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Ilia Itenberg

Ilia Itenberg is a professor at the Université Pierre et Marie Curie (Paris 6), France, and a member of the Institut Universitaire de France. His main fields of interest are Real Algebraic Geometry, topology of algebraic varieties, Symplectic Geometry, Tropical Geometry and Enumerative Geometry. He has authored numerous books, articles, and technical papers on various aspects of mathematics. This includes Tropical Algebraic Geometry, On Total Reality Of Meromorphic Functions, and Mathematical Circles - Russian Experience. The last book was written to encourage students from secondary schools to develop recreational mathematical skills while keeping in line with the Russian tradition of forming mathematics study groups.

 Ilia Itenberg

 

"Tropical geometry and enumeration of curves:"

Tropical geometry can be seen as algebraic geometry based on the so-called tropical numbers. The tropical numbers are the real numbers enhanced with negative infinity and equipped with two arithmetic operations called tropical addition and tropical multiplication. The tropical addition is the operation of taking the maximum. The tropical multiplication is the conventional addition.
These operations are commutative, associative and satisfy the distribution law. It turns out that such tropical algebra describes some meaningful geometric objects, namely, the tropical varieties. For example, tropical curves in the plane are certain rectilinear graphs. We will speak about tropical curves, present several results in tropical geometry (they can be viewed as elementary analogs of certain results in classical algebraic geometry), and then concentrate our attention on applications of tropical geometry in enumerative geometry.