https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
강연자 Raphaël Ponge
소속 서울대학교
date 2013-11-07
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.
Atachment
첨부 '1'
  1. Recent progress on the Brascamp-Lieb inequality and applications

    In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...
    Category수학강연회 소속Saitama University 강연자Neal Bez
    Read More
  2. Existence of positive solutions for φ-Laplacian systems

    SNU-LeeAbstract.pdf
    Category수학강연회 소속이용훈 강연자수학강연회,특별강연,대중강연
    Read More
  3. Riemann-Hilbert correspondence for irregular holonomic D-modules

    The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...
    Category수학강연회 소속서울대학교/RIMS 강연자Masaki Kashiwara
    Read More
  4. Normal form reduction for unconditional well-posedness of canonical dispersive equations

    Normal form method is a classical ODE technique begun by H. Poincare. Via a suitable transformation one reduce a differential equation to a simpler form, where most of nonresonant terms are cancelled. In this talk, I begin to explain the not...
    Category수학강연회 소속KAIST 강연자권순식
    Read More
  5. Random conformal geometry of Coulomb gas formalism

    Several cluster interfaces in 2D critical lattice models have been proven to have conformally invariant scaling limits, which are described by SLE(Schramm-Loewner evolution) process, a family of random fractal curves. As the remarkable achie...
    Category수학강연회 소속서울대학교 강연자강남규
    Read More
  6. Categorification of Donaldson-Thomas invariants

    In 1980s, Donaldson discovered his famous invariant of 4-manifolds which was subsequently proved to be an integral on the moduli space of semistable sheaves when the 4-manifold is an algebraic surface. In 1994, the Seiberg-Witten invariant w...
    Category수학강연회 소속서울대학교 강연자김영훈
    Read More
  7. Noncommutative Surfaces

    Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...
    Category수학강연회 소속서강대학교 강연자Jens Hoppe
    Read More
  8. The Shape of Data

    Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...
    Category수학강연회 소속Stanford University 강연자Gunnar E. Carlsson
    Read More
  9. Topological Mapping of Point Cloud Data

    One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes ...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
    Read More
  10. Structures on Persistence Barcodes and Generalized Persistence

    Persistent homology produces invariants which take the form of barcodes, or nite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
    Read More
  11. Persistent Homology

    Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...
    Category특별강연 소속Stanford University 강연자Gunnar E. Carlsson
    Read More
  12. Topological aspects in the theory of aperiodic solids and tiling spaces

    After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...
    Category수학강연회 소속Georgia Institute of Technology, School of Mathematics and School of Physics 강연자Jean V. Bellissard
    Read More
  13. Subgroups of Mapping Class Groups

    The mapping class group of a surface S is the component group of orientation-preserving homeomorphisms on S. We survey geometric and algebraic aspects of this group, and introduce a technique of using right-angled Artin groups to find geomet...
    Category수학강연회 소속서울대학교 강연자김상현
    Read More
  14. Irreducible Plane Curve Singularities

    It is very interesting to study what problems can be computed in irreducible plane curve singularities in algebraicgeometry? Then, the aim of this talk is to compute the explicit algorithm for finding the correspondence between the family of...
    Category특별강연 소속서울대학교 강연자강정혁
    Read More
  15. Analytic torsion and mirror symmetry

    In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...
    Category수학강연회 소속Kyoto University 강연자Ken-ichi Yoshikawa
    Read More
  16. Fefferman's program and Green functions in conformal geometry

    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. T...
    Category수학강연회 소속서울대학교 강연자Raphaël Ponge
    Read More
  17. 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

    Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4...
    Category특별강연 소속서울대학교 강연자박종일
    Read More
  18. 정년퇴임 기념강연: Volume Conjecture

    Volume conjecture를 설명하고 현재까지의 연구결과 그리고 앞으로의 연구계획을 소개한다.
    Category수학강연회 소속서울대학교 강연자김혁
    Read More
  19. Queer Lie Superalgebras

    The Lie superalgebra q(n) is the second super-analogue of the general Lie algebra gl(n). Due to its complicated structure, q(n) is usually called “the queer superalgebra”. In this talk we will discuss certain old and new results related to t...
    Category특별강연 소속Univ. of Texas, Arlington 강연자Dimitar Grantcharov
    Read More
  20. Regularization by noise in nonlinear evolution equations

    There are some phenomena called "regularization by noise" in nonlinear evolution equations. This means that if you add a noise to the system, the system would have a better property than without noise. As one of examples, I will explain this...
    Category특별강연 소속Dep. Math., Kyoto Univ. 강연자Yoshio Tsutsumi
    Read More
Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Next
/ 15