Combinatorial and computational algebra of toric degenerations of varieties

环面变体在代数几何中占有重要地位。在多面体几何和组合几何中，有几种计算环面变量不变量的方法。学生将研究在代数，组合和几何的界面上的环变。最近在代数几何方面有了一个突破，将牛顿-奥孔科夫体理论与热带几何，特别是在这两种情况下产生的环面变化，直接联系起来。学生项目的主要组成部分是应用代数和组合方法来进一步探索这些联系。

Toric varieties play an important role in algebraic geometry. There are several methods developed in polyhedral and combinatorial geometry to compute the invariants of a toric variety.The student will work on toric varieties which are at the interface of algebra, combinatorics and geometry. Recently there has been a breakthrough in algebraic geometry making a direct connection between the theory of Newton-Okounkov bodies and tropical geometry, and in particular the toric varieties arising in both contexts. The main component of the student's project is to apply algebraic and combinatorial methods to further explore such connections.