I am an Assistant Professor of Mathematics and Rosenberg Scholar in the Department of Mathematics at Caltech. I previously obtained my PhD from Stanford University, where I was very fortunate to be advised by Professor Jacob Fox. I got my BS in Mathematics and MS in Statistics with Honors and Distinction from Stanford University, and a Master of Advanced Study in Mathematics with Distinction from the University of Cambridge.
The ICM 2026 Satellite conference on Synergies in Combinatorics and Theoretical Computer Science (co-organized with David Conlon, Irit Dinur, Jacob Fox, and Raghu Meka) will be held at the Merkin Center (Caltech) from August 3 to August 7, 2026.
Links: Conference webpage | Registration form
Probabilistic and extremal combinatorics, additive combinatorics, probability theory, theoretical computer science, deep learning.
Probabilistic and Extremal Combinatorics
On Graham's rearrangement conjecture,
H. T. Pham, Lisa Sauermann, (arXiv)
Random Cayley graphs and random sumsets,
Noga Alon, H. T. Pham, (arXiv)
A Sharp Version of Talagrand's Selector Process Conjecture and an
Application to Rounding Fractional Covers,
H. T. Pham, STOC 2025. (arXiv)
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes,
Jinyoung Park, H. T. Pham, Annals of Mathematics. (arXiv)
A proof of the Kahn-Kalai Conjecture,
Jinyoung Park, H. T. Pham, J. Amer. Math. Soc (2024). A preliminary version appears in FOCS 2022. (arXiv) (Talk) (an interview with Two Sigma)
On the clique number of random Cayley graphs and related topics,
David Conlon, Jacob Fox, H. T. Pham, Liana Yepremyan, (arXiv)
Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings,
Vishesh Jain, H. T. Pham. SODA 2024 (arXiv)
A Toolkit for Robust Thresholds,
H. T. Pham, Ashwin Sah, Mehtaab Sawhney, Michael Simkin. (arXiv)
Regularity method and large deviations principles for the Erdos-Renyi hypergraph,
Nicholas Cook, Amir Dembo, H. T. Pham, Duke Math. J. (2024). (arXiv)
Short proof of the hypergraph container theorem,
Rajko Nenadov, H. T. Pham. (arXiv)
Spread blow-up lemma with an application to perturbed random graphs,
Rajko Nenadov, H. T. Pham. (arXiv)
Sunflowers in set systems with small VC-dimension,
J. Balogh, A. Bernshteyn, M. Delcourt, A. Ferber, H. T. Pham. (arXiv)
The largest subgraph without a forbidden induced subgraph,
Jacob Fox, Rajko Nenadov, H. T. Pham. (arXiv)
Equivalence between Erdos-Hajnal and polynomial Rodl and Nikiforov conjectures,
Matija Bucic, Jacob Fox, H. T. Pham. (arXiv)
Set-coloring Ramsey numbers and error-correcting codes near the zero-rate threshold,
David Conlon, Jacob Fox, H. T. Pham, Yufei Zhao, IEEE Trans. Inform. Theory. (arXiv)
On random irregular subgraphs,
Jacob Fox, Sammy Luo, H. T. Pham, Random Struct. Algorithms. (arXiv)
A multipartite analogue of Dilworth's Theorem,
Jacob Fox, H. T. Pham. (arXiv)
Additive Combinatorics
Sharp bound for the Erdos-Straus non-averaging set problem,
H. T. Pham, Dmitrii Zakharov. (arXiv)
Homogeneous structures in subset sums and non-averaging sets,
David Conlon, Jacob Fox, H. T. Pham. (arXiv)
Subset sums, completeness and colorings,
David Conlon, Jacob Fox, H. T. Pham. (arXiv)
Small subsets with large sumset: Beyond the Cauchy–Davenport bound,
Jacob Fox, Sammy Luo, H. T. Pham, Yunkun Zhou, Comb. Probab. Comput. (arXiv)
The upper logarithmic density of monochromatic subset sums,
David Conlon, Jacob Fox, H. T. Pham, Mathematika (2022). (arXiv)
Tower-type bounds for Roth's theorem with popular differences,
Jacob Fox, H. T. Pham, Yufei Zhao, J. Eur. Math. Soc. (2022). (arXiv)
Popular progression differences in vector spaces,
Jacob Fox, H. T. Pham, Int. Math. Res. Not. IMRN 7 (2021), 5261–5289. (arXiv)
Popular progression differences in vector spaces II,
Jacob Fox, H. T. Pham, Discrete Anal., 2019:16. (arXiv)
Common and Sidorenko linear equations,
Jacob Fox, H. T. Pham, Yufei Zhao, Q. J. Math. 72 (2021), 1223–1234. (arXiv)
Popular monochromatic progression differences,
Jacob Fox, H. T. Pham.
