Postdoctoral researcher in Mathematics
Institut de Mathématiques d’Orsay,
Université Paris-Saclay, France
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.
Density of shapes of periodic tori in arbitrary
rank (in preparation) with N.T Dang, J. Li.
(ab43a313…c649f1)
Poisson processes with short vectors in module
lattices (in preparation) with S. Kim, V. Serban
(08b0b4d8…48eb)
* An all genus 4/3 lower bound on the hyperbolic systole
problem with Yifei Cai, Mingkun Liu (formalization)
* A cyclotomic gluing construction for lattice sphere
packings with M. Gröbner, M. Simkin (arxiv)
* On two counterexamples in the geometry of
numbers (arxiv)
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)
- 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
- Module lattices and their shortest vectors (2026)
Des. Codes Cryptogr. with V. Serban, M. Viazovska, I. Viglino
(arxiv)
- Integral matrices of fixed rank over number fields
(2026) Res. Number Theory with V. Serban, M. Viazovska, I.
Viglino (arxiv) (formalization)
- 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)
An asterisk (*) 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 19, 2026.
