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.
|November 2019||January 2020|
Events for 10 December 2019
A Wieferich prime is a prime number p such that 2^(p-1) is congruent to 1 modulo p^2. These numbers originally arose in the context of Fermat's last theorem. At present very little is known about them, although there are some conjectures. One can analogously define Wieferich primes for 3, or 5, or for a point on an abelian variety. In this talk I will explain what Wieferich primes for abelian varieties have to do with p-adic integrals and rational points on curves, and will also describe some (unconditional) results on the heights of rational points on higher genus curves.
Population protocols are a model of distributed computing, where n agents with limited computational power and memory interact randomly, in order to jointly perform a global task. A fundamental problem in this setting is that of leader election, where all agents start from the same state, and they seek to reach and maintain a global state where exactly one agent is in a dedicated leader state. We establish that if agents have Omega(\log\log n) states, the expected time complexity of leader election is Theta(n \log n). Unlike existing protocols, ours does not decrease the set of candidate leaders monotonically. Our protocol has both optimal time and space complexity. Joint work with George Giakkoupis and Peter Kling
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