Geometry and Topology Seminar

This seminar discusses geometry and topology in a broad sense including (but not exclusively) Riemannian geometry, low dimensional topology and geometry, and geometric group theory.

Details

On the structure of conformally covariant powers of the Laplacian

by Andreas Juhl | Humboldt University, Berlin
Time: 16:10  (Monday, Apr. 18, 2011)
Location: HU1018, 215 Huron St
Abstract:
It is well-known that in two dimensions the Laplace-Beltrami operator is conformally covariant. The Yamabe operator extends this fact to higher dimensions. It arises by correcting the Laplacian by a multiple of scalar curvature. More generally, one can also correct powers of the Laplacian as to obtain conformally covariant operators. Such operators were constructed by Graham, Jenne, Mason and Sparling using the Fefferman-Graham ambient metric construction. In recent years, these GJMS-operators have found central interest in conformal geometry (in particular, through their relation to Branson's Q-curvature). However, the structure of the lower order correction terms is notoriously complicated. In the lecture we describe how one can resolve that structure in an esthetically appealing way.

Dates in this series

· Monday, Mar. 08, 2010: The fundamental group of random 2-complexes (Matthew Kahle)
· Monday, Mar. 15, 2010: Three Dimensional Manifolds All of Whose Geodesics Are Closed (John Olsen)
· Monday, Mar. 22, 2010: Curves on surfaces with large topology (Hugo Parlier)
· Friday, Mar. 26, 2010: New invariants in singularity theory (Rustam Sadykov)
· Friday, Mar. 26, 2010: The hidden smoothness of the space of stable maps (Jonathan Wise)
· Monday, Apr. 05, 2010: Moduli spaces of conics in curves (Chris Judge)
· Monday, Sep. 20, 2010: Total Q-curvature for CR manifolds (Kengo Hirachi)
· Monday, Sep. 27, 2010: Group completions of moduli spaces (Rustam Sadykov)
· Tuesday, Oct. 12, 2010: Pontryagin invariants and integral formulas for Milnor's triple linking number (Herman Gluck)
· Monday, Oct. 18, 2010: Positively curved polar manifolds (Fuquan Fang)
· Monday, Nov. 01, 2010: Rational formality and special holonomy (Manuel Amann)
· Monday, Nov. 08, 2010: Isoperimetric Inequalities -- methods and applications (Emanuel Milman)
· Monday, Nov. 15, 2010: From the sandwich to the waist (Alfredo Hubard)
· Monday, Nov. 29, 2010: TBA (Keith Burns)
· Monday, Nov. 29, 2010: Conjugate points and non-injectivity of the exponential map (Keith Burns)
· Monday, Jan. 17, 2011: Loop products and resonance for loop homology on spheres (Nancy Hingston)
· Monday, Jan. 31, 2011: A Variational Characterization of the Catenoid (Jacob Bernstein)
· Monday, Apr. 18, 2011: On the structure of conformally covariant powers of the Laplacian (Andreas Juhl)
· Monday, May. 09, 2011: Causality, Low conjecture and globally hyperbolic spacetimes (Vladimir Chernov)
· Monday, Sep. 26, 2011: Mapping degrees of self-maps of simply-connected manifolds (Manuel Amann)
· Monday, Oct. 17, 2011: Formality of Positive Quaternion Kähler manifolds (Vitali Kapovitch)
· Friday, Oct. 21, 2011: Kahler-Einstein metrics singular along a divisor (Yanir Rubinstein)
· Monday, Oct. 24, 2011: Diastolic inequality on a 2-sphere (Yevgeny Liokumovich)
· Monday, Nov. 14, 2011: TBA (Ian Hambleton)
· Monday, Nov. 14, 2011: Coarse geometry and group actions (Ian Hambleton)
· Monday, Nov. 21, 2011: Fundamental groups of manifolds with lower Ricci curvature bounds (Vitali Kapovitch)
· Monday, Nov. 28, 2011: Fundamental groups of manifolds with lower Ricci curvature bounds II (Vitali Kapovitch)
· Tuesday, Nov. 29, 2011: Asymptotic geometry, finite generation of fundamental groups, and harmonic functions (Bruce Kleiner)
· Friday, Dec. 09, 2011: Topological Complexity and H-Spaces (Gregory Lupton)
· Tuesday, Jan. 24, 2012: A new construction of compact $G_2$ manifolds by glueing families of Eguchi-Hanson spaces (Spiro Karigiannis)
· Thursday, Jan. 26, 2012: Coarse Differentiation and the rank of Teichmüller space (Kasra Rafi)
· Thursday, Feb. 16, 2012: Manifolds and spaces with Ricci curvature bounds (Toby Colding)
· Monday, Feb. 27, 2012: Homological and homotopical filling functions (Robert Young)
· Monday, Mar. 12, 2012: Algorithmic decidability of Thurston equivalence and geometrization of branched coverings (Michael Yampolsky)
· Monday, Mar. 26, 2012: On some problems in the geometry of surfaces in normed spaces (Dmitri Burago)
· Monday, Apr. 02, 2012: CANCELLED -- Scattering rigidity with trapped geodesics; the two dimensional case (Chris Croke)
· Monday, Sep. 10, 2012: Realisation and dismantlability (Piotr Przytycki)
· Friday, Oct. 05, 2012: The metric completion of Outer Space (Yael Algom Kfir)
· Monday, Oct. 15, 2012: Complexes which require large filling distortion in Euclidean space (Dominic Dotterrer)
· Tuesday, Nov. 06, 2012: A theorem of existence for Asymptotically Conical Calabi-Yau manifolds (Ronan Conlon)
· Monday, Nov. 19, 2012: Ricci Solitons of Cohomogeneity One (McKenzie Wang)
· Monday, Nov. 26, 2012: Complete affine 3-manifolds, Lorentzian and hyperbolic geometry (Bill Goldman)
· Monday, Dec. 03, 2012: Hyperbolic Group Boundaries and Cannon-Thurston Maps (Owen Baker)