These are the show notes for episode 51 of the Travels in a Mathematical World Podcast. 51 is the smallest number which can be written with all the digits from 1 to 5 (without repetition) as a sum of primes: 51 = 2 + 3 + 5 + 41. More about 51 from Number Gossip.

Dr. Sebastien Guenneau of the University of Liverpool talked to me in episode 50 about his work in invisibility cloaks. Here he follows this up by giving some examples from optical wave guides and other areas to highlight the processes which drive applied mathematics research and collaboration. You can read an introduction to optical wave guides at electron9.phys.utk.edu. You can read about the 2009 Nobel Prize for Physics at nobelprize.org. Sebastien talks about Professor Alexander B. Movchan and Professor I. David Abrahams.

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