Research interests: number theory, analytic number theory, Diophantine geometry

Here is a list of my recent preprints and publications.

• Optimal quantitative weak approximation for projective quadrics (with Z. Huang and A. Shute), 52 pp, arXiv  

• Points of bounded height on certain subvarieties of toric varieties (with M. Pieropan), 22 pp, arXiv 

• Rational points near manifolds, homogeneous dynamics, and oscillatory integrals (with R. Srivastava and N. Technau), submitted, arXiv 

• Generalised quadratic forms over totally real number fields (with T.  D. Browning and L. B. Pierce), accepted for publication in Journal of the Institute of Mathematics of Jussieu, arXiv 

• Hyperbola method on toric varieties (with M. Pieropan), Journal de l'École polytechnique - Mathématiques 11 (2024), 107 -- 157, arXiv

• Density of rational points near/on compact manifolds with certain curvature conditions (with S. Yamagishi), Adv. Math 403 (2022), Paper No. 108358, 36pp, arXiv 

• On prime values of binary quadratic forms with a thin variable (with P. Lam and S. Xiao), J. London Math. Soc. 102 (2) (2020), 749 - 772, arXiv

• Diophantine inequalities for generic ternary diagonal forms, Int. Math. Res. Not., no.11 (2020), 3396–3416, arXiv

• On the algebraic Brauer classes on open degree four del Pezzo surfaces (with J. Jahnel), J. Number Theory 203 (2019), 376 - 427,  arXiv

• On the frequency of algebraic Brauer classes (with J. Jahnel), Canad. Math. Bull. 62 (2019), 551 - 563, arXiv

• Sarnak's saturation problem for complete intersections (with E. Sofos), Mathematika 65 (2019), no. 1, 1 - 56, arXiv

• Strong approximation and a conjecture of Harpaz and Wittenberg (with T. D. Browning), Int. Math. Res. Not. 14 (2019), 4340 - 4369, arXiv

• On integral points on degree four del Pezzo surfaces (with J. Jahnel), Israel J. Math. 222 (2017), no. 1, 21 - 62, arXiv

• Counting rational points on hypersurfaces and higher order expansions, J. Number Theory 173 (2017), 332-370, arXiv

• Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme (with J. Jahnel), Annales de l'Institut Fourier 67, no.4 (2017), 1783-1807, arXiv

• Representations of integers by systems of three quadratic forms (with L. B. Pierce and M. M. Wood), J. London Math. Soc. (3) 113, no.3 (2016), 289-344, arXiv

• On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle (with J. Jahnel), Journal of Number Theory 162 (2016), 224-254, arXiv

• On the Brauer-Manin obstruction for degree four del Pezzo surfaces (with J. Jahnel), Acta Arithmetica 176 (2016), 301-319, arXiv

• Manin's conjecture for certain biprojective hypersurfaces, J. reine angew. Math. 714 (2016), 209-250, arXiv

• A variant of Weyl's inequality for systems of forms and applications, Advances in the theory of numbers, 207–218, Fields Inst. Commun. 77, Fields Inst. Res. Math. Sci., Toronto, ON, 2015, arXiv

• Symmetries of rational functions arising in Ecalle's study of multiple zeta values (with A. Salerno and A. Tucker), in Women in Numbers Europe, Springer 2015, pp 153--166.

• Bihomogeneous forms in many variables, J. Th. Nombres Bordeaux 26 (2014), 483-506, arXiv

• Norms as products of linear polynomials (with A. N. Skorobogatov), J. London Math. Soc. 89 (2014), 559-580, pdf

Reports

• Field Arithmetic, Oberwolfach report 25/2018, 'The local-global principle for rational points and a conjecture of Harpaz and Wittenberg'

Thesis 

   On Diophantine equations involving norm forms and bihomogeneous forms, (Ph.D. Thesis) 2013