Publications

I have authored , across 29 journals, and along with related works, as detailed below. My research focuses on , , and . I have collaborated with 45 researchers, notably with Balázs Bárány, Tapio Rajala, and Ville Suomala, each on at least five projects. Additionally, I have co-authored at least four papers with 7 researchers, three papers with 12, and two papers with 22. For comprehensive bibliometric details, consult my MathSciNet, zbMATH Open, and Google Scholar profiles.

  1. Projections of self-affine sets onto lines
    (with B. Bárány and I. Kolossváry)
    Preprint, 2026

  2. On the Marstrand projection theorem for the Assouad spectrum
    (with K. J. Falconer and J. M. Fraser)
    Preprint, 2026

  3. Level sets of prevalent Weierstrass functions
    (with Z. Buczolich and B. Maga)
    Preprint, 2025

  4. Self-affine sponges with random contractions
    (with B. Bárány and M. Rams)
    Probab. Theory Related Fields, to appear

  5. Tangents and slices of self-affine carpets
    (with A. Rutar)
    Preprint, 2024

  6. Regularity of non-autonomous self-similar sets
    (with A. Rutar)
    Math. Proc. Cambridge Philos. Soc., 179 (2025), no. 3, 623-648

  7. Thermodynamic formalism of countably generated self-affine sets
    (with I. D. Morris)
    Trans. Amer. Math. Soc., 379 (2026), no. 5, 3161-3210

  8. Level sets of prevalent Hölder functions
    (with R. Anttila and B. Bárány)
    Proc. Amer. Math. Soc., 153 (2025), no. 5, 2023-2035

  9. Local dimension spectrum for dominated planar self-affine sets
    (with A. Batsis and T. Kempton)
    Math. Z., 312 (2026), no. 4, Paper No. 115

  10. Tangents of invariant sets
    (with A. Rutar)
    Preprint, 2023

  11. Scaling limits of self-conformal measures
    (with B. Bárány, A. Pyörälä, and M. Wu)
    Preprint, 2023

  12. Dimension of planar non-conformal attractors with triangular derivative matrices
    (with B. Bárány)
    Comm. Math. Phys., 405 (2024), no. 11, Paper No. 256

  13. Covering number on inhomogeneous graph-directed self-similar sets
    (with B. Bárány and P. Nissinen)
    J. Fractal Geom., 13 (2026), no. 3-4, 241-262

  14. Slices of the Takagi function
    (with R. Anttila and B. Bárány)
    Ergodic Theory Dynam. Systems, 44 (2024), no. 9, 2361-2398

  15. Non-invertible planar self-affine sets
    (with P. Nissinen)
    Math. Proc. Cambridge Philos. Soc., 177 (2024), no. 1, 49-65

  16. Finer geometry of planar self-affine sets
    (with B. Bárány and H. Yu)
    Adv. Math., 493 (2026), Paper No. 110914

  17. Minkowski dimension for measures
    (with K. J. Falconer and J. M. Fraser)
    Proc. Amer. Math. Soc., 151 (2023), no. 2, 779-794

  18. Super-exponential condensation without exact overlaps | Numerical calculations
    (with B. Bárány)
    Adv. Math., 379 (2021), Paper No. 107549

  19. Assouad dimension of planar self-affine sets
    (with B. Bárány and E. Rossi)
    Trans. Amer. Math. Soc., 374 (2021), no. 2, 1297-1326

  20. Absolute continuity in families of parametrised non-homogeneous self-similar measures
    (with T. Orponen)
    J. Fractal Geom., 10 (2023), no. 1, 169-207

  21. Attainable values for the Assouad dimension of projections
    (with J. M. Fraser)
    Proc. Amer. Math. Soc., 148 (2020), no. 8, 3393-3405

  22. On the Hausdorff dimension of microsets
    (with J. M. Fraser, D. C. Howroyd, and H. Yu)
    Proc. Amer. Math. Soc., 147 (2019), no. 11, 4921-4936

