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Felix Flicker Email address for Felix Flicker

Research

Please see the Publications tab for an up-to-date list of my papers, theses, etc.; this page has some popular write-ups of work I've been involved with.

Hamiltonian Cycles on Ammann Beenker Tilings

A Hamiltonian cycle visits every vertex on a graph exactly once before returning to the start. A classic example is a Knight's Tour on a chessboard. Finding these paths is, in general, a very hard problem (NP-complete). Unexpectedly, we found a way to construct them on certain quasicrystals. As a result, many formerly intractable problems can now be solved in this setting. The Hamiltonian cycles also make fantastically complicated mazes. The work has been written up here:

Aperiodic Monotiles

2023 saw the discovery of an aperiodic monotile: a shape (dubbed 'The Hat') that can tile a plane perfectly, but only without periodicity. To celebrate this inspirational result we organised Hatfest at Oxford University's Mathematical Institute.

I have subsequently worked to understand how physics behaves in these fascinating settings. Some of this work, published in Physical Review Letters, received a write-up here:

Magnetic Monopoles in Spin Ice

Published in Nature.

My experimental collaborators detected signatures of magnetic monopoles in the spin ice material dysprosium titanate, based on our earlier theoretical predictions. You can read some popular summaries here:

and an article about the original proposal here:

The Excitonic Insulator State in Titanium Diselenide

Published in Science.

Charge Density Waves in Niobium Diselenide