Speaker: Stepan Orevkov (Steklov Mathematical Institute of RAS; Paul Sabatier University, Toulouse)
Time: 16:00-17:00 Beijing time (11:00-12:00 Moscow time)
To Join Zoom Meeting: https://us02web.zoom.us/j/84084958194?pwd=b2QxSTVGVzN6NVorc2NJSFQ2TUpCZz09
Meeting ID: 840 8495 8194
Password: 775348
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).
