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The seminar will take place at the
Université de Nantes,
Bâtiment de Mathématiques, salle Eole.
Directions
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| Programme |
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10:30 |
- Lukas Nakamura (Uppsala)
- The size of an overtwisted disk
- Abstract: In this talk, we introduce a notion of size of an overtwisted disk in a strict contact manifold M, which in the case of the standard overtwisted contact form is the action of the simple closed Reeb orbit in the overtwisted disk. In terms of the size, we give an upper bound on the Shelukhin-Chekanov-Hofer distance between Legendrians in the complement of the overtwisted disk and a lower bound on the capacity of a Liouville ball that guarantees that its product with M is overtwisted. This is based on joint work in progress with Á. del Pino Gómez.
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14:00 |
- Yuan Yao (Nantes)
- Products on Fixed point Floer cohomology and closed string mirror symmetry for nodal curves
- Abstract: The fixed point Floer cohomology is a cochain complex generated by the fixed points of a symplectomorphism. It has been computed for all symplectomorphisms on (2 real-dimensional) surfaces, but it enjoys additional algebraic structure coming from a pair of pants "product". We explain the computation of this "product" in the case of iterations of a Dehn twists on a surface. We find surprisingly, it forms a polynomial ring. Via the lens of mirror symmetry, we relate this ring to sections of tensor powers of a degree 1 line bundle on a nodal elliptic curve. Finally, using the product structure, we explain how to define a "quantum cohomology" for nodal Riemann surfaces and compute it. All of this joint work with Maxim Jeffs and Ziwen Zhao.
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15:30 |
- Discussions
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