  23. Birkhoff and Lyapunov spectra on planar self-affine sets
    (with B. Bárány, T. Jordan, and M. Rams)
    Int. Math. Res. Not., IMRN 2021, no. 10, 7966-8005

  24. Self-conformal sets with positive Hausdorff measure | Numerical calculations
    (with J. Angelevska and S. Troscheit)
    Bull. Lond. Math. Soc., 52 (2020), no. 1, 200-223

  25. Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
    (with B. Bárány and I. D. Morris)
    Israel J. Math., 239 (2020), no. 1, 173-214

  26. A Marstrand-type restricted projection theorem in R^3
    (with T. Orponen and L. Venieri)
    Amer. J. Math., 147 (2025), no. 1, 81-123

  27. Dynamics of the scenery flow and conical density theorems
    Banach Center Publ., 115 (2018), 99-143

  28. Self-affine sets in analytic curves and algebraic surfaces
    (with D.-J. Feng)
    Ann. Acad. Sci. Fenn. Math., 43 (2018), no. 1, 109-119

  29. Dimension of self-affine sets for fixed translation vectors
    (with B. Bárány and H. Koivusalo)
    J. Lond. Math. Soc., 98 (2018), no. 1, 223-252

  30. Genericity of dimension drop on self-affine sets
    (with B. Li)
    Statist. Probab. Lett., 126 (2017), 18-25

  31. Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
    (with I. D. Morris)
    Proc. Lond. Math. Soc., 116 (2018), no. 4, 929-956

  32. Measures with predetermined regularity and inhomogeneous self-similar sets
    (with J. Lehrbäck)
    Ark. Mat., 55 (2017), no. 1, 165-184

  33. Rigidity of quasisymmetric mappings on self-affine carpets
    (with T. Ojala and E. Rossi)
    Int. Math. Res. Not., IMRN 2018, no. 12, 3769-3799

  34. A note on correlation and local dimensions
    (with J. Yang and M. Wu)
    Chaos Solitons Fractals, 97 (2017), 39-43

  35. Ledrappier-Young formula and exact dimensionality of self-affine measures
    (with B. Bárány)
    Adv. Math., 318 (2017), 88-129

  36. Weak separation condition, Assouad dimension, and Furstenberg homogeneity
    (with E. Rossi)
    Ann. Acad. Sci. Fenn. Math., 41 (2016), no. 1, 465-490

  37. Self-affine sets with fibered tangents
    (with H. Koivusalo and E. Rossi)
    Ergodic Theory Dynam. Systems, 37 (2017), no. 6, 1915-1934

  38. Local dimensions in Moran constructions
    (with B. Li and V. Suomala)
    Nonlinearity, 29 (2016), no. 3, 807-822

  39. Scenery flow, conical densities, and rectifiability
    Fractal Geometry and Stochastics V, Springer International Publishing, 2015, 27-38

  40. Dynamics of the scenery flow and geometry of measures
    (with T. Sahlsten and P. Shmerkin)
    Proc. Lond. Math. Soc., 110 (2015), no. 5, 1248-1280

  41. Structure of distributions generated by the scenery flow
    (with T. Sahlsten and P. Shmerkin)
    J. Lond. Math. Soc., 91 (2015), no. 2, 464-494

  42. Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets
    (with H. W. J. Reeve)
    J. Fractal Geom., 1 (2014), no. 1, 83-152

  43. Dimensions, Whitney covers, and tubular neighborhoods
    (with J. Lehrbäck and M. Vuorinen)
    Indiana Univ. Math. J., 62 (2013), no. 6, 1861-1889

  44. Local conical dimensions for measures
    (with D.-J. Feng and V. Suomala)
    Math. Proc. Cambridge Philos. Soc., 154 (2013), no. 3, 465-479

