Combinatorial and computational algebra of toric degenerations of varieties

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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.