Extra Form
Lecturer Raphaël Ponge
Dept. 서울대학교
date Nov 07, 2013
Motivated by the analysis of the singularity of the Bergman kernel of a strictly pseudoconvex domain, Charlie Fefferman launched in the late 70s the program of determining all local biholomorphic invariants of strictly pseudoconvex domain. This program has since evolved to include other geometries such as conformal geometry. Green functions play an important role in conformal geometry at the interface of PDEs and geometry. In this talk, I shall explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Laplacian arising from scattering theory for asymptotically hyperbolic Einstein metrics. The results are formulated in terms of explicit conformal invariants defined by means of the ambient metric of Fefferman-Graham. Although the problems and the final formulas only refer to analysis and geometry, the computations actually involves a lot of representation theory and ultimately boils down to some elaboration on Schur's duality.
Attachment '1'
  1. Hybrid discontinuous Galerkin methods in computational science and engineering

  2. How to solve linear systems in practice

  3. High dimensional nonlinear dynamics

  4. Heavy-tailed large deviations and deep learning's generalization mystery

  5. Hamiltonian dynamics, Floer theory and symplectic topology

  6. Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology

  7. Green’s function for initial-boundary value problem

  8. Global result for multiple positive radial solutions of p-Laplacian system on exterior domain

  9. Geometry, algebra and computation in moduli theory

  10. Geometric structures and representation spaces

  11. Geometric Langlands theory: A bridge between number theory and physics

  12. Generalized multiscale HDG (hybridizable discontinuous Galerkin) methods for flows in highly heterogeneous porous media

  13. Gaussian free field and conformal field theory

  14. From mirror symmetry to enumerative geometry

  15. Freudenthal medal, Klein medal 수상자의 수학교육이론

  16. Free boundary problems arising from mathematical finance

  17. Fixed points of symplectic/Hamiltonian circle actions

  18. Fermat´s last theorem

  19. 08Nov
    by Editor
    in Math Colloquia

    Fefferman's program and Green functions in conformal geometry

  20. Fano manifolds of Calabi-Yau Type

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 Next
/ 12