Seminar za simplektičku topologiju, 16. april 2024.

Naredni sastanak Seminara za simplektičku topologiju biće održan u utorak, 16. aprila 2024, u sali 840 Matematičkog fakulteta sa početkom u 16.15č.

Predavač: Nikolay Turin

Naslov predavanja: SPECIAL BOHR - SOMMERFELD GEOMETRY: TOWARD THE MODULI SPACE

Apstrakt:
As once Yuri Manin said: Mirror Symmetry is a duality between complex and symplectic geometries of Kahler manifolds. But complex geometry is rather rigid: variations of complex submanifolds of a compact Kahler manifold are finite dimensional, the same happens for stable holomorphic vector bundles over algebraic varieties etc. while symplectic geometry is rather flexible.
 
So if one beliefs that in some sense lagrangian submanifolds correspond to vector bundles, sheaves of whatever it should be a way how to derive some finite dimensional moduli spaces with the elements presented by certain lagrangian submanifolds. For the Calabi - Yau case one knows the way: it is called Special Lagrangian geometry, extremely popular subject during last 30 years. But this program can be applied in the case of Calabi - Yau only; one can remember a relative construction presented by D. Auroux for "open Calabi - Yau", but this program was not finished yet.
 
Special Bohr - Sommerfeld geometry is an attempt to construct finite dimensional moduli space for any compact simply connected algebraic variety.
 
Unexpectedly the SBS - story turned out to be related to the theory of Weinstein structures and Eliashberg conjectures. And the most intriguing is the fact that for the known examples these moduli spaces are itself algebraic varieties.


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