I am a Visiting Clay Fellow and Stanford Science Fellow in the Department of Mathematics at Stanford University. 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.

Probabilistic combinatorics, additive 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)

A proof of the Kahn-Kalai Conjecture,

*Jinyoung Park, H. T. Pham,*to appear in J. Amer. Math. Soc. A preliminary version appears in FOCS 2022. (arXiv) (Talk) (an interview with Two Sigma)

Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings,

*Vishesh Jain, H. T. Pham.*(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,*to appear in Duke Math. J. (arXiv)

Small subsets with large sumset: Beyond the Cauchy–Davenport bound,

*Jacob Fox, Sammy Luo, H. T. Pham, Yunkun Zhou.*(arXiv)

On random irregular subgraphs,

*Jacob Fox, Sammy Luo, H. T. Pham.*(arXiv)

A multipartite analogue of Dilworth's Theorem,

*Jacob Fox, H. T. Pham.*

**Additive Combinatorics**

Subset sums, completeness and colorings,

*David Conlon, Jacob Fox, H. T. Pham.*(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,*Journal of the European Mathematical Society (2022). (arXiv)

Small subsets with large sumset: Beyond the Cauchy-Davenport bound,

*Jacob Fox, Sammy Luo, H. T. Pham, Yunkun Zhou.*(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.*

Universality for Low-Degree Factors of Random Polynomials over Finite Fields,

*Jimmy He, H. T. Pham, Max Wenqiang Xu,*International Mathematics Research Notices (2022). (arXiv)

Mixing time of fractional random walk on finite fields,

*Jimmy He, H. T. Pham, Max Wenqiang Xu,*Electronic Journal of Probability 27 (2022). (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*.*(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**

Optimal mixing of the down- up walk on independent sets of a given size,

*Marcus Michelen, Vishesh Jain, H. T. Pham, Thuy-Duong Vuong,*, to appear in 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,*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,*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.*(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. (arXiv)

Almost periodicity and its applications to Roth's theorem,

*H. T. Pham.*(pdf)

CMU ACO Seminar, February 2023.

Brown Probability Seminar, December 2022.

MIT Combinatorics Seminar, December 2022.

Ohio State University Combinatorics Seminar, November 2022.

University of Illinois at Chicago Combinatorics and Probability Seminar, November 2022.

University of Illinois at Chicago Colloquium, November 2022.

University of Chicago Combinatorics and TCS Seminar, November 2022.

FOCS 2022, November 2022.

UC Berkeley Probability Seminar, October 2022.

AMS Special Session on Extremal Graph Theory, Utah, October 2022.

Online Asymptotic Geometric Analysis Seminar, October 2022.

University of Washington Theory Seminar, October 2022.

Banff Extremal Combinatorics and Geometry Workshop, August 2022.

UCSB Summer school, August 2022.

LA Probability Forum, June 2022.

UCSD Theory Seminar, June 2022.

UCLA Combinatorics Seminar, May 2022.

Stanford Theory Seminar, May 2022.

Percolation Today, May 2022.

Stanford Probability Seminar, May 2022.

UC Berkeley Theory Lunch, May 2022.

Stanford Combinatorics Seminar, April 2022.

Oberwolfach Workshop in Combinatorics, Probability and Computing, April 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.