Pure Maths Colloquium: Diane Maclagan

Tropical geometry is geometry over the tropical semiring, where multiplication is replaced by addition and addition is replaced by minimum. This “tropicalization” procedure turns algebraic varieties (solutions to polynomial equations) into polyhedral complexes, which are combinatorial objects. A surprisingly large amount of information about the variety is still present in tropical “combinatorial shadow”. In this talk I will introduce tropical varieties, and indicate some of their applications, both inside and outside algebraic geometry.