Michael Björklund

Contact

Office H4017
Tel.nr: +46 (0)31-772 3554

Chalmers University
Mathematical Sciences
Chalmers Tvärgata 3
SE-412 96 Gothenburg
Sweden

Email: micbjo (you know what) chalmers.se

I am an associate professor (docent) at Chalmers University, Gothenburg. My research is mostly concerned with the various interactions between ergodic theory, random walks, number theory and arithmetic combinatorics.

Research interests

Ergodic theory, arithmetic combinatorics (mostly approximate groups), geometry and dynamics on homogeneous spaces.

Teaching at Chalmers and elsewhere

Arithmetic Combinatorics. Lecture notes (essentially complete)
Representation Theory, Part I. Lecture notes (partially complete)
Topological Dynamics, Lecture notes (far from complete)

Submitted preprints

Kudo-continuity of entropy functionals

Joint with Y. Hartman and H. Oppelmayer

Sets of transfer times with small densities

Joint with A. Fish and I. Shkredov.

Aperiodic order and spherical diffraction II: Translation bounded measures on homogeneous spaces.

Joint with T. Hartnick and F. Pogorzelski

Aperiodic order and spherical diffraction III: The shadow transform and the diffraction formula.

Joint with T. Hartnick and F. Pogorzelski.

Patterns in sets of positive density in trees and affine buildings.

Joint with A. Fish and J. Parkinson.

Spectral theory of approximate lattices in nilpotent groups

Joint with Tobias Hartnick

Ergodicity and type of non-singular Bernoulli actions

Joint with Zemer Kosloff and Stefaan Vaes.

Bernoulli actions of amenable groups

Joint with Zemer Kosloff

Publications and Accepted Papers

Analytic properties of approximate lattices
Joint with T. Hartnick. Annales Inst. Fourier (2019).

Borel density for approximate lattices

Joint with Tobias Hartnick and Thierry Stulemeijer. Forum of Math, Sigma (2019).

Central limit theorem for diophantine approximants.
Joint with Alexander Gorodnik. Math. Annalen (2019).

Approximate invariance for ergodic actions of amenable groups.
Joint with A. Fish. Discrete analysis, 2019.

Central Limit Theorems for group actions which are exponentially mixing of all orders
Joint with A. Gorodnik. To appear in Journal d'Analyse Mathematique (2018)

Bohr sets in triple products of large sets in amenable groups
Joint with J. Griesmer. To appear in Journal of Fourier Analysis and Applications (2018).

Approximate lattices
Joint with T. Hartnick. To appear in Duke Journal of Math. (2018).

Quantitative multiple mixing
Joint with M. Einsiedler and A. Gorodnik. To appear in Journal of the Eur. Math. Soc. (2017).

Aperiodic order and spherical diffraction, Part I: Auto-correlation of model sets
Joint with T. Hartnick and F. Pogorzelski. Proc. London Math. Soc. (2017)

Central Limit Theorems in the Geometry of Numbers
Joint with A. Gorodnik. Electronic Research Announcements (AMS)

Twisted patterns in large subsets of Z^N
Joint with K. Bulinski. Commentarii Math (2017).

Product set phenomena for measured groups.
Ergodic theory and Dynamical systems - (2017).

Small product sets in compact groups.
Fundamenta Math. - (2016).

Random walks on countable groups.
Israel Journal of Math. - (2016).

Characteristic Polynomial Patterns in differnce sets of matrices
with A. Fish. Bull. London Math. Soc. - (2016).

Ergodic Theorems for coset spaces
with A. Fish. Journal d'Analyse Mathematique - (2015).

Quasi-state rigidity for finite-dimensional Lie algebras
with T. Hartnick. Israel Journal of Mathematics (2015).

Plünnecke inequalities for countable abelian groups
with A. Fish. Journal fur die Reine und Angewandte Mathematik (Crelle) - (2015).

Product set phenomena for countable groups
with A. Fish. Advances in Mathematics - (2015).

Biharmonic functions on groups and limit theorems for quasimorphisms along random walks
with T. Hartnick. Geom. Topol. 15 (2011), no. 1, 123-143.

The Asymptotic Shape Theorem for Generalized First Passage Percolation
Annals of Probability. 38 (2010), no. 2, 632-660.

Ergodic Theorems for Random Clusters
Stochastic Process. Appl. 120 (2010), no. 3, 296-305.

Ergodic Theorems for Homogeneous Dilations
Random walks, boundaries and spectra, 75-89, Progr. Probab., 64, Birkhäuser/Springer Basel AG, Basel, 2011.

Central Limit Theorems for Gromov Hyperbolic Groups
J. Theoret. Probab. 23 (2010), no. 3, 871-887.

Equidistribution of dilations of polynomial curves in nilmanifolds
with A. Fish. Proc. Amer. Math. Soc. 137 (2009), 2111-2123.

Continuous Measures on Homogeneous Spaces
with A. Fish. Ann. Inst. Fourier (Grenoble) 59 (2009), no. 6, 2169-2174.

Almost Sure Absolute Continuity of Subordinated Bernoulli Convolutions
with D. Schnellmann. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 3, 888-893.

Almost Sure Equidistribution in Expansive Families
with D. Schnellmann. Indag. Math. (N.S.) 20 (2009), no. 2, 167-177.

Entropy range problems and actions of locally normal groups
with R. Miles. Discrete Contin. Dyn. Syst. 25 (2009), no. 3, 981-989.

The g-theorem matrices are totally nonnegative
with A. Engström. Journal of Combinatorial Theory, Series A, Volume 116, Issue 3, April 2009, Pages 730-732.