【学术报告】Real algebraic and real pseudoholomorphic curves

• 主讲人：Stepan Orevkov (Steklov Mathematical Institute of RAS; Paul Sabatier University, Toulouse)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2022-01-21 16:00 - 2022-01-21 17:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/297519F065FD06FE91B6405B19FE9693
Valid Until: 2026-06-30 23:59

 

Abstract: According to Gromov's theory, smooth symplectic 2-surfaces in CP^2 share many properties with complex algebraic curves. The same phenomenon takes place in the real case. Namely, smooth symplectic surfaces invariant under the complex conjugation (we call them real pseudoholomorphic curves) have many common properties with plane projective real algebraic curves.

An open question (Symplectic Isotopy Problem): does each connected component of the space of symplectic surfaces contain an algebraic curve? The same question can be asked in the real case and a negative answer will be given in the talk. We shall prove certain inequalities for the complex orientations of plane real algebraic curves which are not satisfied by an infinite series of real pseudoholomorphic curves.

 

Bio: Stephan Orevkov, PhD (Phys&Math), is a senior researcher at Steklov Mathematical Institute, a lead researcher at MIPT, and also a researcher at Université Toulouse III - Paul Sabatier, France. His academic interests include topology of flat real algebraic curves and surfaces, the theory of braids, complex surface mapping (as applicable to the Jacobian hypothesis).