**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 university assistant professor 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.

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 aMy email is jdrs2 (at) cam (dot) ac (dot) uk.

**Selected Papers**

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 **

* Submitted. * pdf

M. Campos, S. Griffiths, R. Morris, J. Sahasrabudhe

** An exponential improvement for diagonal Ramsey **

* Submitted. * pdf

M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe

** The least singular value of a random symmetric matrix **

* Forum of Math: Pi. * To appear. pdf

M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe

** The singularity probability of a random symmetric matrix is exponentially small **

* J. Amer. Math. Soc. * To appear pdf

P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba

**Flat Littlewood polynomials exist **

* Ann. Math. * 192 (3), 2020, pp 977-1004. 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, 2022, pp 377–414 . pdf

M. Michelen, J. Sahasrabudhe

**Central limit theorems and the geometry of polynomials **

* Submitted. * 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, 2018, pp 13-42. pdf

P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba

** The structure and number of Erdős covering systems **

* J. Eur. Math. Soc. (JEMS) * Accepted. pdf

**Ramsey numbers**

M. Campos, S. Griffiths, R. Morris, J. Sahasrabudhe

** An exponential improvement for diagonal Ramsey **

* Submitted. * pdf

**Random matrices and polynomials**

A. Sah, J. Sahasrabudhe, M. Sawhney

**The limiting spectral law for sparse iid matrices **

* Submitted. * pdf

A. Sah, J. Sahasrabudhe, M. Sawhney

**The sparse circular law, revisited **

* Submitted. * pdf

M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe

** The least singular value of a random symmetric matrix **

* Forum of Math: Pi. * To appear. pdf

M. Campos, M. Jensen, M. Michelen, J. Sahasrabudhe

** The singularity probability of a random symmetric matrix is exponentially small **

* J. Amer. Math. Soc. * To appear. 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. pdf

**Probability and the geometry of polynomials **

M. Michelen, J. Sahasrabudhe

**Central limit theorems and the geometry of polynomials **

* Submitted * : 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) * Accepted. 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