https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
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.
Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
Math Colloquia Riemann-Hilbert correspondence for irregular holonomic D-modules file 서울대학교/RIMS Masaki Kashiwara
Math Colloquia Convex and non-convex optimization methods in image processing file Hong Kong Baptist University Michael Ng
Math Colloquia A new view of Fokker-Planck equations in finite and Infinite dimensional spaces file Bielefeld Univ./Purdue Univ. Michael Roeckner
Math Colloquia Unprojection file University of Warwick / 서강대 Miles Reid
Math Colloquia Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
Math Colloquia Connes's Embedding Conjecture and its equivalent file RIMS Narutaka Ozawa
Math Colloquia Recent progress on the Brascamp-Lieb inequality and applications file Saitama University Neal Bez
Math Colloquia Unique ergodicity for foliations file Université Paris-Sud Nessim Sibony
Math Colloquia Idempotents and topologies file University of Waterloo Nico Spronk
Math Colloquia Contact Homology and Constructions of Contact Manifolds file 서울대 Otto van Koert
Math Colloquia <학부생을 위한 ɛ 강연> Symplectic geometry and the three-body problem file 서울대학교 Otto van Koert
Math Colloquia Q-curvature in conformal geometry file 서강대 Pak Tung Ho
Math Colloquia Symmetry Breaking in Quasi-1D Coulomb Systems file 서강대학교 Paul Jung
Math Colloquia It all started with Moser file Univ. of Wisconsin/포항공대 Paul Rabinowitz
Math Colloquia Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry file 서울대학교 Raphael Ponge
Math Colloquia Fefferman's program and Green functions in conformal geometry file 서울대학교 Raphaël Ponge
Math Colloquia Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients file University of Illinois Renming Song
Math Colloquia Green’s function for initial-boundary value problem file National Univ. of Singapore Shih-Hsien Yu
Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 Next
/ 12