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.

Notes, diary and wiki

• I write this wiki.
• I try to scribe talks that I attend here.
• A small sample of my notes is here.

Organization

• With Nalini Anantharaman, Mingkun Liu and Ilaria Viglino, I co-organized the Random Geometry and Number Theory Conference, Lausanne 2026. Here is the website.
• With Ilaria Viglino, I co-organized the Combinatorial Geometry and Number Theory Conference, Lausanne 2024. Find all information here.

List of Publications

In the pipeline

In order to avoid accidental or intentional AI-assisted plagiarism, I have publically declared SHA256-checksums for my ongoing projects here. This way, I can prove using my github commits that there was indeed a PDF draft of our results on the date when this webpage was updated.

I advise more mathematicians to adopt this practice.

AI-assisted

• An all genus 4/3 lower bound on the hyperbolic systole problem with Yifei Cai, Mingkun Liu (in preparation)
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• A cyclotomic gluing construction for lattice sphere packings with M. Gröbner, M. Simkin (arxiv)
• On two counterexamples in the geometry of numbers (arxiv)

AI-free

• Density of shapes of periodic tori in arbitrary rank (in preparation) with N.T Dang, J. Li.
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• Poisson processes with short vectors in module lattices (in preparation) with S. Kim, V. Serban
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Under review

• *Gaussian kernel lattices and smoothing bounds from theta integrals (2026) with E. Tairi, S. Düzlü (eprint)
• Density of shapes of periodic tori in the cubic case (2025) with N.T Dang, J. Li. (arxiv) (formalization)
• *Stochastically evolving ellipsoid with symmetries with E. Abuya, Y. Zhao (arxiv)
• Module lattices and their shortest vectors (2025) with V. Serban, M. Viazovska, I. Viglino (arxiv)
• Integral matrices of fixed rank over number fields (2025) with V. Serban, M. Viazovska, I. Viglino (arxiv) (formalization)
• Mean value for random ideal lattices (2024) with M. Viazovska. (arxiv) (formalization)
• Moments of the number of points in a bounded set for number field lattices (2023) with V. Serban and M. Viazovska. (arxiv)

Published

• Integral matrices of fixed rank over number fields (2026) Res. Number Theory with V. Serban, M. Viazovska, I. Viglino (arxiv)
• Buildings for synthesis with Clifford+R (2026) Proc. QPL 2026, Electron. Proc. Theor. Comput. Sci with M. Deaconu, N. Gargava, A. Kalra, M. Mosca, J. Yard (arxiv)
• 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)

Misc.

• Effective module lattices and their shortest vectors (2024) with V. Serban, M. Viazovska and I. Viglino. (arxiv)
• 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)

The * indicates AI-assisted mathematics

List of recent talks

• Fouvry73, EPFL Lausanne, August 2026: A counterexample to a question of Sarnak
• Quadratic Lattices in Prague, Charles University, August 2026: Shapes of unit lattices of totally real orders form a dense set of lattices
• AI for Math, TIFR, Mumbai, August 2026: How I learned to stop worrying and love AI (and some geometry of numbers)
• Séminaire de Probabilités commun ICJ/UMPA, Lyon, July 2026: Stochastically evolving ellipsoids, symmetries and AI
• Séminare de Cryptographie , Université de Rennes, June 2026: Gaussian heuristics for random ideal and module lattices
• Dynamics Seminar, Shanghai Center of Mathematical Sciences, April 2026: Density of shapes of periodic tori II: the general case
• Seminar, Shanghai Institute for Mathematics and Interdisciplinary Sciences, April 2026: Random lattices that are \(\mathcal{O}_{K}\)-modules
• Séminaire de Théorie Ergodique et Systèmes Dynamiques, Université Sorbonne Paris Nord, March 2026: Shapes of unit lattices of totally real orders form a dense set of lattices

See full list of past year talks here.

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

This page was updated on October 12, 2026.