Lecturer:
Stefano Urbinati (University of Udine)

Board Contact:
Stefano Urbinati

Tropical geometry is algebraic geometry over the min-plus algebra. This young subject has both established itself as an area of its own right and unveiled its deep connections to numerous branches of pure and applied mathematics. One passes from algebraic geometry to combinatorics, by replacing algebraic varieties over a valued field with polyhedral complexes. This process retains much information about the original varieties. This course offers a systematic introduction to this subject.

Plan:

• Definition of Tropical Geometry
• Basic Concepts of Algebraic Geometry
• Introduction to Tropical Numbers
• Tropical Monomials and Affine Integral Geometry
• Amoebas of Affine Algebraic Varieties and Their Limits
• Introduction to Polyhedral Geometry
• The Balance Condition
• Tropical Plane Curves
• Tropical Toric Varieties
• Tropical Projective Space and Projective Hypersurfaces
• Tropical Cycles, Subspaces and Stable Intersection
• Applications and Examples