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.

**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, submitted. (arXiv)

**Regularity method and large deviations principles for the Erdos-Renyi hypergraph**, Nicholas Cook, Amir Dembo, H. T. Pham, submitted. (arXiv)

**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)

**On the sampling Lovasz Local Lemma for atomic constraint satisfaction problems**, Vishesh jain, H. T. Pham, Thuy Duong Vuong, to be 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)

** Spectral independence, coupling with the stationary distribution,
and the spectral gap of the Glauber dynamics**, Vishesh Jain, H. T. Pham, Thuy Duong Vuong, to be submitted. (arXiv)

**A multipartite analogue of Dilworth's Theorem**, Jacob Fox, H. T. Pham, in preparation.

**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, accepted to Discrete Analysis. (arXiv)

**Tower-type bounds for Roth's theorem with popular differences**, Jacob Fox, H. T. Pham, Yufei Zhao, submitted. (arXiv)

**Popular monochromatic progression differences**, Jacob Fox, H. T. Pham, to be submitted.

**Popular progression differences in vector spaces**, Jacob Fox, H. T. Pham, International Mathematics Research Notices, to appear. (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, to appear. (arXiv)

**Almost periodicity and its applications to Roth's theorem**, H. T. Pham. (pdf)

**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.

**Deansâ€™ 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.