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In this note, I will describe some highlights of Oded Schramm's work in circle packings and the Koebe conjecture, as well as on SLE.
P. Koebe, Ueber die Uniformisierung beliebiger analytischer Kurven (Dritte Mitteilung),
1908
Earlier work this paper cites.
C. Loewner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, I,
1923
Earlier work this paper cites.
P. Koebe, Kontaktprobleme der Konformen Abbildung,
1936
Earlier work this paper cites.
R. Brooks, C. Smith, A. Stone, W. Tutte, The dissection of squares into squares,
1940
Earlier work this paper cites.
R. Courant, B. Manel, M. Shiffman, A general theorem on conformal mapping of multiply connected domains,
1940
Earlier work this paper cites.
P. Kufarev, A remark on integrals of Löwner’s equation,
1947
Earlier work this paper cites.
K. Strebel, Über das Kreisnormierungsproblem der konformen Abbildung,
1951
Earlier work this paper cites.
R. Duffin, The extremal length of a network,
1962
Earlier work this paper cites.
C. Pommerenke, On the Loewner differential equation,
1966
Earlier work this paper cites.
E. Andreev, Convex polyhedra in Lobacevskii space,
1970
Earlier work this paper cites.
E. Andreev, Convex polyhedra of finite volume in Lobacevskii space,
1970
Earlier work this paper cites.
M. Brandt, Ein Abbildungssatz fuer endlich-vielfach zusammenhängende Gebiete,
1980
Earlier work this paper cites.
G. Lawler, A self avoiding walk,
1980
Earlier work this paper cites.
W. Thurston, The geometry and Topology of 3-manifolds, Chap. 13 (Math. Notes, Princeton) Princeton University Press 1980
1980
Earlier work this paper cites.
T. Witten, L. Sander, Diffusion-limited aggregation, a kinetic phenomenon,
1981
Earlier work this paper cites.
A. Harrington, Conformal mappings onto domains with arbitrarily specified boundary shapes, J. Analyse Math. 41 (1982), 39–53
1982
Earlier work this paper cites.
B. Mandelbrot, The beauty of fractals, Freeman 1982
1982
Earlier work this paper cites.
P. Duren, Univalent functions, Springer-Verlag, New York, 1983
1983
Earlier work this paper cites.
B. Rodin, D. Sullivan, The convergence of circle packings to the Riemann mapping,
1987
Earlier work this paper cites.
B. Duplantier, K. Kwon, Conformal invariance and intersection of random walks,
1988
Earlier work this paper cites.
K. Burdzy, Cut points on Brownian paths,
1989
Earlier work this paper cites.
C. de Verdière, Empilements de cercles: Convergence d’une méthode de point fixe,
1989
Earlier work this paper cites.
D. Marshall, C. Sundberg, Harmonic measure and radial projection,
1989
Earlier work this paper cites.
G. Miller, W. Thurston, Separators in two and three dimensions, In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 300309. ACM, Baltimore, 1990
1990
Earlier work this paper cites.
O. Schramm, Combinatorially prescribed packings and applications to conformal and quasiconformal maps, Ph. D. thesis, Princeton (1990)
1990
Earlier work this paper cites.
A. Beardon, K. Stephenson, Circle packings in different geometries,
1991
Earlier work this paper cites.
A. Beardon, K. Stephenson, The Schwarz-Pick lemma for circle packings,
1991
Earlier work this paper cites.
C. de Verdière, Une principe variationnel pour les empilements de cercles,
1991
Earlier work this paper cites.
Z.-X. He, An estimate for hexagonal circle packings,
1991
Earlier work this paper cites.
Z.-X. He, O. Schramm, A hyperbolicity criterion for circle packings, preprint, 1991
1991
Earlier work this paper cites.
R. Pemantle, Choosing a spanning tree for the integer lattice uniformly,
1991
Earlier work this paper cites.
