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Extra Form
Lecturer Raphael Ponge
Dept. 서울대학교
date Sep 22, 2011
A general goal of noncommutative geometry (in the sense of A. Connes) is to translate the main tools of differential geometry into the Hilbert space formalism of quantum mechanics by taking advantage of the familiar duality between spaces and algebras. In this setting noncommutative spaces are only represented through noncommutative algebras that play formally the role of algebras of functions on these (ghost) noncommutative spaces.?As?a?result,?this allows us to deal with a variety of geometric problems whose noncommutative nature prevent us from using tools of classical differential geometry. In particular, the Atiyah-Singer index theorem untilmately holds in the setting of noncommutative geometry.
The talk will be an overview of the subject with a special emphasis on quantum space-time and diffeomorphism invariant geometry. In particular, if time is permitted, ?it is planned to allude to recent projects in biholomorphism invariant geometry of complex domains and contactomorphism invariant geometry of contact manifolds.
Atachment
Attachment '1'
  1. Existence of positive solutions for φ-Laplacian systems

  2. Riemann-Hilbert correspondence for irregular holonomic D-modules

  3. Normal form reduction for unconditional well-posedness of canonical dispersive equations

  4. Random conformal geometry of Coulomb gas formalism

  5. Categorification of Donaldson-Thomas invariants

  6. Noncommutative Surfaces

  7. The Shape of Data

  8. Topological Mapping of Point Cloud Data

  9. Structures on Persistence Barcodes and Generalized Persistence

  10. Persistent Homology

  11. Topological aspects in the theory of aperiodic solids and tiling spaces

  12. Subgroups of Mapping Class Groups

  13. Irreducible Plane Curve Singularities

  14. Analytic torsion and mirror symmetry

  15. Fefferman's program and Green functions in conformal geometry

  16. 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

  17. 정년퇴임 기념강연: Volume Conjecture

  18. Queer Lie Superalgebras

  19. Regularization by noise in nonlinear evolution equations

  20. A New Approach to Discrete Logarithm with Auxiliary Inputs

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