Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem

분야Field	Math Colloquium
날짜Date	2019-03-15 ~ 2019-03-15	시간Time	15:50 ~ 18:00
장소Place	Math. Bldg. 404	초청자Host
연사Speaker	Yong-Geun Oh	소속Affiliation	POSTECH
TOPIC	Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem
소개 및 안내사항Content	<1부> Title: Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem Abstract: I will first  explain how the classical remnant of Heisenberg's uncertainly principle is manifested as a nonsqueezing phenomenon in Hamiltonian dynamics.  A precise questioin called Nonsqueezing Conjecture was formulated by Arnold and Gromov in the 1960's. Then I will explain how Gromov invented an analytic framework of (pseudo)holomorphic curves  and proved the conjecture (Gromov's Nonsqueezing Theorem) by combining it with classical isoperimetric inequality, continuation method of elliptic partial differential equation and  Fredholm theory of Banach manifolds. I will also explain ramifications of this development in symplectic topology. <2부> Title: Fukaya category, hyperbolic geometry and knot invariants Abstract: In this lecture, I will explain some symplectic topology and categorical construction of  knot invariants and how special geometry of knot complement such as hyperbolic structure constrains the structure of the invariants. This lecture is based on the joint works with Youngjin Bae and Seonhwa Kim.

학회명Field	Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem
날짜Date	2019-03-15 ~ 2019-03-15	시간Time	15:50 ~ 18:00
장소Place	Math. Bldg. 404	초청자Host
소개 및 안내사항Content	<1부> Title: Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem Abstract: I will first  explain how the classical remnant of Heisenberg's uncertainly principle is manifested as a nonsqueezing phenomenon in Hamiltonian dynamics.  A precise questioin called Nonsqueezing Conjecture was formulated by Arnold and Gromov in the 1960's. Then I will explain how Gromov invented an analytic framework of (pseudo)holomorphic curves  and proved the conjecture (Gromov's Nonsqueezing Theorem) by combining it with classical isoperimetric inequality, continuation method of elliptic partial differential equation and  Fredholm theory of Banach manifolds. I will also explain ramifications of this development in symplectic topology. <2부> Title: Fukaya category, hyperbolic geometry and knot invariants Abstract: In this lecture, I will explain some symplectic topology and categorical construction of  knot invariants and how special geometry of knot complement such as hyperbolic structure constrains the structure of the invariants. This lecture is based on the joint works with Youngjin Bae and Seonhwa Kim.

성명Field	Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem
날짜Date	2019-03-15 ~ 2019-03-15	시간Time	15:50 ~ 18:00
소속Affiliation	POSTECH	초청자Host
소개 및 안내사항Content	<1부> Title: Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem Abstract: I will first  explain how the classical remnant of Heisenberg's uncertainly principle is manifested as a nonsqueezing phenomenon in Hamiltonian dynamics.  A precise questioin called Nonsqueezing Conjecture was formulated by Arnold and Gromov in the 1960's. Then I will explain how Gromov invented an analytic framework of (pseudo)holomorphic curves  and proved the conjecture (Gromov's Nonsqueezing Theorem) by combining it with classical isoperimetric inequality, continuation method of elliptic partial differential equation and  Fredholm theory of Banach manifolds. I will also explain ramifications of this development in symplectic topology. <2부> Title: Fukaya category, hyperbolic geometry and knot invariants Abstract: In this lecture, I will explain some symplectic topology and categorical construction of  knot invariants and how special geometry of knot complement such as hyperbolic structure constrains the structure of the invariants. This lecture is based on the joint works with Youngjin Bae and Seonhwa Kim.

성명Field	Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem
날짜Date	2019-03-15 ~ 2019-03-15	시간Time	15:50 ~ 18:00
호실Host		인원수Affiliation	Yong-Geun Oh
사용목적Affiliation		신청방식Host	POSTECH
소개 및 안내사항Content	<1부> Title: Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem Abstract: I will first  explain how the classical remnant of Heisenberg's uncertainly principle is manifested as a nonsqueezing phenomenon in Hamiltonian dynamics.  A precise questioin called Nonsqueezing Conjecture was formulated by Arnold and Gromov in the 1960's. Then I will explain how Gromov invented an analytic framework of (pseudo)holomorphic curves  and proved the conjecture (Gromov's Nonsqueezing Theorem) by combining it with classical isoperimetric inequality, continuation method of elliptic partial differential equation and  Fredholm theory of Banach manifolds. I will also explain ramifications of this development in symplectic topology. <2부> Title: Fukaya category, hyperbolic geometry and knot invariants Abstract: In this lecture, I will explain some symplectic topology and categorical construction of  knot invariants and how special geometry of knot complement such as hyperbolic structure constrains the structure of the invariants. This lecture is based on the joint works with Youngjin Bae and Seonhwa Kim.