*Adaptive Analysis* of algorithms and data structures, i.e. refining the worst case analysis over instances of fixed size n by adding more parameters to it, in order to intuitively measure the "difficulty" of the instance.

Carlos Ochoa (PhD, 2013-now) "Adaptive Algorithms on Convex Hull, Voronoi Diagrams and Delaunay Triangulations"
Carlos is working on the adaptive computation of Convex Hulls and Delaunay Triangulations, taking advantage of the order of the input (adaptive computation independent of the input order is impossible in 2 or 3 dimensions [FOCS2009]), inspired from adaptive results for sorting permutations. He will later work on other adaptive algorithms for computing and merging Convex Hulls, Delaunay Triangulations and Voronoi Diagrams.

Javiel Rojas (PhD, 2013-now) "Adaptive Algorithms for computing Klee's measure in High Dimension"
Javiel is working on the adaptive computation of the Klee's measure of a set of rectangles in high dimensions, focusing on algorithms taking advantage of the degeneracy of the input (something which was not done before in Computational Geometry). He will later work on potential finer measures of adaptivity for this problem.

Manuel Ramirez (Internship, 2014) "Repositorium for Music Sheets"
Manuel is working on the design of a solution permitting musicians to collaborate on a database of music sheets, by submitting new ones, evaluating collaboratively the submissions, searching and downloading them.