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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


Arithmetic Study Group: Diophantine properties of Markoff-Hurwitz varieties

Presented by Michael Magee, Durham University
19 November 2019 13:00 in CM219

Beginning with the simple question
'when is the sum of the squares of a tuple of integers equal to a multiple of their product?',
one arrives at a family of Diophantine equations called Markoff-Hurwitz equations.
I will give a `high-level' accessible talk about these Diophantine equations with two broad themes:
Firstly, the Markoff-Hurwitz equations are important as a `critical' case in Diophantine geometry, and as such, have strange Diophantine properties.
Secondly, the Markoff-Hurwitz equations are intimately connected with a family of fractals that includes the `Rauzy gasket': a fractal that pops up in seemingly disparate areas of mathematics including triply periodic surfaces, dynamics of maps on the circle, higher dimensional generalizations of continued fractions, Teichmuller theory, and now, in Diophantine geometry.
This is partly based on joint work with Alex Gamburd and Ryan Ronan.

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