removal natural identification everywhere

can be removed because?

Huy Tuan Pham

[email protected])

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.

Research Interests

Additive combinatorics, probabilistic methods in combinatorics, extremal combinatorics, probability theory, theoretical computer science, deep learning.

Publications

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. (arXiv) (Talk)

• On random irregular subgraphs,
  Jacob Fox, Sammy Luo, 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)

Expositions

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

Past and upcoming seminars

• 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.

Selected Awards and Distinctions

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.