Isogeny and Ramanujan Graphs
I (Jack) know nothing about this. At all. But it will need to be talked about.
  • Isogeny graph (general definition, degree, duals...).
  • Starting vertex (Bröker's algorithm).
  • Isogeny Volcanos: Sutherland might be a good source
  • Supersingular isogeny graphs
    • Size, everything is defined over GF(p^2). (*as long as the degree divides (p+1)^2 or (p-1)^2).
    • Random walks are probably the best motivation to define Ramanujanness, and are directly applicable to cryptography. A (perhaps too large) source is Hoory-Linial-Wigderson.
    • Consequence from Ramanujan + random walk convergence: O(log p) diameter.
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