Torus actions on secant varieties.

I will present a new point of view on the (first) secant varieties of
certain classical toric varieties, focusing on the Segre variety. The
secant variety, although much more complicated than the Segre, turns
out to be \almost toric\. This allows studying the geometric
properties of the secant using combinatorial techniques. The method
that I will present has possible applications to other varieties, like
Grassmannians. The majority of the results are from the joint work
with Luke Oeding and Piotr Zwiernik.