A new lower bound for the Ramsey numbers R(3, k)
Submitted. arXiv
Selected papers
Upper bounds for multicolour Ramsey numbers
J. Amer. Math. Soc. 39(3) (2026), 765–780. arXiv
On the Spielman–Teng conjecture
Geom. Funct. Anal. 35(2) (2025), 633–671. arXiv
A new lower bound for sphere packing
Submitted. arXiv
The limiting spectral law for sparse iid matrices
Forum Math. Pi, to appear. arXiv
An exponential improvement for diagonal Ramsey
Ann. of Math. (2) 203(3) (2026), 869–932. arXiv
The least singular value of a random symmetric matrix
Forum Math. Pi 12 (2024), e3, 69 pp. arXiv
The singularity probability of a random symmetric matrix is exponentially small
J. Amer. Math. Soc. 38(1) (2025), 179–224. arXiv
Flat Littlewood polynomials exist
Ann. of Math. (2) 192(3) (2020), 977–1004. arXiv
On the Erdős covering problem: the density of the uncovered set
Invent. Math. 228 (2022), 377–414. arXiv
Central limit theorems and the geometry of polynomials
J. Eur. Math. Soc. 28(5) (2026), 2261–2305. arXiv
Counting zeros of cosine polynomials: on a problem of Littlewood
Adv. Math. 343 (2019), 495–521. arXiv
Central limit theorems from the roots of probability generating functions
Adv. Math. 358 (2019), 106840. arXiv
Exponential patterns in arithmetic Ramsey theory
Acta Arith. 182(1) (2018), 13–42. arXiv
The structure and number of Erdős covering systems
J. Eur. Math. Soc. 26(1) (2024), 75–109. arXiv
Papers by topic
Ramsey numbers
On the Erdős–Rogers function
Submitted. arXiv
The multicolour size Ramsey number of a path
Submitted. arXiv
A polynomial improvement for the odd cycle–complete Ramsey numbers
Submitted. arXiv
A new lower bound for the Ramsey numbers R(3, k)
Submitted. arXiv
Upper bounds for multicolour Ramsey numbers
J. Amer. Math. Soc. 39(3) (2026), 765–780. arXiv
An exponential improvement for diagonal Ramsey
Ann. of Math. (2) 203(3) (2026), 869–932. arXiv
Random matrices and polynomials
On the Spielman–Teng conjecture
Geom. Funct. Anal. 35(2) (2025), 633–671. arXiv
The limiting spectral law for sparse iid matrices
Forum Math. Pi, to appear. arXiv
The least singular value of a random symmetric matrix
Forum Math. Pi 12 (2024), e3, 69 pp. arXiv
The sparse circular law, revisited
Bull. Lond. Math. Soc. 57(2) (2025), 330–358. arXiv
The singularity probability of a random symmetric matrix is exponentially small
J. Amer. Math. Soc. 38(1) (2025), 179–224. arXiv
Random polynomials: the closest roots to the unit circle
Submitted. arXiv
Singularity of random symmetric matrices revisited
Proc. Amer. Math. Soc. 150(7) (2022), 3147–3159. arXiv
Probability and the geometry of polynomials
Central limit theorems and the geometry of polynomials
J. Eur. Math. Soc. 28(5) (2026), 2261–2305. arXiv
Anti-concentration of random variables from zero-free regions
Discrete Anal. 2022:13, 29 pp. arXiv
Central limit theorems from the roots of probability generating functions
Adv. Math. 358 (2019), 106840. arXiv
A characterization of polynomials whose high powers have non-negative coefficients
Discrete Anal. 2020:20, 16 pp. arXiv
Littlewood problems on polynomials
Cosine polynomials with few zeros
Bull. Lond. Math. Soc. 53(3) (2021), 877–892. arXiv
Flat Littlewood polynomials exist
Ann. of Math. (2) 192(3) (2020), 977–1004. arXiv
Counting zeros of cosine polynomials: on a problem of Littlewood
Adv. Math. 343 (2019), 495–521. arXiv
Erdős covering systems
On the Erdős covering problem: the density of the uncovered set
Invent. Math. 228 (2022), 377–414. arXiv
The structure and number of Erdős covering systems
J. Eur. Math. Soc. 26(1) (2024), 75–109. arXiv
The Erdős–Selfridge problem with square-free moduli
Algebra Number Theory 15(3) (2021), 609–626. arXiv
Arithmetic Ramsey theory
Exponential patterns in arithmetic Ramsey theory
Acta Arith. 182(1) (2018), 13–42. arXiv
Monochromatic solutions to systems of exponential equations
J. Combin. Theory Ser. A 158 (2018), 548–559. arXiv
Graph theory
On existentially complete triangle-free graphs
Israel J. Math. 236(2) (2020), 591–601. arXiv
The multiplication table problem for bipartite graphs
Combinatorica 37(5) (2017), 991–1010. arXiv
Ramsey graphs induce subgraphs of many different sizes
Combinatorica 39(1) (2019), 215–237. arXiv
A stability theorem for maximal Kr+1-free graphs
J. Combin. Theory Ser. B 132 (2018), 236–257. arXiv
Expository
Erdős covering systems
Acta Math. Hungar. 161 (2020), 540–549. journal