Articles

  1. On the \(2\)-torsion in class groups of number fields (with D. Bonolis)
    Forthcoming.
  2. Random Diophantine equations of large degree (with T. Browning and W. Sawin)
    Forthcoming.
  3. Arithmetic dynamics of random polynomials (with M. Mavraki)
    Submitted for publication.
  4. The Hasse principle for random Fano hypersurfaces (with T. Browning and W. Sawin)
    Ann. of Math. (2) 197 (2023), no. 3, 1115–1203.
  5. Height of rational points on random Fano hypersurfaces
    Algebra Number Theory 15 (2021), no. 3, 657–672.
  6. A statistical view on the conjecture of Lang about the canonical height on elliptic curves
    Trans. Amer. Math. Soc. 372 (2019), no. 12, 8347–8361.
  7. Height of rational points on congruent number elliptic curves
    Submitted for publication.
  8. Average rank in families of quadratic twists: a geometric point of view
    Math. Ann. 371 (2018), no. 1-2, 695–705.
  9. On the distribution of squarefree integers in arithmetic progressions
    Math. Z. 290 (2018), no. 1-2, 421–429.
  10. Height of rational points on quadratic twists of a given elliptic curve
    Bull. Lond. Math. Soc. 48 (2016), no. 1, 99–108.
  11. Linear growth for certain elliptic fibrations
    Int. Math. Res. Not. IMRN (2015), no. 21, 10859–10871.
  12. Density of rational points on a certain smooth bihomogeneous threefold
    Int. Math. Res. Not. IMRN (2015), no. 21, 10703–10715.
  13. Affine congruences and rational points on a certain cubic surface
    Algebra Number Theory 8 (2014), no. 5, 1259–1296.
  14. Manin's conjecture for a cubic surface with \(2\mathbf{A}_2+\mathbf{A}_1\) singularity type
    Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 3, 419–455.
  15. Power-free values of the polynomial \(t_1 \cdots t_r-1\)
    Bull. Aust. Math. Soc. 85 (2012), no. 1, 154–163.
  16. Manin's conjecture for a quartic del Pezzo surface with \(\mathbf{A}_3\) singularity and four lines
    Monatsh. Math. 167 (2012), no. 3-4, 481–502.
  17. Manin's conjecture for two quartic del Pezzo surfaces with \(3\mathbf{A}_1\) and \(\mathbf{A}_1+\mathbf{A}_2\) singularity types
    Acta Arith. 151 (2012), no. 2, 109–163.

Thesis

  1. Distribution of rational points on certain del Pezzo surfaces
    PhD Thesis, July 2012, 186 pages.