List of publications

2021

  • M. Aka, A. Musso, and A. Wieser. Equidistribution of rational subspaces and their shapes . arXiv:2103.05163

    To any $k$-dimensional subspace of $\mathbb{Q}^n$ one can naturally associate a point in the Grassmannian $\mathrm{Gr}_{n,k}(\mathbb{R})$ and two shapes of lattices of rank $k$ and $n-k$ respectively. These lattices originate by intersecting the $k$-dimensional subspace with the lattice $\mathbb{Z}^n$. Using unipotent dynamics we prove simultaneous equidistribution of all of these objects under a congruence conditions when $(k,n)\neq (2,4)$.

2020

  • M. Aka, M. Luethi, Ph. Michel and A. Wieser. Simultaneous supersingular reductions of CM elliptic curves . arXiv:2005.01537.

    We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show - under additional congruence assumptions on the CM order - that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large. This variant of the equidistribution theorems of Duke and Cornut-Vatsal is an(other) application of the recent work of Einsiedler and Lindenstrauss on the classification of joinings of higher-rank diagonalizable actions.

    Here is a talk by my coauthor Manuel Luethi on the topic.

2019

  • M. Aka, M. Einsiedler and A. Wieser. Planes in four space and four associated CM points. arXiv:1901.05833.

    Abstract: To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian $\operatorname{Gr}(2,4)$ and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement and the second two essentially arise from the accidental local isomorphism between $\operatorname{SO}(4)$ and $\operatorname{SO}(3)\times \operatorname{SO}(3)$. As an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings we prove simultaneous equidistribution of all of these objects under two splitting conditions.

    Here are the slides for this talk I gave at the conference Smooth and homogeneous dynamics at ICTS in Bangalore.

  • A. Wieser. Linnik's problems and maximal entropy methods. Monatshefte für Mathematik, https://doi.org/10.1007/s00605-019-01320-7.

    Abstract: We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011.

    Note: the first version on the ArXiv treats a simpler special case.