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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.


 

Geometry and Topology Seminar: Rigidity for the discrete Bonnet-Myers diameter bound. Which graphs look like a sphere ?

Presented by Supanat Kamtue, Durham
7 June 2018 13:00 in CM301

The Bonnet-Myers theorem is a classical theorem which gives an estimate of the diameter in term of the positive Ricci curvature bound of a manifold. In the discrete setting of graphs, Ollivier’s notion of Ricci curvature provides a discrete analogue of Bonnet-Myers theorem. In view of Cheng’s rigidity result, it is natural to ask for which graphs the Bonnet-Myers estimates is sharp. We call such graphs Bonnet-Myers sharp graphs.

We prove that, under an extra condition of antipodalness (i.e. each vertex has a vertex whose distance between them is equal to the diameter), a Bonnet-Myers sharp graph must be ``strongly spherical”, which is a combinatorial property that has been completely classified. The proof includes a new method of transport geodesic, which I will explain in my talk.

This is joint work with Bourne, Cushing, Koolen, Liu, M\”{u}nch, and Peyerimhoff.

Contact mark.a.powell@durham.ac.uk or andrew.lobb@durham.ac.uk or wilhelm.klingenberg@durham.ac.uk for more information