Publications of Jouni Parkkonen

Monograph

  1. (with Anne Broise-Alamichel and Frédéric Paulin) Equidistribution and counting under equilibrium states in negative curvature and trees. Applications to non-Archimedean Diophantine approximation, Progress in Mathematics 329, Birkhäuser, 2019.

Preprints

  1. (with Frédéric Paulin) Equidistribution of common perpendiculars in negative curvature
  2. (with Frédéric Paulin) Divergent geodesics, ambiguous closed geodesics and the binary additive divisor problem.

Articles

  1. (with Frédéric Paulin) Pair correlations of logarithms of complex lattice points, Research in Number Theory 10:24 (2024).
  2. (with Frédéric Paulin) Sectorial Mertens and Mirsky formulae for imaginary quadratic number fields, Archiv der Mathematik 122(2024), 415-428.
  3. (with Frédéric Paulin) Joint partial equidistribution of Farey rays in negatively curved manifolds and trees, Ergodic Theory and Dynamical Systems 44(2024), 2700-2736.
  4. (with Lauri Kettunen, Sanna Mönkölä and Tuomo Rossi) Systematic Imposition of Partial Differential Equations in Boundary Value Problems in Impact of Scientific Computing on Science and Society, Computational Methods in Applied Sciences 58, Springer, 2023, pages 25-44.
  5. (with Frédéric Paulin) From exponential counting to pair correlations, Bull. Soc. Math. France 151(2023), 171-193.
  6. (with Frédéric Paulin) On the statistics of pairs of logarithms of integers (with an appendix by Etienne Fouvry), Moscow Journal of Combinatorics and Number Theory 11(2022), 335-372.
  7. (with Frédéric Paulin) Counting and equidistribution in quaternionic Heisenberg groups, Math. Proc. Camb. Phil. Soc 173(2022), 67-104.
  8. (with Frédéric Paulin) Rigidity, counting and equidistribution of quaternionic Cartan chains, Ann. Math. Blaise Pascal 28(2021), 45-69.
  9. (with Anne Broise-Alamichel and Frédéric Paulin) Rate of mixing for equilibrium states in negative curvature and trees in Thermodynamic Formalism, CIRM Jean-Morlet Chair Subseries, Lecture Notes in Mathematics 2290, Springer, 2021, pages 291-315.
  10. (with Frédéric Paulin) Integral binary Hamiltonian forms and their waterworlds, Conformal Geometry and Dynamics 25 (2021), 126-169.
  11. (with Frédéric Paulin) On the nonarchimedean quadratic Lagrange spectra, Math. Z. 294 (2020), 1065-1084.
  12. (with Frédéric Paulin) A classification of $\mathbb R$-Fuchsian subgroups of Picard modular groups, Confluentes Mathematici 10 (2018), 75-92.
  13. (with Frédéric Paulin) A classification of $\mathbb C$-Fuchsian subgroups of Picard modular groups, Mathematica Scandinavica 121 (2017) 57-74.
  14. (with Frédéric Paulin) A survey of some arithmetic applications of ergodic theory in negative curvature, in Ergodic theory and negative curvature, CIRM Jean-Morlet Chair Subseries, Lecture Notes in Mathematics 2164, Springer, 2017, pages 293-326.
  15. (with Frédéric Paulin) Counting common perpendicular arcs in negative curvature, Ergodic Theory and Dynamical Systems 37 (2017) 900-938.
  16. (with Frédéric Paulin) Counting and equidistribution in Heisenberg groups, Mathematische Annalen 367 (2017) 81-119.
  17. (avec Anne Broise-Alamichel et Frédéric Paulin) Equidistribution non-archimédienne et actions de groupes sur les arbres, C. R. Math. Acad. Sci. Paris, Ser. I 354 (2016) 971-975.
