We study the algebra of Weyl modules in types $A$ and $C$ using methods arcs over toric degenerations functional realization dual space. compute generators relations this construct its basis.

These are notes for a series of five lectures on “Moduli and degenerations of algebraic curves via tropical geometry” delivered at the CIMPA-CIMAT-ICTP School on Moduli of Curves, February 29-March 4, 2016 in Guanajuato, Mexico.

One fundamental question in the context of the geometric complexity theory approach to the VP vs. VNP conjecture is whether VP = VP, where VP is the class of families of polynomials that can be computed by arithmetic circuits of polynomial degree and size, and VP is the class of families of polynomials that can be approximated infinitesimally closely by arithmetic circuits of polynomial degree ...