Maike Buchin
 Algorithms for comparing curves and surfaces using the Frechet distance
 Algorithms for curves
 Finding good matchings
 Approximation algorithms
 Applications to Analysis of Trajectories
 Lower bounds
 Algorithms for surfaces
 Homotopy (after download change name to homotopy.key)
Jeff Erickson

Homotopy in the plane
Consider a planar environment with polygonal obstacles. Two paths in this environment are HOMOTOPIC if one can be continuously deformed into the other without intersecting the obstacles. In this first lecture, I will discuss two key algorithm problems related to homotopy. First, given two paths, decide whether they are homotopic. Second, given a single path P, find the shortest path that is homotopic to P.  Surface maps
In the second lecture, I will describe standard data structures and structural properties of planar decompositions and of embeddings of graphs on topological surfaces. Specific topics include rotation systems, duality, treecotree decompositions, Euler’s formula, systems of loops and polygonal schemas, and homotopy and homology on surfaces.  Short interesting cycles
In the third lecture, I will describe fast algorithms for finding shortest topoligically interesting cycles, minimum cuts, and other optimal structures in surface graphs. As a key ingredient, I will describe an algorithm for the multiplesource shortest path problem, which asks for an implicit encoding of all shortest path distances where one of the vertices lies on a particular face. 
Surface homotopy
In the fourth lecture, I will return to basic questions about continuous deformation of curves on surfaces. I will describe a modern implementation of an algorithm of Max Dehn, first described in 1916, to decide if one curve on a surface can be continuously deformed into another. I will also sketch an algorithm to find the shortest path homotopic to a given path. 
Untangling curves
In the final lecture, I will return to basic questions about deforming curves in the plane. Any closed curve in the plane can be continuously deformed into a SIMPLE closed curve using a finite sequence of local transformations called homotopy moves. But how many such moves are required? I will describe an algorithm that uses at most O(n^{3/2}) moves, and prove that this bound is optimal in the worst case. I will also discuss extensions of this problem to more complex surfaces, and connections to DeltaY reduction of planar graphs.  Algorithms for Comparing Curves and Surfaces(Introduction and classical algorithms)
 Algorithms for Comparing Curves and Surfaces(Other ways of searching the free space)
 Algorithms for Comparing Curves and Surfaces(Lower Bounds)
 Algorithms for Comparing Curves and Surfaces(Finding a middle curve)
Matias Korman
 Consistent Digital Segments in two dimensions
An introduction to the concept of consistent digital segments and a survey in the known results for the two dimensional case  Consistent Digital Segments in higher dimensions
In this session I will further explore the concept of CDS and discuss the difficulties of higher dimensions  Extremal distances in simple polygons
Introduction to simple polygons, extremal distances (center and diameter), as well as the stateoftheart algorithms for finding center and diameter  Extremal distances in polygonal domains
Extension of the topics of the third talk to polygonal domains and highlight of why such a small change in the environment makes the problem so difficult.  TimeSpace Tradeoff
quick introduction to the model and discussion of last result for computing Voronoi diagrams of high order and its applications to other problems  TimeSpace Tradeoﬀs for Triangulating a Simple Polygon
 TimeSpace Tradeoffs for Computing (High Order) Voronoi Diagrams