Publications

1. On integer distance sets (with R. Greenfeld, S. Peluse) (2024).

Quanta Magazine: Merging Fields, Mathematicians Go the Distance on Old Problem. 

2. Some sharp inequalities of Mizohata-Takeuchi-type  (with A. Carbery, H. Wang), to appear in Rev. Mat. Iberoam.  (2023).

3. Sharp L^p estimates for oscillatory integral operators of arbitrary signature (with J. Hickman), Math. Z. 301, 1143-1189 (2022).

4. Inequalities of Riesz-Sobolev type for compact connected Abelian groups (with M. Christ),  Amer. J. Math. 144, no. 5, 1367-1435 (2022).

5. Joints formed by lines and a k-plane, and a discrete estimate of Kakeya type (with A. Carbery), Discret. Anal., https://doi.org/10.19086/da.18361 (2020).

6. Sharp estimates for oscillatory integral operators via polynomial partitioning (with L. Guth, J. Hickman), Acta Math. 223, no. 2, 251-376 (2019).

7. A multilinear Fourier extension identity on R^n (with J. Bennett), Math. Res. Lett. 25, no. 4, 1089-1108 (2018).

8. A sharp k-plane Strichartz inequality for the Schrödinger equation (with J. Bennett, N. Bez, T. Flock, S. Gutierrez), Trans. Amer. Math. Soc. 370, no. 8, 5617-5633 (2018).

9. Incidence bounds on multijoints and generic joints, Discrete Comput. Geom. 54, no. 2, 481-512 (2015). 

10. Counting multijoints, J. Combin. Theory Ser. A 136, 143-163 (2015). 

11. Flow monotonicity and Strichartz inequalities (with J. Bennett, N. Bez), Int. Math. Res. Not. 19, 9415-9437 (2015). 

12. Counting joints in vector spaces over arbitrary fields (with A. Carbery) (2014).

13. Counting joints with multiplicities, Proc. Lond. Math. Soc. (3) 106, no. 3, 675-702 (2013). 

Together with L. Guth and J. Hickman, we received one of the Frontiers of Science Awards 2018-22 for our paper Sharp estimates for oscillatory integral operators via polynomial partitioning.

PhD thesis

Discrete analogues of Kakeya problems, University of Edinburgh, 2013.