PROGRAM
11:00 (GMT+3)
| Stepan Orevkov | Steklov Mathematical Institute of RAS; Paul Sabatier University |
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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). |
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Real algebraic and real pseudoholomorphic curves.
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 an 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.
12:00 (GMT+3)
| Song-Yan Xie | |
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Bio: Song-Yan Xie got his Ph.D. from Paris-Sud (Orsay) University in 2016. In his thesis he proved an ampleness conjecture of Debarre —— the cotangent bundles of a large class of complete intersections are ample. He is currently an associate professor at the Academy of Mathematics and Systems Science. His research interest is complex geometry, especially complex hyperbolicity and Nevanlinna theory. |
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On Ahlfors currents.
We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve which produces infinitely many cohomologically different Ahlfors currents. Moreover, concerning Siu's decomposition, for an arbitrary positive integer k or k=infinity, some of the obtained Ahlfors currents have singular parts supported on k irreducible curves. In addition, they can have nonzero diffuse parts as well, which answers a question of Brunella. This is joint work with Dinh Tuan Huynh.
The meeting will be held in the form of a webinar on the Zoom platform.
Pre-registration for the event is not required.
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https://us02web.zoom.us/j/84084958194?pwd=b2QxSTVGVzN6NVorc2NJSFQ2TUpCZz09
Meeting ID : 840 8495 8194
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