Abstract: The Goursat structures are non-integrable 2-plane fields which are "completely non-integrable". When the manifold is 3-dimensional, it is a contact structure. When the manifold is 4-dimensional, it is an Engel structure. From the view point of Goursat surgeries, I will explain some operation on Engel manifolds.
Abstract: An explicit contactomorphism between two standard contact structures on the cosphere bundle of the 2-d plane will be given.
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Abstract: A Lefschetz–Bott fibration on a symplectic manifold is a smooth map to a surface with only Lefschetz–Bott critical points, which are modeled on Morse–Bott critical points. As Lefschetz fibrations have played an important role in the study of Stein fillings of contact manifolds, we expect Lefschetz–Bott fibrations to help us understand symplectic fillings of contact manifolds. In this talk, I will explain a relationship between Lefschetz-Bott fibrations and strong symplectic fillings of contact manifolds. Moreover, by using this, I will provide some examples of strong symplectic fillings of links of isolated singularities.
Abstract: In this talk, I examine an asymptotic behavior of Vianna's infinite family of monotone Lagrangian tori $T_{a,b,c}$ in $\CP^2$ associated to Markov triples $(a,b,c)$. I will show that there exists a uniform lower bound independent of $(a, b, c)$ for the Gromov capacity of the complement of the tori for all Markov triple $(a,b,c)$. I will also provide some estimate of the lower bound. This is based on a joint work with my student Wonmo Lee in POSTECH.
Abstract: In this talk I will give an overview of some aspects of Hamiltonian dynamics on contact type hypersurfaces. The focus will mostly be on existence and non-existence of open books, and bifurcations of periodic orbits. I will also discuss some open problems from symplectic dynamics.
Abstract: I will give new examples of closed non-orientable Lagrangian submanifolds in the standard symplectic 6-space. These Lagrangians are constructed by concatenating a Lagrangian filling and a Lagrangian cap. The existence of a Lagrangian cap is a consequence of Eliashberg-Murphy's h-principle. The main part of the proof is to construct a Lagrangian filling of a loose Legendrian torus in the standard contact 5-space.