Research

I am currently working on the circle method and its application to quadratic forms. In general, I am interested in problems surrounding integral and rational points.

Refined obstructions to local-global principles for 0-cycles
Joint work with Francesca Balestrieri, Rachel Newton, Soumya Sankar, Katerina Santicola and Manoy Trip
arXiv: 2605.08972


We introduce new ‘refined’ obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate–Shafarevich groups, we show that the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces are controlled by obstructions of this new type. As an additional application of our refined obstructions, we answer a question of Zhang about the relationship between the Brauer–Manin and connected descent obstructions for 0-cycles. We also show that a Corwin–Schlank style refined obstruction set coincides with the set of global 0-cycles, conditionally on the Section Conjecture.

We introduce new ‘refined’ obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate–Shafarevich groups, we show that the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces are controlled by obstructions of this new type. As an additional application of our refined obstructions, we answer a question of Zhang about the relationship between the Brauer–Manin and connected descent obstructions for 0-cycles. We also show that a Corwin–Schlank style refined obstruction set coincides with the set of global 0-cycles, conditionally on the Section Conjecture.

Msc Thesis: Asymptotics for Integral Points of Bounded Height on a log Fano Variety
Advisors: Marta Pieropan & Gunther Cornelissen
University: Utrecht University


In this thesis I studied integral points of bounded height on three log Fano threefolds, following the paper ‘Integral Points of Bounded Height on a log Fano Threefold’ by Florian Wilsch. We parametrize the integral points on the log Fano threefolds using the universal torsor method and obtain lattice points satisfying certain (coprimality) conditions. With the height function induced by log-anticanonical bundles on the threefolds, we bound the integral points, leading to three counting functions. To obtain asymptotic formulae for two of the counting functions, we apply Möbius inversion and we replace sums by integrals. We show that this method cannot be extended in a straightforward way to the third counting function and instead we determine an upper bound.

In this thesis I studied integral points of bounded height on three log Fano threefolds, following the paper ‘Integral Points of Bounded Height on a log Fano Threefold’ by Florian Wilsch. We parametrize the integral points on the log Fano threefolds using the universal torsor method and obtain lattice points satisfying certain (coprimality) conditions. With the height function induced by log-anticanonical bundles on the threefolds, we bound the integral points, leading to three counting functions. To obtain asymptotic formulae for two of the counting functions, we apply Möbius inversion and we replace sums by integrals. We show that this method cannot be extended in a straightforward way to the third counting function and instead we determine an upper bound.