Electrons subjected to the dual effect of a perpendicular magnetic and electric fields show a very curious behaviour known as the Hall Effect. When the applied magnetic field is sufficiently high, the Hall conductance becomes quantised in integer quantities of e^2/h. This quantisation is so precise that it is now used as a universal standard for resistance calibrations! Perhaps surprisingly, this phenomenon seems to have deep connections with electromagnetic gauge invariance and topology!

Most chess players are familiar with problems of the type “White to play and win in 3 moves”. However, here you will explore a very different genre of chess puzzles, retrograde analysis. Or perhaps, a more accurate description would be: utilising the rich set of chess rules to build interesting logic puzzles

What are closed convex sets? How do curves and width correlate? What are these to do with Minkowski sums? How does the Barbier theorem unfold the beauty of convex sets?