Wednesday, January 16, 18:30, room 306

Alexander Esterov

Lattice polytopes and systems of polynomial equations

The fundamental theorem of algebra states that the number of roots of the univariate polynomial (counted with multiplicities) equals the degree of the polynomial. We shall discuss several generalizations of this fact to systems of polynomial equations of several variables.
The most geometric generalization (the Kouchnirenko theorem) states that, for generic systems of equations, the number of solutions of the system equals the volume of a certain lattice polytope, associated to this system. Motivated by this application, we shall overview geometry of lattice polytopes and briefly discuss the seminar topics for this term.