Julian Sahasrabudhe
I am a Canadian mathematician interested in extremal and probabilistic combinatorics, and intersections with probability, analysis and combinatorial number theory.
Most recently, I have been interested in Ramsey theory on graphs, random polynomials and random matrices.
I am a professor of mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge. I started in September 2021. In August 2021, I was awarded the European Prize in Combinatorics. In October 2023, I was awarded the Salem prize. In June 2024, I was awarded the Whitehead prize and in July 2025 I was awarded the MCA prize (Mathematical Congress of the Americas).
In 2024 I was awarded a European Research Council (ERC) starter grant.
Prior to my appointment at Cambridge, I was a Junior Research Fellow at Peterhouse, University of Cambridge (2017-2021).
In 2017-2018, I was visiting Rob Morris at IMPA (Instituto Nacional de Matemática Pura e Aplicada) in Rio de Janerio, Brazil as a post-doc of excellence.
I did my PhD under the supervision of Béla Bollobás at the University of Memphis, defending in March of 2017.
My email is jdrs2 (at) cam (dot) ac (dot) uk.
Selected Papers
M. Campos, M. Jenssen, M. Michelen, J. Sahasrabudhe
A new lower bound for the Ramsey numbers R(3,k)
Submitted. pdf
P. Balister, B. Bollobás, M. Campos, S. Griffiths, E. Hurley, R. Morris, J. Sahasrabudhe, M. Tiba
Upper bounds for multicolour Ramsey numbers
Submitted. pdf
A. Sah, J. Sahasrabudhe. M. Sawhney
On the Spielman-Teng Conjecture
Geom. Funct. Anal. (GAFA). Vol 35, pp. 633–671, 2025. pdf
M. Campos, M. Jenssen, M. Michelen, J. Sahasrabudhe
A new lower bound for sphere packing
Submitted. pdf
A. Sah, J. Sahasrabudhe, M. Sawhney
The limiting spectral law for sparse iid matrices
Forum Math: Pi. To appear. pdf
M. Campos, S. Griffiths, R. Morris, J. Sahasrabudhe
An exponential improvement for diagonal Ramsey
Ann. Math. To appear. pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
The least singular value of a random symmetric matrix
Forum of Math: Pi. Volume 12, 69 pages, 2024. pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
The singularity probability of a random symmetric matrix is exponentially small
J. Amer. Math. Soc. 38(1), pp. 179-224, 2025. pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Flat Littlewood polynomials exist
Ann. Math. 192 (3), pp. 977-1004, 2020. pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
On the Erdős Covering Problem: the density of the uncovered set
Invent. Math. 228, pp. 377–414, 2022. pdf
M. Michelen, J. Sahasrabudhe
Central limit theorems and the geometry of polynomials
J. Eur. Math. Soc. (to appear). pdf
J. Sahasrabudhe
Counting Zeros of Cosine Polynomials: On a Problem of Littlewood
Adv. Math. 343, (5), 2019, pp. 495-521. pdf
M. Michelen, J. Sahasrabudhe
Central limit theorems from the roots of probability generating functions
Adv. Math. 358 (15), 2019. pdf
J. Sahasrabudhe
Exponential Patterns in Arithmetic Ramsey Theory
Acta Arith. 182, pp. 13-42, 2018. pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The structure and number of Erdős covering systems
J. Eur. Math. Soc. (JEMS) , no. 1, pp. 75–109, 2024. pdf
Ramsey numbers
M. Campos, M. Jenssen, M. Michelen, J. Sahasrabudhe
A new lower bound for the Ramsey numbers R(3,k)
Submitted. pdf
P. Balister, B. Bollobás, M. Campos, S. Griffiths, E. Hurley, R. Morris, J. Sahasrabudhe, M. Tiba
Upper bounds for multicolour Ramsey numbers
Submitted. pdf
M. Campos, S. Griffiths, R. Morris, J. Sahasrabudhe
An exponential improvement for diagonal Ramsey