  18. (with Frédéric Paulin) Counting arcs in negative curvature, in Geometry, Topology, and Dynamics in Negative Curvature, LMS Lecture Notes 426, 2016, 289-344.
  19. (with Frédéric Paulin) On the hyperbolic orbital counting problem in conjugacy classes, Math. Z. 279 (2015) 1175-1196.
  20. (with Frédéric Paulin) Dentelles et flocons de neige arithmétiques, Images des Mathématiques, CNRS (2015).
  21. (with Frédéric Paulin) On the arithmetic of crossratios and generalised Mertens' formulas, ``Aux croisements de la géométrie hyperbolique et l'arithmétique'' Ann. Fac. Sci. Toulouse Vol. XXIII (2014) 967-1022.
  22. (with Frédéric Paulin) Skinning measures in negative curvature and equidistribution of equidistant submanifolds, Ergodic Theory and Dynamical Systems 34(2014) 1310-1342.
  23. (with Frédéric Paulin) On the arithmetic and geometry of binary Hamiltonian forms (with an appendix by Vincent Emery), Algebra & Number Theory 7-1 (2013) 75-115.
  24. (with Frédéric Paulin) On strictly convex subsets in negatively curved manifolds, J. Geom. Anal. 22(2012), 621-632.
  25. (avec Frédéric Paulin) Équidistribution, comptage et approximation par irrationnels quadratiques, J. Mod. Dyn. 6(2012), 1-40.
  26. (with Frédéric Paulin) On the representation of integers by indefinite binary Hermitian forms, Bull. London Math. Soc. 43(2011), 1048-1058.
  27. (with Frédéric Paulin) Spiraling spectra of geodesic lines in negatively curved manifolds, Math. Z. 268 (2011), 101-142. (Erratum Math. Z. 276 (2014), 1215-1216)
  28. (with Frédéric Paulin) Prescribing the behaviour of geodesics in negative curvature, Geometry & Topology 14 (2010) 277-392
  29. (with Frédéric Paulin) Equidistribution, counting and arithmetic applications, Oberwolfach Reports 7 (2010), 1737-1739.
  30. (with Frédéric Paulin) On the closedness of approximation spectra, Journal de théorie des nombres de Bordeaux 21 (2009) 701-710.
  31. (with Vesa Ruuska) Finite degree branched covers of compact Riemann surfaces, Acta Mathematica Sinica 23 (2007) 89-94.
  32. (with Yohei Komori) On the shape of Bers-Maskit slices, Ann. Acad. Sci. Fenn. 32 (2007) 179-198.
  33. (avec Frédéric Paulin) Sur les rayons de Hall en approximation diophantienne, C. R. Math. Acad. Sci. Paris Ser. I 344 (2007) 611-614.
  34. (with Frédéric Paulin) Unclouding the sky of negatively curved manifolds, Geom. Funct. Anal. 15 (2005) 491-533
  35. Geometric limits of cyclic groups and the shape of Schottky space, Math. Proc. Cambridge Philos. Soc. 137 (2004) 55-68.
  36. Conformal Dehn surgery and the shape of Maskit's embedding, Conformal Geometry and Dynamics 8 (2004), 143-157.
  37. (with Frédéric Paulin) Diophantine Approximation on Hyperbolic Surfaces, in ``Rigidity, geometry and number theory (Cambridge, 2000)'', M. Burger, A. Iozzi eds, Springer Verlag, 2002.
  38. The outside of the Teichmüller space of punctured tori in Maskit's embedding. Ann. Acad. Sci. Fenn. Math. 24 (1999) 305-342. A slightly expanded version can be found here
  39. (with John R. Parker) Coordinates for quasi-Fuchsian punctured torus spaces. The Epstein birthday schrift, Geom. Topol. Monogr. 1, 451-478, 1998.
  40. Geometric complex analytic coordinates for deformation spaces of Koebe groups. Ann. Acad. Sci. Fenn. Math. Diss. No. 102 (1995).

Popularisation

Illustrations

Some limit sets and deformation spaces of Koebe groups can be found here.