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UID:20260205T220633EST-5318A53WSE@132.216.98.100
DTSTAMP:20260206T030633Z
DESCRIPTION:Title:  Connections between ergodic theory and multiplicative n
 umber theory\n	 \n	Abstract: In this talk\, we will discuss several connecti
 ons between ergodic theory and multiplicative number theory. Given a proba
 bility space (X\, A\, µ)\, a multiplicative action S = (Sn)n∈N on (X\, A\,
  µ) is a sequence of measure-preserving transformations Sn : X → X satisfy
 ing Snm = Sn ◦ Sm for all n\, m ∈ N. This object can be viewed as the natu
 ral ergodic analog of a completely multiplicative function f : N → S 1 . W
 e will present new results on multiplicative actions\, applications of erg
 odic methods to problems in number theory\, and open questions in both are
 as. In particular\, we will focus on recurrence phenomena for multiplicati
 ve actions and their numbertheoretic consequences. Namely\, we characteriz
 e the integers a\, b\, c\, d for which lim inf n→∞ |f(an + b) − f(cn + d)|
  = 0 holds for all completely multiplicative functions f : N → S 1 . This 
 extends a theorem of Klurman and Mangerel corresponding to the pair (n\, n
  + 1). The talk will conclude with a discussion of how ergodic methods can
  be employed to address problems on the partition regularity of homogeneou
 s quadratic equations\, presenting current progress and highlighting the c
 hallenges involved.\n\nVenue: Concordia University LB 921-04\n
DTSTART:20260205T191500Z
DTEND:20260205T191500Z
SUMMARY:Dimitrios Charamaras (CRM)
URL:/biology/channels/event/dimitrios-charamaras-crm-3
 71120
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