**Fabrizio Frati**

#### Tuesday, May 15 at 9:00 AM

**Abstract**

In this talk I will survey the state of the art on morphing geometric representations of graphs. Suppose that one is given two topologically-equivalent geometric representations of a graph. Can one representation be continuously transformed into the other one while preserving the graph topology during the transformation? This question has been studied for more than a century and yet answering it completely is still an elusive goal. The study of morphs of graph representations has proved to be intertwined with several areas of mathematics and computer science. I will talk about some of the most natural versions of the above question, related to morphing planar representations, non-planar representations, and three-dimensional representations. I will present the main methodologies currently used in this field, as well as a large number of open problems at various levels of difficulty.