A question of Erdos and Graham on Egyptian fractions,
David Conlon, Jacob Fox, Xiaoyu He, Dhruv Mubayi, H. T. Pham, Andrew Suk, Jacques Verstraete. (arXiv)
An explicit economical additive basis,
Vishesh Jain, H. T. Pham, Mehtaab Sawhney, Dmitrii Zakharov. (arXiv)
On monochromatic solutions to linear equations over the integers,
Dingding Dong, Nitya Mani, H. T. Pham, Jonathan Tidor. (arXiv)
Universality for Low-Degree Factors of Random Polynomials over Finite Fields,
Jimmy He, H. T. Pham, Max Wenqiang Xu, Int. Math. Res. Not. IMRN (2022). (arXiv)
Mixing time of fractional random walk on finite fields,
Jimmy He, H. T. Pham, Max Wenqiang Xu, Electron. J. Probab. 27 (2022). (arXiv)
Irreducibility of random polynomials of bounded degree,
H. T. Pham, Max Wenqiang Xu, Discrete Anal., 2021:7. (arXiv)
Deep Learning Theory
A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks,
Phan-Minh Nguyen*, H. T. Pham*, Mathematical Statistics and Learning 6 (2023). (arXiv) (Slides) (Talk)
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training,
H. T. Pham*, Phan-Minh Nguyen*. (arXiv, NeurIPS 2021)
Global convergence of three-layer neural networks in the mean field regime,
Phan-Minh Nguyen*, H. T. Pham*. (ICLR 2021 Oral)
A Note on the Global Convergence of Multilayer Neural Networks in the Mean Field Regime,
H. T. Pham*, Phan-Minh Nguyen*. (arXiv)
*: Author ordering is randomized.
Theoretical Computer Science, approximate sampling and counting
Sampling from Spherical Spin Glasses in Total Variation via Algorithmic Stochastic Localization,
Brice Huang, Andrea Montanari, H. T. Pham. (arXiv)
Optimal mixing of the down-up walk on independent sets of a given size,
Marcus Michelen, Vishesh Jain, H. T. Pham, Thuy-Duong Vuong, FOCS 2023. (arXiv)
On the sampling Lovasz Local Lemma for atomic constraint satisfaction problems,
Vishesh jain, H. T. Pham, Thuy-Duong Vuong. (arXiv)
Towards the sampling Lovasz Local Lemma,
Vishesh Jain, H. T. Pham, Thuy-Duong Vuong, FOCS 2021. (arXiv)
Entropic Independence: Optimal mixing of down-up random walks,
Nima Anari, Vishesh Jain, Frederic Koehler, H. T. Pham, Thuy-Duong Vuong, STOC 2022.
Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Polynomials and High-Temperature Ising Model,
Nima Anari, Vishesh Jain, Frederic Koehler, H. T. Pham, Thuy-Duong Vuong. (arXiv)
Entropic Independence II: Optimal Sampling and Concentration via Restricted Modified Log-Sobolev Inequalities,
Nima Anari, Vishesh Jain, Frederic Koehler, H. T. Pham, Thuy-Duong Vuong. (arXiv)
Spectral independence, coupling with the stationary distribution, and the spectral gap of the Glauber dynamics,
Vishesh Jain, H. T. Pham, Thuy-Duong Vuong, Information Processing Letters 177 (2022). (arXiv)
Universality of Spectral Independence with Applications to Fast Mixing in Spin Glasses,
Nima Anari, Vishesh Jain, Frederic Koehler, H. T. Pham, Thuy-Duong Vuong, SODA 2024. (arXiv)
Almost periodicity and its applications to Roth's theorem,
H. T. Pham. (pdf)
Simons Symposium on New Frontiers in Combinatorics & Computer Science, August 2025
Plenary talk at the ICBS, July 2025
UChicago Chern-Weil Symposium, May 2025.
Plenary talk at the 2nd Brazillian School of Combinatorics, March 2025.
IAS Computer Science/Discrete Mathematics Seminar II, 1\& 2, February 2025.
IBS Winter school on Synergies of Extremal and Probabilistic Combinatorics, January 2025.
VIASM Minicourse on Synergies of Extremal and Probabilistic Combinatorics, August 2024.
ICBS Frontiers of Science Award talk, July 2024.
VIASM Annual meeting, July 2024.
Plenary talk and Konig prize lecture at the SIAM Conference on Discrete Mathematics, July 2024.
IAS Computer Science/Discrete Mathematics Seminar I, II, May 2024.
Denes Konig Prize - 2024.
ICBS Frontiers of Science Award - 2024.
Clay Research Fellowship - 2023-2028.
Stanford Science Fellowship - 2023-2024.
Rank 1 - Part III of the Mathematical Tripos - University of Cambridge, 2019.
Pure Mathematics Prize - University of Cambridge, 2019.
Awarded to best student in Pure Mathematics at Part III of the Mathematical Tripos.
Morgan Prize Honorable Mention, 2018.
Kennedy Thesis Prize in the Natural Sciences - Stanford University, 2018.
Awarded to the best senior honors thesis in each of the following areas of study: humanities, social sciences, natural sciences, and engineering and applied sciences.
Deans’ Award for Academic Achievement - Stanford University, 2017.
Awarded to between five and ten extraordinary undergraduate students, based on excellent academic achievements and independent research.
Gold Medal - International Mathematical Olympiad, 2014, 2013.