Resumen de Computing toric degenerations of grassmannians and flag varieties arising from tropical geometry
Fatemeh Mohammadi
A toric variety is a certain algebraic variety modeled on a convex polyhedron. Toric varieties play an important role in commutative algebra. I give an overview talk on toric degenerations of flag varieties and Grassmannians arising from tropical geometry and representation theory. I will compare toric degenerations arising from string polytopes with those obtained from tropical cones of flag varieties and will explain how the corresponding toric polytopes can be seen as Newton-Okounkov bodies for the valuations associated to each tropical cone. I will also present the necessary condition to obtain a toric initial ideal of Grassmannian of 3-planes explaining computational challenges around this problem. This is based on joint works with Kristin Shaw and with Lara Bossinger, Sara Lamboglia, and Kalina Mincheva.
