Nihar Prakash Gargava

I am a mathematician living in the Paris region. I am funded by the Swiss National Science Foundation

I study number theory and its connections to lattices, hyperbolic surfaces, error-correcting codes, sphere packings, quantum computing. I finished my PhD in 2023 supervised by Prof. Maryna Viazovska.

Before this, I was a masters student at EPFL and before that, a bachelor student at IIT Kanpur.

Lecture notes

Here is a collection of various notes that I scribed.

Organization

• With Nalini Anantharaman, Mingkun Liu and Ilaria Viglino, I am co-organizing the Random Geometry and Number Theory Conference, Lausanne 2026. More details upcoming.
• With Ilaria Viglino, I co-organized the Combinatorial Geometry and Number Theory Conference, Lausanne 2024. Find all information here.

List of Publications

• Module lattices and their shortest vectors (2025) with V. Serban, M. Viazovska, I. Viglino (arxiv) (in review)
• Buildings for synthesis with Clifford+R (2025) with M. Deaconu, N. Gargava, A. Kalra, M. Mosca, J. Yard (arxiv)
• Integral matrices of fixed rank over number fields (2025) with V. Serban, M. Viazovska, I. Viglino (arxiv) (in review)
• Density of shapes of periodic tori in the cubic case (2025) with N.T Dang, J. Li. (arxiv) (in review)
• Mean value for random ideal lattices (2024) with M. Viazovska. (arxiv)
• Effective module lattices and their shortest vectors (2024) with V. Serban, M. Viazovska and I. Viglino. (arxiv)
• Moments of the number of points in a bounded set for number field lattices (2023) with V. Serban and M. Viazovska. (arxiv) (in review)
• Dense packings via lifts of codes to division rings (2022) IEEE Trans. Inf. Theory with V. Serban. (arxiv) (journal)
• Lattice packings through division algebras (2022) Mathematische Zeitschrift (arxiv) (journal)
• A localized version of the basic triangle theorem (2019) with G. Duchamp, H.N. Minh, P. Simonnet (arxiv)

Doctoral thesis

Mean value theorems for collections of lattices with a prescribed group of symmetries (2023) (link)

List of recent talks

• Séminaire Mathématiques Discrètes, Codes et Cryptographie, LAGA, Paris 8, October 2025: Integral Matrices of Fixed Rank and Rogers’ Integration Formula
• 9th Number Theory Meeting, Torino, September 2025: Shapes of Unit Lattices of Totally Real Orders form a Dense Set of Lattices
• C2 Seminar, Inria Paris, July 2025: Gaussian Heuristics for Random Module and Ideal Lattices
• 33èmes Journées Arithmétiques, University of Luxembourg, July 2025: Random Lattices, Sphere Packings and Symmetries
• Charm workshop, Bordeaux, June 2025: Gaussian Heuristics for Random Module and Ideal Lattices
• Séminaire de Géométrie, Topologie & Dynamique, Orsay, January 2025: Random Lattices, Sphere Packings and Symmetries
• Séminaire Géométrie et Topologies, IMJ-PRG, Paris, January 2025: Random Lattices, Sphere Packings and Symmetries

See full list of past year talks here.

Contact : nihar.gargava [AT] universite-paris-saclay.fr

This page was updated on November 28, 2025.