Office: Lunt 210

Department of Mathematics, Northwestern University

2033 Sheridan Road, Evanston, IL 60208

E-mail: lhvietbao AT gmail DOT com

I am an Associate Professor at Northwestern University.

I am interested in Algebraic Number Theory, especially on various aspects of the Langlands Correspondence (global, mod p, p-adic,...) and related aspects in Modular Representation Theory and Geometric Representation Theory.

I am especially interested in studying the moduli space of p-adic local Galois representation, with its links to various flavors of geometric representation theory and the categorical form of the mod p local Langlands correspondence.

My research is partially supported by NSF Grants DMS-1952678 and DMS-2302619.

Here is my CV .

- * Mirror symmetry and the Breuil-Mezard conjecture *, arXiv:2310.07006 (submitted), 77 pages (with T. Feng).

- * Colength one deformation rings: results and applications *, arXiv:2304.03061 (submitted), 45 pages (with D. Le, S. Morra, C. Park and Z. Qian).

- * Extremal weights and a tameness criterion for mod p Galois representations *, arXiv:2206.06442 (submitted), 65 pages (with D. Le, B. Levin and S. Morra).

- * Serre weights for three-dimensional wildly ramified Galois representations *, Algebra and Number Theory (to appear) (with D. Le, B. Levin and S. Morra).

- * Serre weights, Galois deformation rings, and local models *, Proceedings of the International Colloquium on Arithmetic Geometry, TIFR (to appear), 24 pages (with D. Le).

- * Moduli of Fontaine--Laffaille representations and a mod-p local-global compatibility result *, Memoirs of the AMS (to appear) (with D. Le, S. Morra, C. Park and Z. Qian).

- * Local models for Galois deformation rings and applications *, Inventiones Mathematicae 231, 1277-1488 (2023) (with D. Le, B. Levin and S. Morra).

- * Potential automorphy over CM fields *, Annals of Mathematics (2) 197 no. 3, 897-1113 (2023) (with P. Allen, F. Calegari, A. Caraiani, T. Gee, D. Helm, J. Newton, P. Scholze, R. Taylor, and J. Thorne).

- * Serre weights and Breuil's lattice conjecture in dimension three *, Forum of Mathematics, Pi 8 (2020), 1-135 (with D. Le, B. Levin and S. Morra).

- * ** Weight elimination in Serre type conjectures*, Duke Mathematical Journal 168 (2019) no.13, 2433-2506 (with D. Le and B. Levin).

- * Potentially crystalline deformation rings and Serre weight conjectures: Shapes and Shadows *, Inventiones Mathematicae 212 (2018), 1-107 (with D. Le, B. Levin and S. Morra).

- * Level raising mod 2 and arbitrary 2-Selmer ranks *, Compositio Mathematica 152 (2016) no.8, 1576-1608 (with C. Li).

- * On the image of complex conjugation in certain Galois representations *, Compositio Mathematica 152 (2016) no.7, 1476-1488 (with A. Caraiani).

- * Elliptic curves over real quadratic fields are modular *, Inventiones Mathematicae 201 (2015), 159-206 (with N. Freitas and S. Siksek).

Chair d'Excellence de la FSMP course * Algebraic local models and Galois representations *.