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.
|May 2018||July 2018|
Events for 25 June 2018
Do local constraints demand global coordination? I'll address a
particularly simple formulation of this question: can the vertices of a
graph be assigned random colours in a stationary way, so that neighboring
colours always differ, but without long-range dependence? The quest to
answer this has led to the discovery of beautiful yet mysterious new
stochastic processes that seemingly have no right to exist.
Contact firstname.lastname@example.org for more information about this event.
Markoff triples are integer solutions of the equation $x^2+y^2+z^2=3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields in mathematics and beyond. After reviewing some of these, we will discuss joint work with Bourgain and Sarnak on the connectedness of the set of solutions of the Markoff equation modulo primes under the action of the group generated by Vieta involutions, showing, in particular, that for almost all primes the induced graph is connected. Similar results for composite moduli enable us to establish certain new arithmetical properties of Markoff numbers, for instance the fact that almost all of them are composite. We will also discuss recent joint work with Magee and Ronan on the asymptotic formula for integer points on Markoff-Hurwitz surfaces $x_1^2+x_2^2 + \dots + x_n^2 = x_1 x_2 \dots x_n$, giving an interpretation for the exponent of growth in terms of certain conformal measure on the projective space.
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