Contact instantons and entanglement of Legendrian links

Contact instantons and entanglement of Legendrian links

5380
https://www.youtube.com/embed/ne87FwWXGQU  + 1056
강연자 오용근
소속 IBS-CGP /POSTECH

We introduce a conformally invariant nonlinear sigma model on the bulk of contact manifolds with boundary condition on the Legendrian links in any odd dimension. We call any finite energy solution a contact instanton. We also explain its Hamiltonian-perturbed equation and establish the Gromov-Floer-Hofer type convergence result for (Hamiltonian-perturbed) contact instantons of finite energy and construct its compactification of the moduli space. Then we explain how we can apply this analytical machinery in the study of contact topology and contact Hamiltonian dynamics. As an example, we explain our proof of a conjecture of Sandon and Shelukhin on the translated points of contactomorphisms on compact contact manifold. This is the contact analog to the Arnold's conjecture type in symplectic geometry.

 

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Now

현재 Contact instantons and entanglement of Legendrian links

강연자 : 오용근 | 소속 : IBS-CGP /POSTECH

We introduce a conformally invariant nonlinear sigma model on the bulk of contact manifolds with boundary condition on the Legendrian links in any odd dimension. We call any finite energy solution a contact instanton. We also explain its Hamiltonian-perturbed equation and establish the Gromov-Floer-Hofer type convergence result for (Hamiltonian-perturbed) contact instantons of finite energy and construct its compactification of the moduli space. Then we explain how we can apply this analytical machinery in the study of contact topology and contact Hamiltonian dynamics. As an example, we explain our proof of a conjecture of Sandon and Shelukhin on the translated points of contactomorphisms on compact contact manifold. This is the contact analog to the Arnold's conjecture type in symplectic geometry.

 

<학부생을 위한 ɛ 강연> Self-Supervised Learning in Computer Vision

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In recent years, artificial intelligence has made remarkable progress in developing algorithms that can learn from vast amounts of carefully labeled data. This paradigm of supervised learning has made great success in training specialist models that perform extremely well on the task they were trained to do, but there’s a limit to building more intelligent, generalized models without a massive amount of labeled data.
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