curvature, and Band Width
  Authors: H. Guo, Z. Xie, G. Yu
  Year: 2020
  Citations: 18
  Source: Perspectives on Scalar Curvature, edited by M.L. Gromov and H.B. Lawson Jr., pp. 763–798

• Title: Positive Scalar Curvature and Poincaré Duality for Proper Actions
  Authors: H. Guo, V. Mathai, H. Wang
  Year: 2019
  Citations: 14
  Source: Journal of Noncommutative Geometry, Vol. 13(4), pp. 1381–1433

• Title: Equivariant Callias Index Theory via Coarse Geometry
  Authors: H. Guo, P. Hochs, V. Mathai
  Year: 2021
  Citations: 12
  Source: Annales de l’Institut Fourier, Vol. 71(6), pp. 2387–2430

• Title: Index of Equivariant Callias-Type Operators and Invariant Metrics of Positive Scalar Curvature
  Authors: H. Guo
  Year: 2021
  Citations: 10
  Source: The Journal of Geometric Analysis, Vol. 31(1), pp. 1–34

• Title: A Lichnerowicz Vanishing Theorem for the Maximal Roe Algebra
  Authors: H. Guo, Z. Xie, G. Yu
  Year: 2023
  Citations: 8
  Source: Mathematische Annalen, Vol. 385(1), pp. 717–743

• Title: Coarse Geometry and Callias Quantisation
  Authors: H. Guo, P. Hochs, V. Mathai
  Year: 2021
  Citations: 8
  Source: Transactions of the American Mathematical Society, Vol. 374(4), pp. 2479–2520

• Title: Positive Scalar Curvature and an Equivariant Callias-Type Index Theorem for Proper Actions
  Authors: H. Guo, P. Hochs, V. Mathai
  Year: 2021
  Citations: 5
  Source: Annals of K-Theory, Vol. 6(2), pp. 319–356

• Title: Functoriality for Higher Rho Invariants of Elliptic Operators
  Authors: H. Guo, Z. Xie, G. Yu
  Year: 2021
  Citations: 3
  Source: Journal of Functional Analysis, Vol. 280(10), Article 108966

• Title: Covering Complexity, Scalar Curvature, and Quantitative K-Theory
  Authors: H. Guo, G. Yu
  Year: 2022
  Citations: 2
  Source: arXiv preprint, arXiv:2203.15003

• Title: An Equivariant Poincaré Duality for Proper Cocompact Actions by Matrix Groups
  Authors: H. Guo, V. Mathai
  Year: 2022
  Citations: 1
  Source: Journal of Noncommutative Geometry, Vol. 16(4)

• Title: Positive Scalar Curvature and Callias-Type Index Theorems for Proper Actions
  Authors: H. Guo
  Year: 2019
  Citations: 1
  Source: Bulletin of the Australian Mathematical Society, Vol. 99(2), pp. 342–343

• Title: A Higher Index and Rapidly Decaying Kernels
  Authors: H. Guo, P. Hochs, H. Wang
  Year: 2025
  Source: arXiv preprint, arXiv:2505.02498

• Title: A Higher Index on Finite-Volume Locally Symmetric Spaces
  Authors: H. Guo, P. Hochs, H. Wang
  Year: 2024
  Source: arXiv preprint, arXiv:2407.16275

• Title: Higher Localised Â-Genera for Proper Actions and Applications
  Authors: H. Guo, V. Mathai
  Year: 2022
  Source: Journal of Functional Analysis, Vol. 283(12), Article 109695

✅ Conclusion

Dr. Hao Guo stands out as a rising leader in pure mathematics, combining rigorous theoretical research with a global academic presence. 🌟 His work on scalar curvature, index theory, and noncommutative geometry has garnered international attention, bolstered by prestigious awards and high-impact publications. 📚 As an educator, speaker, and mentor, he has made meaningful contributions to mathematical communities across Asia, Australia, and the U.S. 🌏 With strong research momentum, cross-disciplinary skills, and leadership in academic initiatives, Dr. Guo exemplifies the qualities of a world-class scholar. 🧑‍🔬 He is exceptionally well-suited for recognition through a Best Researcher Award and promises continued innovation in the mathematical sciences. 🏅📐