This mini-course will cover the basics of tropical algebraic geometry. From this perspective a tropical variety is the tropicalization of a subvariety of an algebraic torus, and many invariants of (compactifications of) the original variety can be computed from the tropical variety. The lectures will focus on the multiple alternate descriptions of a tropical variety (via valuations or Gröbner bases or polyhedral geometry), and the combinatorial constraints on a tropical variety (that it is a balanced weighted polyhedral complex that is connected in codimension-one and pure if the original variety is irreducible). The lectures should be accessible to graduate students and mathematicians coming from other areas.

Lecture #13852

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