Ann. Math. To appear. pdf
Random matrices and polynomials
A. Sah, J. Sahasrabudhe. M. Sawhney
On the Spielman-Teng Conjecture
Geom. Funct. Anal. (GAFA). Vol 35, pp. 633–671, 2025. pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
The least singular value of a random symmetric matrix
Forum of Math: Pi. Volume 12, 69 pages, 2024. pdf
A. Sah, J. Sahasrabudhe, M. Sawhney
The sparse circular law, revisited
Bull. London Math. Soc. 57: 330-358, 2024. pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
The least singular value of a random symmetric matrix
Forum of Math: Pi. Volume 12, 69 pages, 2024. pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
The singularity probability of a random symmetric matrix is exponentially small
J. Amer. Math. Soc. 38(1), pp. 179-224, 2025. pdf
M. Michelen, J. Sahasrabudhe
Random polynomials: the closest roots to the unit circle
Submitted : pdf
M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe
Singularity of random symmetric matrices revisited
Proc. Amer. Math. Soc. 150, 3147-3159, 2020. pdf
Probability and the geometry of polynomials
M. Michelen, J. Sahasrabudhe
Central limit theorems and the geometry of polynomials
J. Eur. Math. Soc. (to appear). pdf
M. Michelen, J. Sahasrabudhe
Anti-concentration of random variables from zero-free regions
Discrete Analysis : 2022:13 pdf
M. Michelen, J. Sahasrabudhe
Central limit theorems from the roots of probability generating functions
Advances in Math. 358 (15), 2019. pdf
M. Michelen, J. Sahasrabudhe
A characterization of polynomials whose high powers have non-negative coefficients
Discrete Analysis 20, 2020, 16 pp. pdf
Littlewood problems on polynomials
T. Juškevičius, J. Sahasrabudhe
Cosine polynomials with few zeros
Bull. London Math. Soc. To appear : pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Flat Littlewood polynomials exist
Annals of Math. 192 (3), 2020, pp 977-1004 : pdf
J. Sahasrabudhe
Counting Zeros of Cosine Polynomials: On a Problem of Littlewood
Advances in Math. 343 (5), 2019, pp 495-521. pdf
Erdős covering systems
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
On the Erdős Covering Problem: the density of the uncovered set
Inventiones Math. 228, 2022, pp 377–414. pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The structure and number of Erdős covering systems
J. Eur. Math. Soc. (JEMS) , no. 1, pp. 75–109, 2024. pdf
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The Erdős-Selfridge problem with square-free moduli
Algebra and Number theory 15 (3), 2021, pp 609–626.
pdf
Arithmetic Ramsey theory
J. Sahasrabudhe
Exponential Patterns in Arithmetic Ramsey Theory
Acta Arithmetica 182, 2018, pp 13-42. pdf
J. Sahasrabudhe
Monochromatic Solutions to Systems of Exponential Equations
Journal of Combinatorial Theory Series A 158, 2018, pp 548-559 . pdf
Graph theory
S. Letzter, J. Sahasrabudhe
On Existentially Complete Triangle-free Graphs
Israel Journal of Math 236, 2020, pp 591–601, to appear. pdf
B. Narayanan, J. Sahasrabudhe, I. Tomon
The multiplication table problem for bipartite graphs
Combinatorica 37(5), 2019, pp 991-1010 pdf
B. Narayanan, J. Sahasrabudhe, I. Tomon
Ramsey graphs induce subgraphs of many different sizes
Combinatorica 39(1), 2019, pp 215-237 pdf
K. Popielarz, J. Sahasrabudhe, R. Snyder
A Stability Theorem for Maximal Kr+1-free Graphs
Journal of Combinatorial Theory Series B 132, 2019, pp 236-257. pdf
Expository
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Erdős Covering systems
Acta Mathematica Hungarica volume 161, 2020, 540–549. pdf