**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