About

Bao Le Hung received his PhD from Harvard University in 2014. He then held postdoctoral positions at the Mathematical Sciences Research Institute in Berkeley, the University of Chicago, and the Institute for Advanced Study in Princeton. Le Hung joined the faculty of Northwestern University in 2018. His research focuses on algebraic number theory, particularly on aspects of the Langlands correspondence, modular representation theory, and geometric representation theory. His work especially concentrates on the moduli space of p-adic local Galois representations. Le Hung was awarded an Alfred P. Sloan Fellowship in 2019 and held the Fondation Sciences Mathématiques de Paris Research Chair in 2021.

Research topics

• Pure mathematics
• Mathematics
• Arithmetic
• Discrete mathematics
• Environmental science
• Environmental engineering
• Environmental chemistry
• Combinatorics
• Chemistry

Selected publications

• Potential automorphy over CM fields

  Annals of Mathematics · 2023 · 45 citations

  • Mathematics
  • Pure mathematics
  • Discrete mathematics

  Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and furthermore satisfy the Sato--Tate conjecture. As an application of a different sort, we also prove the Ramanujan Conjecture for weight zero cuspidal automorphic representations for $\mathrm{GL}_2(\mathbb{A}_F)$.

  PublisherOA PDFDOI

• Mirror symmetry and the Breuil-Mézard Conjecture

  arXiv (Cornell University) · 2023

  Senior authorCorresponding
  • Mathematics
  • Pure mathematics
  • Combinatorics

  The Breuil-Mézard Conjecture predicts the existence of hypothetical "Breuil-Mezard cycles" in the moduli space of mod $p$ Galois representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_q/\mathbb{Q}_q)$ that should govern congruences between mod $p$ automorphic forms. For generic parameters, we propose a construction of Breuil-Mézard cycles in arbitrary rank, and verify that they satisfy the Breuil-Mézard Conjecture for all sufficiently generic tame types and small Hodge-Tate weights. Our method is purely local and group-theoretic, and completely distinct from previous approaches to the Breuil-Mézard Conjecture. In particular, we leverage new connections between the Breuil-Mézard Conjecture and phenomena occurring in homological mirror symmetry and geometric representation theory.

  DOI

• Ambient air monitoring around the dioxin remediation site in Da Nang, Vietnam, using passive air samplers

  Environmental Monitoring and Assessment · 2021 · 15 citations

  • Environmental science
  • Environmental chemistry
  • Environmental engineering
  DOI

Recent grants

• Moduli of Galois Representations and Applications

  NSF · $180k · 2018–2024

Frequent coauthors

• Chol Park

  Laboratoire Analyse, Géométrie et Applications

  37 shared

• Daniel Le

  Purdue University West Lafayette

  37 shared

• Stefano Morra

  Université Paris Cité

  37 shared

• Zicheng Qian

  Laboratoire Analyse, Géométrie et Applications

  37 shared

• Frank Calegari

  2 shared

• Ana Caraiani

  Imperial College London

  2 shared

• Richard Taylor

  1 shared

• James Newton

  1 shared

Awards & honors

• Alfred P. Sloan Fellowship (2019)
• Fondation Sciences Mathématiques de Paris Research Chair (20…

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• Tobin J. Marksh-176
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