I am a Third year PhD student in the Department of Mathematics at Stanford University. I am very fortunate to be advised by Professor Jacob Fox. I previously obtained 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. I am currently supported by a Two Sigma Fellowship.
Additive combinatorics, probabilistic methods in combinatorics, extremal combinatorics, probability theory, theoretical computer science, deep learning.
Probabilistic Combinatorics
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes,
Jinyoung Park, H. T. Pham. (arXiv)
Regularity method and large deviations principles for the Erdos-Renyi hypergraph,
Nicholas Cook, Amir Dembo, H. T. Pham, submitted. (arXiv)
A multipartite analogue of Dilworth's Theorem,
Jacob Fox, H. T. Pham, in preparation.
Additive Combinatorics
Subset sums, completeness and colorings,
David Conlon, Jacob Fox, H. T. Pham, submitted. (arXiv)
The upper logarithmic density of monochromatic subset sums,
David Conlon, Jacob Fox, H. T. Pham, Mathematika, to appear. (arXiv)
Tower-type bounds for Roth's theorem with popular differences,
Jacob Fox, H. T. Pham, Yufei Zhao, Journal of the European Mathematical Society, to appear. (arXiv)
Popular progression differences in vector spaces,
Jacob Fox, H. T. Pham, International Mathematics Research Notices 7 (2021), 5261–5289. (arXiv)
Popular progression differences in vector spaces II,
Jacob Fox, H. T. Pham, Discrete Analysis, 2019:16. (arXiv)
Common and Sidorenko linear equations,
Jacob Fox, H. T. Pham, Yufei Zhao, Quarterly Journal of Mathematics 72 (2021), 1223–1234. (arXiv)
Popular monochromatic progression differences,
Jacob Fox, H. T. Pham, to be submitted.
Mixing time of fractional random walk on finite fields,
Jimmy He, H. T. Pham, Max Wenqiang Xu, submitted. (arXiv)
Irreducibility of random polynomials of bounded degree,
H. T. Pham, Max Wenqiang Xu, Discrete Analysis, 2021:7. (arXiv)
Deep Learning Theory
Limiting fluctuation and trajectorial stability of multilayer neural networks with mean field training,
H. T. Pham*, Phan-Minh Nguyen*. (arXiv, NeurIPS 2021)
A Rigorous Framework for the Mean Field Limit of Multilayer Neural Networks,
Phan-Minh Nguyen*, H. T. Pham*, to be submitted. (arXiv) (Slides) (Talk)
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
On the sampling Lovasz Local Lemma for atomic constraint satisfaction problems,
Vishesh jain, H. T. Pham, Thuy-Duong Vuong, submitted. (arXiv)
Towards the sampling Lovasz Local Lemma,
Vishesh Jain, H. T. Pham, Thuy-Duong Vuong, to appear in 62nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2021). (arXiv)
Entropic Independence: Optimal mixing of down-up random walks,
Nima Anari, Vishesh Jain, Frederic Koehler, H. T. Pham, Thuy-Duong Vuong, to appear in 54th ACM Symposium on Theory of Computing (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, to be submitted. (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, to be submitted. (arXiv)
Spectral independence, coupling with the stationary distribution, and the spectral gap of the Glauber dynamics,
Vishesh Jain, H. T. Pham, Thuy-Duong Vuong, to appear in Information Processing Letters. (arXiv)
Almost periodicity and its applications to Roth's theorem,
H. T. Pham. (pdf)
LA Probability Forum, June 2 2022.
UCSD Theory Seminar, June 1 2022.
UCLA Combinatorics Seminar, May 26 2022.
Stanford Theory Seminar, May 11 2022.
Percolation Today, May 10 2022.
Stanford Probability Seminar, May 9 2022.
UC Berkeley Theory Lunch, May 5 2022.
Stanford Combinatorics Seminar, April 28 2022.
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.