Research
I'm working on geometric theory, harmonic analysis, and fractal geometry.
Co-authors:
Talks / expository notes
Slides from talks (and some other expository notes) are available at Seminarchive.
On the Hausdorff dimension of circular Furstenberg sets, with K. Fässler and J. Liu, Discrete Analysis (to appear)
How much can heavy lines cover?, with D. Dabrowski and H. Wang, J. London Math. Soc. 109 (5) (2024)
On the Hausdorff dimension of radial slices, Ann. Fenn. Math. 49 (1) (2024)
Cheeger's differentiation theorem via the multilinear Kakeya inequality, with D. Bate and I. Kangasniemi, Pure Appl. Funct. Anal. 8(6) (2023), 1587-1602
On the discretised ABC sum-product problem, Trans. Amer. Math. Soc. (to appear)
Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem, with P. Shmerkin and H. Wang, Geom. Funct. Anal. 34 (2024), 164-201
Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences, with K. Fässler, Adv. Math. 431 (15) (2023)
A note on Kakeya sets of horizontal and SL(2) lines, with K. Fässler, Bull. London Math. Soc. 55 (5) (2023), 2195-2204
Additive properties of fractal sets on the parabola, Ann. Fenn. Math. 48 (1) (2023), 113-139
On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane, with P. Shmerkin, Duke Math. J. 172(18) (2023), 3559-3632
Absolute continuity in families of parametrised non-homogeneous self-similar measures, joint with A. Käenmäki, J. Fractal Geom. 10 (1/2) (2023), 169-207
Structure of sets with nearly maximal Favard length, with A. Chang, D. Dabrowski, and M. Villa, Anal. PDE (to appear)
A Marstrand-type restricted projection theorem in R^3, with A. Käenmäki and L. Venieri, Amer. J. Math. (to appear)
Integrability of orthogonal projections, and applications to Furstenberg sets, with D. Dabrowski and M. Villa, Adv. Math. 407 (8) (2022)
On a continuous Sárközy type problem, with B. Kuca and T. Sahlsten, Int. Math. Res. Notices 2023 (13) (2023), 11291-11315
Sub-elliptic boundary value problems in flag domains, with M. Villa, Adv. Calc. Var. 16 (4) (2023), 975-1059
On arithmetic sums of Ahlfors-regular sets, Geom. Funct. Anal. 32 (2022), 81-134
Metric rectifiability of H-regular surfaces with Hölder continuous horizontal normal, with K. Fässler and D. Di Donato, Int. Math. Res. Notices 2022(22) (2022), 17909-18975
Riesz transform and vertical oscillation in the Heisenberg group, with K. Fässler, Anal. PDE 16(2) (2023), 309-340
Plenty of big projections imply big pieces of Lipschitz graphs, Invent. Math. 226 (2021), 653-709
Singular integrals on regular curves in the Heisenberg group, with K. Fässler, J. Math. Pures Appl. 153 (2021), 30-113
On the dimension of visible parts J. Eur. Math. Soc. (to appear)
Combinatorial proofs of two theorems of Lutz and Stull, Math. Proc. Cambridge Philos. Soc. 171 (2) (2021), 503-514
Dorronsoro's theorem in Heisenberg groups, with K. Fässler, Bull. London Math. Soc. 52 (3) (2020), 472-488
Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group, with K. Fässler and S. Rigot, Trans. Amer. Math. Soc. 373 (2020), 5957-5996
Vertical versus horizontal Sobolev spaces, with K. Fässler, J. Funct. Anal. 279 (2) (2020)
Quantitative absolute continuity of planar measures with two independent Alberti representations, with D. Bate, Calc. Var. PDE 59 (2020)
On the Assouad dimension of projections, Proc. London Math. Soc. 122 (2) (2021), 317-351
Boundedness of singular integrals on C^{1,alpha} intrinsic graphs in the Heisenberg group, with V. Chousionis and K. Fässler, Adv. Math. 354 (1) (2019)
An integralgeometric approach to Dorronsoro estimates, Int. Math. Res. Notices 2021 (22) (2021), 17170-17200
Metric currents and the Poincaré inequality, with K. Fässler, Calc. Var. PDE 2(2) (2019)
On the dimension and smoothness of radial projections, Anal. PDE 12 (5) (2019), 1273-1294
Improved bounds for restricted families of projections to planes in R^3, with L. Venieri, Int. Math. Res. Noices 2020 (19) (2020), 5797–5813
Absolute continuity and alpha-numbers on the real line, Anal. PDE 12(4) (2019), 969-996
Intrinsic Lipschitz graphs and vertical beta-numbers in the Heisenberg group, with V. Chousionis and K. Fässler, Amer. J. Math. 141(4) (2019), 1087-1147
