lgebraic geometry is the study of solutions to systems of polynomial equations. Such sets of solutions (often with additional structure) are usually referred to as algebraic varieties. Combinatorial algebraic geometry is an aspect of algebraic geometry where either combinatorial techniques are used to study algebraic varieties or methods (and analogies) from algebraic geometry are used to study combinatorial objects. Tropical geometry is a branch of algebraic geometry that is based on transforming an algebraic variety into a “polyhedral subset” called its tropicalisation. Tropicalisation has proven to be an efficient technique for dealing with limits of algebraic varieties called degenerations. This is a thriving area with connections to several other areas such as number theory and topics in physics. Real algebraic geometry is a related active area of mathematics that is inspired by Hilbert’s sixteenth and seventeenth problems, and is a fertile ground for rich interactions between alg...
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