Welcome to the homepage of Alexander P. Kartun-Giles.

On way back from Margate, UK, June 2023

Hello! I am currently a Postdoctoral Research Fellow in Complex Networks at University College London, working on the European Research Council (ERC) project LINKS, applying network science in the area of climate finance.

I was recently Postdoctoral Research Fellow in the Division of Mathematics at NTU Singapore,
working on random geometric graphs with Nicolas Privault. Previously, I've held postdoctoral positions at the School of Mathematics, University of Bristol, the Wireless Systems Laboratory at Hanyang University, Seoul, with Jürgen Jost's Geometry, Analysis and Theoretical Physics Group at The Max Plank Institute for Mathematics in the Sciences, Leipzig, and the Complex Systems and Networks Group at QMUL. I'm also currently in ongoing collaboration with Vincenzo Nicosia at Queen Mary, University of London, looking at the Kuramoto model on hyperbolic random geometric graphs, and with Kostas Koufos at The University of Warwick on soft random geometric graphs in communication theory.

From 2011 to 2016, I worked with Prof. Carl Dettmann and Orestis Georgiou at the University of Bristol,
reading for a PhD in Communications Engineering entitled "Connectivity and Centrality in Dense Random Geometric Graphs".

Before that I did an MSci in Physics at the University of Bristol.

Here is my cv.

For a list of my publications, see my Google Scholar page, or Scopus profile.

My email is alexander.giles@ucl.ac.uk.

I recently completed a visiting position at the Max Plank Institute for Mathematics in the Sciences in Leipzig,
working with Prof. Jürgen Jost and his Geometry, Analysis and Theoretical Physics group
on discrete notions of curvature in networks, as well as random topology in complex networks.

Hyperbolic random geometric graph Hyperbolic random geometric graph Hyperbolic random geometric graph (native model)
Hyperbolic random geometric graphs.

I was previously a visiting postdoc at Queen Mary University of London,
working in the Complex Systems group with Dr Ginestra Bianconi, from 2017 until 2018,
where we worked on inference in complex networks with Dimitri Krioukov, James P. Gleeson and Yamir Moreno,
as well as the statistical mechanics of simplicial complexes in complex networks.

Random geometric graph in non-convex domain

From 2016 to 2017, I worked with Prof. Sunwoo Kim and his Wireless Systems Laboratory at Hanyang University in Seoul,
working on random geometric graphs, localisation in random networks, as well as Euclidean matching theory in ultra-dense 5G networks.

From 2015 to 2016, after my PhD, I worked as a Postdoctoral Research Fellow in the School of Mathematics at the Bristol University,
after receiving EPSRC funding for a project entitled "Random Walks on Random Geometric Networks".
We also held a one-day meeting as part of the British Mathematical Colloquim 2016.

Wifi domain
Random geometric graph in a non-convex "WiFi" domain. The non-convexity blocks connections between some pairs of nodes, see e.g.

Connectivity of soft random geometric graphs over annuli, A.P. Giles, O. Georgiou and C.P. Dettmann, Journal of Statistical Physics 162, 2016.

How does this affect the connectivity of the graph? See also the Boltzmann-Grad limit of the periodic Lorentz gas, Jens Marklof and Andreas Strombergsson, Ann. Maths 174, 2011. Millions of miniscule obstacles in a 2d region block the path of a bouncing electron. Can help understand ideas of physics e.g. Ohms law.

Recent papers.

See "Shortest routes in random proximity networks" on this list of open problems of David Aldous.

Tracy-Widom distribution article At the Far Ends of a New Universal Law.

Spatial networks wikipedia article, which is being updated.

Review article on spatial networks by Marc Barthélemy.


This is a photo of Bristol in 2018, by Cliftonwood Crescent.

Clifton, Bristol, UK.

Leipzig near MPI Leipzig and the Schumann-Haus

Leipzig 2018.