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 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.

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. Jensen, M. Michelen, J. Sahasrabudhe

The least singular value of a random symmetric matrix

Submitted. pdf


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

The singularity probability of a random symmetric matrix is exponentially small

Submitted. pdf


M. Michelen, J. Sahasrabudhe

Central limit theorems and the geometry of polynomials

Submitted. 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


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


J. Sahasrabudhe

Counting Zeros of Cosine Polynomials: On a Problem of Littlewood

Advances in Math. 343, (5), 2019, pp 495-521. pdf


M. Michelen, J. Sahasrabudhe

Central limit theorems from the roots of probability generating functions

Advances in Math. 358 (15), 2019. pdf


J. Sahasrabudhe

Exponential Patterns in Arithmetic Ramsey Theory

Acta Arithmetica 182, 2018, pp 13-42. pdf


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

The structure and number of Erdős covering systems

European Journal of Math. (JEMS) Accepted. pdf


Random matrices and polynomials


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

The least singular value of a random symmetric matrix

Submitted. pdf


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

The singularity probability of a random symmetric matrix is exponentially small

Submitted 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

Submitted : 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

European Journal of Math. (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