**Julian Sahasrabudhe**

I am a mathematician interested in mix of extremal and probabilistic combinatorics, roots of polynomials, Fourier analysis and combinatorial number theory.
I am currently a Junior Research Fellow at Peterhouse, University of Cambridge and have been since 2017. 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 *. Prior to this, 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 Publications:**

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 **

* Submitted * : pdf

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

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

* Submitted * : pdf

J. Sahasrabudhe

** Counting Zeros of Cosine Polynomials: On a Problem of Littlewood **

* Advances in Mathematics * 343:495-521 pdf

J. Sahasrabudhe

**Exponential Patterns in Arithmetic Ramsey Theory **

*Acta Arithmetica * 182(1):13-42 pdf

** Combinatorial Number theory / Ramsey Theory:**

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

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

* Submitted * : pdf

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

** The Erdős-Selfridge problem with square-free moduli **

* Submitted * : 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

** (short note) Covering Intervals with Arithmetic Progressions **

* Acta Math. Hungarica * To appear.

J. Sahasrabudhe

**Exponential Patterns in Arithmetic Ramsey Theory **

* Acta Arithmetica * 182(1):13-42 pdf

J. Sahasrabudhe

** Monochromatic Solutions to Systems of Exponential Equations **

* Journal of Combinatorial Theory. * Series A 158:548-559 A. pdf

**Polynomials :**

M. Michelen, J. Sahasrabudhe

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

* 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 **

* Submitted * : pdf

M. Michelen, J. Sahasrabudhe

** Central limit theorems from the roots of probability generating functions **

* Advances in Math. * To appear pdf

J. Sahasrabudhe

** Counting Zeros of Cosine Polynomials: On a Problem of Littlewood **

* Advances in Math. * 343:495-521 pdf

**Graph Theory:**

S. Letzter, J. Sahasrabudhe

** On Existentially Complete Triangle-free Graphs **

* Israel Journal of Math. *, 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