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Copyright © 2011 Claremont Center for the Mathematical Sciences

**Claremont Mathematics Weekend**

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*Sponsored by Claremont Colleges*

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**January 30 - 31, 2016**

**Speaker:** **Erica Flapan****Title:** Spatial Graph Theory **Abstract:**

Spatial graph theory, which is the study of embeddings of graphs in R^3 and other 3-manifolds, grew out of the study of non-rigid molecules. However, because it considers embeddings of 1-dimensional objects in 3-dimensional manifolds, the field is also closely related to knot theory and low dimensional topology. However, in contrast with knots, the intrinsic structure of a graph can play a key role in determining the topological properties of its embeddings. For example, there are graphs which have the property that all of their embeddings in R^3 contain a non-trivial knot or link, and other graphs which have the property that no embedding of them in R^3 is invariant under an orientation reversing homeomorphism of R^3. This talk will present a survey of some of the open problems in spatial graph theory and its applications.