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 lecturer (assistant professor in the American/Canadian system) 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 with 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 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. accepted . pdf


J. Sahasrabudhe

Counting Zeros of Cosine Polynomials: On a Problem of Littlewood

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


J. Sahasrabudhe

Exponential Patterns in Arithmetic Ramsey Theory

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


M. Michelen, J. Sahasrabudhe

Random polynomials: the closest roots to the unit circle

Submitted : pdf


Polynomials and Matrices


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

Anti-concentration of random variables from zero-free regions

Submitted : pdf


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

Singularity of random symmetric matrices revisited

Proc. Amer. Math. Soc. pdf


M. Michelen, J. Sahasrabudhe

Random polynomials: the closest roots to the unit circle

Submitted : pdf


T. Juškevičius, J. Sahasrabudhe

Cosine polynomials with few zeros

Bull. London Math. Soc. To appear : pdf


M. Michelen, J. Sahasrabudhe

A characterization of polynomials whose high powers have non-negative coefficients

Discrete Analysis 2020:20, 16 pp. 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


M. Michelen, J. Sahasrabudhe

Central limit theorems from the roots of probability generating functions

Advances in Math. 358 (15), 2019 pdf


J. Sahasrabudhe

Counting Zeros of Cosine Polynomials: On a Problem of Littlewood

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



Combinatorial Number theory and Ramsey Theory


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

On the Erdős Covering Problem: the density of the uncovered set

Inventiones math. accepted : pdf


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

The structure and number of Erdős covering systems

Submitted . pdf


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

The Erdős-Selfridge problem with square-free moduli

Algebra and Number theory (to appear). pdf


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

Covering Intervals with Arithmetic Progressions

Acta Math. Hungarica, 161, 2020, pp 197–200.


J. Sahasrabudhe

Exponential Patterns in Arithmetic Ramsey Theory

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


J. Sahasrabudhe

Monochromatic Solutions to Systems of Exponential Equations

Journal of Combinatorial Theory. Series A 158:548-559 A. 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):991-1010 pdf


B. Narayanan, J. Sahasrabudhe, I. Tomon

Ramsey graphs induce subgraphs of many different sizes

Combinatorica 39(1):215-237 pdf


K. Popielarz, J. Sahasrabudhe, R. Snyder

A Stability Theorem for Maximal Kr+1-free Graphs

Journal of Combinatorial Theory. Series B 132:236-257 pdf


B. Bollobás, M. Przykucki, O. Riordan, J. Sahasrabudhe

On the maximum running time in graph bootstrap percolation

Electronic Journal of Combinatorics 24 (2017), #P2.16: pdf


A. Girão, S. Letzter, J. Sahasrabudhe

Partitioning a graph into monochromatic connected subgraphs

J Graph Theory . 2019; 91: 353– 364 pdf


P. Balister, B. Bollobás, J. Sahasrabudhe, A. Veremyev

Dense Subgraphs in Random Graphs

Discrete Applied Mathematics 260:66-74 pdf


Expository


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

Erdős Covering systems

Acta Mathematica Hungarica volume 161, 2020, 540–549. pdf