  45. Dimensions of random affine code tree fractals
    (with E. Järvenpää, M. Järvenpää, H. Koivusalo, Ö. Stenflo, and V. Suomala)
    Ergodic Theory Dynam. Systems, 34 (2014), no. 3, 854-875

  46. Local structure of self-affine sets
    (with C. Bandt)
    Ergodic Theory Dynam. Systems, 33 (2013), no. 5, 1326-1337

  47. Existence of doubling measures via generalised nested cubes
    (with T. Rajala and V. Suomala)
    Proc. Amer. Math. Soc., 140 (2012), no. 9, 3275-3281

  48. Local multifractal analysis in metric spaces
    (with T. Rajala and V. Suomala)
    Nonlinearity, 26 (2013), no. 8, 2157-2173

  49. Local homogeneity and dimensions of measures
    (with T. Rajala and V. Suomala)
    Ann. Sc. Norm. Super. Pisa Cl. Sci., 16 (2016), no. 4, 1315-1351

  50. Equilibrium states for the pressure function for products of matrices
    (with D.-J. Feng)
    Discrete Contin. Dyn. Syst., 30 (2011), no. 3, 699-704

  51. Dimension and measures on sub-self-affine sets
    (with M. Vilppolainen)
    Monatsh. Math., 161 (2010), no. 3, 271-293

  52. On upper conical density results
    Recent Developments in Fractals and Related Fields, Applied and Numerical Harmonic Analysis, 2010, 45-54

  53. Upper conical density results for general measures on R^n
    (with M. Csörnyei, T. Rajala, and V. Suomala)
    Proc. Edinburgh Math. Soc., 53 (2010), no. 2, 311-331

  54. Itseaffiineista joukoista
    Arkhimedes, (2008), no. 2, 17-20

  55. Porosity and regularity in metric measure spaces
    Real Anal. Exchange 2007, 31st Summer Symposium Conference, 245-250

  56. Packing dimension and Ahlfors regularity of porous sets in metric spaces
    (with E. Järvenpää, M. Järvenpää, T. Rajala, S. Rogovin, and V. Suomala)
    Math. Z., 266 (2010), no. 1, 83-105

  57. Overlapping self-affine sets of Kakeya type
    (with P. Shmerkin)
    Ergodic Theory Dynam. Systems, 29 (2009), no. 3, 941-965

  58. Packing dimension of mean porous measures
    (with D. Beliaev, E. Järvenpää, M. Järvenpää, T. Rajala, S. Smirnov, and V. Suomala)
    J. Lond. Math. Soc., 80 (2009), no. 2, 514-530

  59. Separation conditions on controlled Moran constructions
    (with M. Vilppolainen)
    Fund. Math., 200 (2008), no. 1, 69-100

  60. Conical upper density theorems and porosity of measures
    (with V. Suomala)
    Adv. Math., 217 (2008), no. 3, 952-966

  61. Geometric rigidity of a class of fractal sets
    Math. Nachr., 279 (2006), no. 1-2, 179-187

  62. Asymptotically sharp dimension estimates for k-porous sets
    (with E. Järvenpää, M. Järvenpää, and V. Suomala)
    Math. Scand., 97 (2005), no. 2, 309-318

  63. Measures of full dimension on self-affine sets
    Acta Univ. Carolin. Math. Phys., 45 (2004), no. 2, 45-53

  64. Nonsymmetric conical upper density and k-porosity
    (with V. Suomala)
    Trans. Amer. Math. Soc., 363 (2011), no. 3, 1183-1195

  65. Iterated function systems: Natural measure and local structure
    Rep. Univ. Jyväskylä Dept. Math. Stat., 93 (2003)

  66. On natural invariant measures on generalised iterated function systems
    Ann. Acad. Sci. Fenn. Math., 29 (2004), no. 2, 419-458

  67. On the geometric structure of the limit set of conformal iterated function systems
    Publ. Mat., 47 (2003), no. 1, 133-141