**Jan 17, 2017, 4pm**

PDL C-401

**Amy Wiebe, ***Department of **Mathematics, University of Washington*

*Abstract:* In this talk we present a recent result of Hamza Fawzi which answers the question of whether it is possible to express the general positive semidefinite cone using second-order cones. The result shows that the 3 x 3 positive semidefinite cone S^3_+ does not admit a second-order cone representation. The proof relies on the method of Gouveia, Parrilo and Thomas which shows that existence of cone lifts of convex sets is equivalent to a certain factorization of the slack operator of the set. We explain how this framework is used in the paper to show that S^3_+ has no finite second order cone lift.