Real algebraic curves on real algebraic surfaces

14:00 16-02-2014
Colloquium in Mathematics and Computer Science

Real algebraic curves on real algebraic surfaces

Prof. Eugenii Shustin, School of Mathematical Sciences, Tel-Aviv University.

Sunday | February 16 | 14:00 |Science Building 8, Room 424

A simple observation that through any two points in the plane one can draw a line and through any five (generic) points one can draw a conic applies quite efficiently in the Hilbert's 16th problem (isotopy classification of real plane algebraic curves). Generalizing this observation to higher degrees, Rokhlin asked in 70's the following question: given 3D-1 points in the real plane in general position, does there exist a real rational curve of degree D passing through these points? In 2002, the two newly born theories, tropical geometry and Welschinger invariants, came together and provided an affirmative answer to Rokhlin's question. We discuss this exciting result as well as its modern development.

For further information:
Dr. David Garber, Department of Applied Mathematics, Faculty of Sciences,
Holon Institute of Technology
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