GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar

24.01.2022 12:00 – 18:00

Umut Varolgunes. Symplectic degenerations, relative Floer theory and Reynaud models

I will start by explaining the construction of a formal scheme starting with an integral affine manifold Q equipped with a decomposition into convex polytopes. This is a weaker and more elementary version of degenerations of abelian varieties originally constructed by Mumford. Then I will reinterpret this construction using the induced Lagrangian torus fibration X\to Q and the relative Floer theory of its canonical Lagrangian section. Finally, I will discuss a conjectural generalization of the story to symplectic degenerations of CY symplectic manifolds to normal crossing symplectic log CY varieties.

John Alexander Cruz Morales. Towards a Dubrovin conjecture for Frobenius manifolds

In this talk we will report an ongoing work aiming to establish a Dubrovin conjecture for general Frobenius manifolds. Dubrovin conjecture was formulated in 1998 (with a very precise statement in 2018) as a relation between the Frobenius manifold coming from the quantum cohomology of a Fano manifold X and the derived category of coherent sheaves of X. We will give some speculations of how to extend that relation to a one between semisimple Frobenius manifolds and some derived categories We will sketch the situation in a particular example (3-point Ising model) which might be of interest for symplectic geometers.

Lieu

Salle 6-13, Séminaire "GeNeSys"

entrée libre