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Extra Form
강연자 오용근
소속 University of Wisconsin
date 2009-11-26
In this lecture, I will convey subtle interplay between dynamics of Hamiltonian flows and La-grangian intersection theory via the analytic theory of Floer homology in symplectic geometry. I will explain how Floer homology theory (`closed string version') extracts some Morse theoretic invariants, so called `spectral invariants' of Hamiltonian flows which in turn leads to Entov-Polterovich's construction of partial symplectic quasi-states which detect intersection property of certain coisotropic objects. We then relate this study to the study of intersection property of Lagrangian fibers of toric manifolds and its Landau-Ginzburg-type potential carried out by Fukaya, Ohta, Ono and myself via Lagrangian Floer theory (`open string version'). If time permits, I will mention some implication of this study on the simpleness question of the area-preserving homeomorphism group of the two-sphere (and of the two-disc) in dynamical systems.
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첨부 '1'
  1. 행렬함수 Permanent의 극소값 결정과 미해결 문제들

  2. The Mathematics of the Bose Gas and its Condensation

  3. Codimension Three Conjecture

  4. 학부생을 위한 강연: 건축과 수학

  5. Classical and Quantum Probability Theory

  6. Iwasawa main conjecture and p-adic L-functions

  7. 학부생을 위한 강연: Choi's orthogonal Latin Squares is at least 61 years earlier than Euler's

  8. 젊은과학자상 수상기념강연: From particle to kinetic and hydrodynamic descriptions to flocking and synchronization

  9. Sums of squares in quadratic number rings

  10. Fano manifolds of Calabi-Yau Type

  11. 곡선의 정의란 무엇인가?

  12. The significance of dimensions in mathematics

  13. Fermat´s last theorem

  14. It all started with Moser

  15. On some nonlinear elliptic problems

  16. Topology and number theory

  17. Conservation laws and differential geometry

  18. 학부학생을 위한 강연회: 기하학과 우주론

  19. Zeros of linear combinations of zeta functions

  20. Counting circles in Apollonian circle packings and beyond

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