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401-5252-DRL 2 Credits DR D-MATH

Sparse Equidistribution Problems in Dynamics

Lecturers & Examiners: Adam Kanigowski
Doctoral students of I-Math (UZH) need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-06-01 11:33:18

Abstract

Nachdiplom lecture

Content

Let (X,T) be a topological dynamical system. Classical ergodic theory studies asymptotic behavior of averages of the form 1/N ∑_{n≤N} f(T^n x) where x∈X and f∈C(X). There are many fundamental results on convergence of such averages in various norms: the supremum norm, almost everywhere and in L^2 being the main examples (in the latter two we equip (X,T) with a measure μ which is preserved by T). Recently there has been a lot of interest in studying non-classical averages. In the most general form, given a bounded sequence (a_n) one is interested in the asymptotic behavior of averages: 1/∑_{n≤N} |a_n| ∑_{n≤N} a_n⋅f(T^n x). In most applications the sequence (a_n) is a structured sequence coming from number theory. Some of the examples of such sequences include: 1. a_n = Möbius function or Liouville function (or more generally a multiplicative function). 2. for k≥1, a_n=1 if n is a product of at most k primes, a_n=0 otherwise. 3. a_n=1 if n is a k-th power (like square) and a_n=0 otherwise. 4. (a_n) a random sequence of real numbers.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Course Components

Type Title Time & Place Hours
lecture Sparse Equidistribution Problems in Dynamics
If you would like to attend the lecture, please register by 23 February. For the registration form see
  • Wed 10:15-12:00 (HG G 43)
2 h weekly

Offered In

  • Doktorat Mathematik (Mehr Informationen unter: )
    • Vertiefung Fachwissen (Die Liste der Lehrveranstaltungen (samt der zugehörigen Anzahl Kreditpunkte) für Doktoratsstudentinnen und Doktoratsstudenten wird jedes Semester im Newsletter der ZGSM veröffentlicht.)