The Robinson-Schensted-Knuth correspondence gives a very concrete algorithm for converting a permutation into a pair of Young Tableaux, from which we can extract the longest increasing subsequence of the original permutation. Fulton and Viennot's Geometric construction gives a different algorithm for producing these Young Tableaux, without so many intermediate steps. Along the way, it converts longest increasing subsequence(s) into disjoint longest paths in N^2 (the positive integer lattice). We will go over this alternative algorithm, enjoy some of its symmetries, and (time permitting) discuss how we might recover these longest disjoint paths. Speaker(s): Scott Neville