Dr. Khushdil Ahmad | Pure Mathematics | Excellence in Research

Khushdil Ahmad | Government College University | Pakistan

Dr. Khushdil Ahmad is a Visiting Faculty Member in the Department of Mathematics at Government College University, Lahore, specializing in Fixed Point Theory, Nonlinear Analysis, and Algebraic Combinatorics. He earned his Ph.D. in Mathematics from Government College University, Lahore, where his research explored posets at the intersection of combinatorics and category theory under the supervision of Prof. Dr. Khurram Shabbir and Dr. Eric Rubiel Dolores-Cuenca. He also holds an M.Phil. in Mathematics from the same institution, where he investigated the approximation of fixed points of multivalued nonexpansive mappings in ordered CAT(0) spaces, and a BS in Mathematics from Government Post Graduate Jahanzeb College, Swat. Dr. Ahmad has served as a visiting faculty member at both Government College University, Lahore, and Government M.A.O. Graduate College, Lahore, teaching a range of undergraduate and advanced mathematics courses including Real Analysis, Optimization Theory, Graph Theory, and Numerical Analysis. His research contributions encompass over ten peer-reviewed publications in reputed international journals such as Symmetry, Fractal and Fractional, Journal of Function Spaces, AIMS Mathematics, and Journal of Algebraic Combinatorics. His work focuses on iterative schemes, computational methods in Banach and CAT(0) spaces, and applications of fixed point theory in mathematical modeling and dynamic systems. In addition to his research, he actively serves as a reviewer for multiple international journals, including Open Mathematics, Alexandria Engineering Journal, Qeios, Sahand Communications in Mathematical Analysis, and Iraqi Journal of Science. Dr. Ahmad is also an Academic Board Member of Global Open Share Publishing and advisor to Dr. Salam Society for Mathematics at GC University. His scholarly excellence is reflected in his growing citation record and contributions to collaborative global research. He has presented at international conferences, including the 1st International Conference on Mathematics and Mathematics Education, Indonesia, and continues to advance mathematical inquiry through both teaching and research.27 Citations, 11 Documents, h-index: 3.

Profiles: Scopus | ORCID | Google Scholar

Featured Publications

1. Ahmad, K.*., Shabbir, K., & Ahsan, K. (2025). A refined inertial-like subgradient method for split equality problems. AppliedMath, 5(3), 117.

2. Jia, J., Shabbir, K., Ahmad, K.*, Shah, N. A., & Botmart, T. (2022). Strong convergence of a new hybrid iterative scheme for nonexpensive mappings and applications. Journal of Function Spaces, 2022(1), 4855173. Citations: 19

3. Ahmad, K.*., Dolores-Cuenca, E. R., & Shabbir, K. (2025). Shuffle series. Journal of Algebraic Combinatorics, 61(2), 1–40. Citations: 2.

4. Ahmad, K.*., Shabbir, K., & Nazar, N. (2024). Convergence analysis of Picard–Thakur hybrid iterative scheme for α-nonexpansive mappings in uniformly convex Banach spaces. International Journal of Applied Mathematical Research, 13(1), 34–48. Citations: 2.

5. Khan, S. H., Ahmad, K.*, & Abbas, M. (2023). Approximation of fixed points for a pair of certain nonexpansive type mappings with applications. Punjab University Journal of Mathematics, 55(11), 427–449. Citations: 2.

Assist. Prof. Dr. Hao Guo | Pure Mathematics | Best Researcher Award

Assistant Professor at Tsinghua University, China

Dr. Hao Guo 🎓 is a leading early-career mathematician specializing in geometric analysis, noncommutative geometry, and quantitative K-theory 📐📊. Currently a tenure-track Assistant Professor at the Yau Mathematical Sciences Center, Tsinghua University 🏛️, he has authored impactful publications in top-tier journals such as Journal of Functional Analysis and Mathematische Annalen 📚. His research advances understanding of scalar curvature and index theory, with applications in modern mathematical physics 🔬. Dr. Guo is also an invited speaker at prestigious global seminars 🌏 and a co-author of an upcoming CBMS monograph with the AMS 🖋️. His contributions to both teaching and research have earned him the 2024 Ruo Lin Award 🏅. Through academic leadership, global collaboration 🤝, and deep theoretical insight, Dr. Guo exemplifies innovation and excellence in contemporary mathematics.

Professional Profile

🎓 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. 🏅📐

Khushdil Ahmad | Pure Mathematics | Excellence in Research