Events at The University of Manchester
  • University home
  • Events
  • Home
  • Exhibitions
  • Conferences
  • Lectures and seminars
  • Performances
  • Events for prospective students
  • Sustainability events
  • Family events
  • All Events

Projections of random measures on products of $\times m,\times n$-invariant sets and a random Furstenberg sumset conjecture - Dynamical Systems and Analysis Seminar Series

Dates:17 February 2020
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Adults, Alumni, Current University students
Speaker:Catherine Bruce
See travel and contact information
Add to your calendar

More information

  • Department of Mathematics

Other events

  • In category "Seminar"
  • In group "(Maths) Maths seminar series"
  • In group "(Maths) Analysis and dynamical systems"
  • By Department of Mathematics

Catherine Bruce will be speaking at this research seminar, part of the Dynamical Systems and Analysis seminar series. Abstract: In 2012 Hochman and Shmerkin proved that, given Borel probability measures on 0,1 invariant under multiplication by 2 and 3 respectively, the Hausdorff dimension of the orthogonal projection of the product of these measures is equal to the maximum possible value in every direction except the horizontal and vertical directions. Their result holds beyond multiplication by 2,3 to natural numbers m,n which are multiplicatively independent. We discuss a generalisation of this theorem to include random cascade measures on subsets of 0,1 invariant under multiplication by multiplicatively independent m,n. We will define random cascade measures in a heuristic way, as a natural randomisation of invariant measures on symbolic space. The theorem of Hochman and Shmerkin fully resolved a conjecture of Furstenberg originating in the late 1960s concerning sumsets of these invariant sets. We apply our main result to present a random version of this conjecture which holds for products of percolations on $\times m, \times n$-invariant sets.

Speaker

Catherine Bruce

Organisation: University of Manchester

Travel and Contact Information

Find event

G.113
Alan Turing Building
Manchester

Contact event

Tom Kempton

thomas.kempton@manchester.ac.uk

Contact us

  • +44 (0) 161 306 6000

Find us

The University of Manchester
Oxford Rd
Manchester
M13 9PL
UK

Connect with the University

  • Facebook page for The University of Manchester
  • X (formerly Twitter) page for The University of Manchester
  • YouTube page for The University of Manchester
  • Instagram page for The University of Manchester
  • TikTok page for The University of Manchester
  • LinkedIn page for The University of Manchester

  • Privacy /
  • Copyright notice /
  • Accessibility /
  • Freedom of information /
  • Charitable status /
  • Royal Charter Number: RC000797
  • Close menu
  • Home
    • Featured events
    • Today's events
    • The Whitworth events
    • Manchester Museum events
    • Jodrell Bank Discovery Centre events
    • Martin Harris Centre events
    • The John Rylands Library events
    • Exhibitions
    • Conferences
    • Lectures and seminars
    • Performances
    • Events for prospective students
    • Sustainability events
    • Family events
    • All events