Real tropicalization and sums of squares

I am going to introduce tropicalization of semi-algebraic sets and discuss applications in real algebraic geometry. In particular, I’ll focus on (pseudo-)moment cones coming from algebraic certificates of positivity. Tropical geometry can illuminate some classical differences between moments and pseudo-moments from a new perspective. This is based on joint work with Greg Blekherman, Felipe Rincon, Cynthia Vinzant, and Josephine Yu.