### The Banach-Tarski Paradox

Seminar

9th March 2018, 4:30 pm – 5:30 pm

Howard House, 4th Floor Seminar Room

One of the most counter-intuitive results in mathematics is the Banach-Tarski paradox. It says that a ball in R^3 can be broken into finitely many pieces which rearrange using rotations and translations to give two identical copies of the starting ball. The pieces used are constructed using the Axiom of Choice and are not Lebesgue measurable.

I will give a general definition of paradoxes, what B-T means for the existence of certain measures and describe some components of the proof that centre on a paradoxical decomposition of F_2, the free group with two generators. Some surface level intuition of measures might be useful, otherwise I will assume little background knowledge.

*Organiser*: Quantum Information Theory Group

*Organisers*: Harry Petyt, Jordan Frost

*Organisers*: Florian Bouyer, Witold Sadowski

*Organisers*: Emilia Alvarez, Pip Goodman

*Organiser*: Ayalvadi Ganesh

*Organiser*: Karoline Wiesner

*Organiser*: Mathieu Gerber

*Organiser*: Nick Jones

*Organisers*: Philip Welch, Philipp Schlicht

*Organisers*: Andrew Booker, Kirsti Biggs, Chris Lutsko

*Organisers*: Catherine Hsu, Min Lee, Jonathan Bober, Matthew Bisatt

*Organisers*: Ben Barrett, Radhika Gupta, Alex Malcolm, Leonid Monin

*Organisers*: Kevin Grace, Misha Rudnev, Brendan Murphy

*Organisers*: Thomas Jordan, Rhiannon Dougall, Demi Allen

*Organisers*: John Russo, Aurore Loisy

*Organisers*: Michiel van den Berg, Kevin Hughes, John Mackay

*Organisers*: Tyler Helmuth, Ofer Busani

Other Quantum Information Theory seminars
Other Bristol Junior Geometry Seminar (BRIJGES) seminars
Other Mathematical Education seminars
Other Mathematics Postgraduate seminars
Other Colloquia seminars
Other Miscellaneous seminars
Other Statistics seminars
Other Mathematical Physics seminars
Other Logic and Set Theory seminars
Other Linfoot Number Theory seminars
Other Heilbronn Number Theory seminars
Other Algebra and Geometry seminars
Other Combinatorics seminars
Other Ergodic Theory and Dynamical Systems seminars
Other Fluids and Materials seminars
Other Analysis and Geometry seminars
Other Probability seminars

## Comments are closed.