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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

 

"Real Algebraic Curves": The lecture is devoted to the objects that can be described by an algebraic equation f(x, y)=0 in the real plane with Cartesian coordinates x and y (here f is a polynomial in two variables with real coefficients). Examples of such objects are provided by a line (it can be described by a polynomial of degree 1) and an ellipse (it can be described by a polynomial of degree 2). What can be said about curves described by polynomials of higher degrees? In the lecture, we will be mainly interested in topological properties of real algebraic curves.

 

"Tropical Geometry": Tropical geometry is a new mathematical domain which has deep and important relations with many branches of mathematics. It has undergone a spectacular progress during the last ten years. In tropical geometry, algebro-geometric objects are replaced with piecewise-linear ones. For example, tropical curves in the plane are certain rectilinear graphs. We will present basic tropical notions and first results in tropical geometry, as well as applications of tropical geometry in enumerative problems.