On the conformal dimension of product measures, with D. Bate, Proc. London Math. Soc. 117 (2) (2018), 277-302
A sharp exceptional set estimate for visibility, Bull. London Math. Soc. 50 (2018), 1-6
An improved bound on the packing dimension of Furstenberg sets in the plane, J. Eur. Math. Soc. 22 (3) (2020), 797-831
Curve packing and modulus estimates, with K. Fässler, Trans. Amer. Math. Soc. 370 (2018), 4909-4926
Boundedness of the density normalised Jones' square function does not imply 1-rectifiability, with H. Martikainen, J. Math. Pures Appl. 110 (2018), 71-92
On the distance sets of Ahlfors-David regular sets, Adv. Math. 307(5) (2017), 1029-1045
The Assouad dimensions of projections of planar sets, with J. Fraser, Proc. London Math. Soc. 114 (2) (2017), 374-398
Quasisymmetric maps on Kakeya sets, Int. Math. Res. Notices 2017 (2016), 3413--3425
Projections of planar sets in well-separated directions, Adv. Math. 297 (2016), 1--15
Hausdorff dimension, intersection of projections and exceptional plane sections, with P. Mattila, Proc. Amer. Math. Soc. 144 (8) (2016), 3419-3430
Some obstacles in characterising the boundedness of bi-parameter singular integrals, with H. Martikainen, Math. Z. 282(1) (2016), 535-545
Characterising the big pieces of Lipschitz graphs property using projections, with H. Martikainen, J. Eur. Math. Soc. 20 (2018), 1055-1073
On Ahlfors-David regular weighted bound for the extension operator associated to the circle, Bull. London Math. Soc. 47(4) (2015), 575-584
On the tube-occupancy of sets in R^d, Int. Math. Res. Notices 2015 (2015), 9815-9831
Hausdorff dimension estimates for restricted families of projections in R^3, Adv. Math. 275 (2015), 147-183
On the packing measure of the slices of self-similar sets, J. Fractal Geom. 2(4) (2015), 389-401
On Fourier analytic properties of graphs, with J. Fraser and T. Sahlsten, Int. Math. Res. Notices 2014(10) (2014), 2730-2745
Square functions with general measures II, with H. Martikainen and M. Mourgoglou, Indiana Univ. Math. J. 63(5) (2014), 1249-1279
On restricted families of projections in R^3, with K. Fässler, Proc. London Math. Soc. 109 (2) (2014), 353-381
Non-existence of multi-line Besicovitch sets, Publ. Mat. 58(1) (2014), 213-220
Constancy results for special families of projections, with K. Fässler, Math. Proc. Cambridge Philos. Soc. 154(3) (2013), 549-568
On the packing measure of self-similar sets, Nonlinearity 26 (2013), 2929-2934
On the Haar Shift Representations of Calderón-Zygmund Operators, Proc. Amer. Math. Soc. 141 (2013), 2693-2698
On the Distance Sets of Self-Similar Sets, Nonlinearity 25 (2012), 1919-1929
Tangent measures of non-doubling measures, with T. Sahlsten, Math. Proc. Cambridge Philos. Soc. 152 (2012), 555-569
Weak and Strong Type Estimates for Maximal Truncations of Calderón-Zygmund Operators on A_p Weighted Spaces, with T. Hytönen, M. Lacey, H. Martikainen, M. Reguera, E. Sawyer and I. Uriarte-Tuero, J. Anal. Math. 118 (1) (2012), 177-220
Radial projections of rectifiable sets, with T. Sahlsten, Ann. Acad. Sci. Fenn. Math 36 (2011), 677-681
Slicing Sets and Measures, and the Dimension of Exceptional Parameters, J. Geom. Anal. 24 (1) (2014), 47-80
PhD thesis: Exceptional sets in projection and slicing theorems, University of Helsinki (2012), supervised by P. Mattila
Preprints
On the dimension of s-Nikodým sets, with D. Dabrowski and M. Goering (2024)
Large cliques in extremal incidence configurations, with G. Yi (2024)
On Fourier transforms of fractal measures on the parabola, with C. Puliatti and A. Pyörälä (2024)
On the Fourier decay of multiplicative convolutions, with N. de Saxcé and P. Shmerkin (2023)
Projections, Furstenberg sets, and the ABC sum-product problem, with P. Shmerkin (2023)
Notes
Planar incidences and geometric inequalities in the Heisenberg group, with K. Fässler and A. Pinamonti (2020)
Quantitative Alberti representations in spaces of bounded geometry (2019)
A note on expansion in prime fields, with L. Venieri (2018)
Every locally finite Borel measure on R has conformal dimension zero (2017)
A Characterization of the boundedness of the median maximal function on weighted L^p spaces, with H. Martikanen (2011)