O. Schramm, Rigidity of infinite (circle) packings,
1991
Earlier work this paper cites.
O. Schramm, Existence and uniqueness of packings with specified combinatorics,
1991
Earlier work this paper cites.
J. Cardy, Critical percolation in finite geometries,
1992
Earlier work this paper cites.
C. Pommerenke, Boundary behaviour of conformal maps, Springer Verlag, Berlin Heidelberg 1992
1992
Earlier work this paper cites.
Z.-X. He, B. Rodin, Convergence of circle packings of finite valence to Riemann mappings,
1993
Earlier work this paper cites.
Z.-X. He, O. Schramm, Fixed points, Koebe uniformization and circle packings,
1993
Earlier work this paper cites.
O. Schramm, How to cage an egg,
1993
Earlier work this paper cites.
O. Schramm, Square tilings with prescribed combinatorics,
1993
Earlier work this paper cites.
J. Cannon, The combinatorial Riemann mapping theorem,
1994
Earlier work this paper cites.
J. Cannon, W. Floyd, W. Parry, Squaring rectangles: The finite Riemann mapping theorem,
1994
Earlier work this paper cites.
P. Doyle, Z.-X. He, B. Rodin, Second derivatives of circle packings and conformal mappings,
1994
Earlier work this paper cites.
Z.-X. He, O. Schramm, Rigidity of circle domains whose boundary has
1994
Earlier work this paper cites.
H. Sachs, Coin graphs, polyhedra, and conformal mapping,
1994
Earlier work this paper cites.
Z.-X. He, O. Schramm, Hyperbolic and parabolic packings,
1995
Earlier work this paper cites.
Z.-X. He, O. Schramm, Koebe uniformization for “almost circle domains”,
1995
Cited alongside, same era.
Z.-X. He, O. Schramm, The inverse Riemann mapping theorem for relative circle domains,
1995
Cited alongside, same era.
J. Heinonen, P. Koskela, Definitions of quasiconformality,
1995
Cited alongside, same era.
O. Schramm, Transboundary extremal length,
1995
Cited alongside, same era.
I. Benjamini, O. Schramm, Random walks and harmonic functions on infinite planar graphs using square tilings,
1996
Cited alongside, same era.
I. Benjamini, O. Schramm, Harmonic functions on planar and almost planar graphs and manifolds, via circle packings,
1996
Cited alongside, same era.
I. Gruzberg, L. Kadanoff, The Loewner equation: maps and shapes,
2004
Later among the works it cites.
W. Kager, B. Nienhuis, A Guide to Stochastic Loewner Evolution and its Applications,
2004
Later among the works it cites.
T. Kennedy, Conformal invariance and stochastic Loewner evolution predictions for the 2D self-avoiding walk–Monte Carlo tests,
2004
Later among the works it cites.
G. Lawler, O. Schramm, W. Werner, Conformal invariance of planar loop-erased random walks and uniform spanning trees,
2004
Later among the works it cites.
G. Lawler, O. Schramm, W. Werner, On the scaling limit of planar self-avoiding walk,
2004
Later among the works it cites.
G. Lawler, W. Werner, The Brownian loop soup,
2004
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Z.-X. He, O. Schramm, On the convergence of circle packings to the Riemann map,
1996
Cited alongside, same era.
O. Schramm, Conformal uniformization and packings,
1996
Cited alongside, same era.
K. Stephenson, A probabilistic proof of Thurston’s conjecture on circle packings,
1996
Cited alongside, same era.
C. Bishop, P. Jones, R. Pemantle, Y. Peres, The dimension of the Brownian frontier is greater than 1,
1997
Cited alongside, same era.
Z.-X. He, O. Schramm, On the distortion of relative circle domain isomorphisms,
1997
Cited alongside, same era.
R. Lyons, A bird’s-eye view of uniform spanning trees and forests, Microsurveys in discrete probability (Princeton, NJ, 1997), 135–162
1997
Cited alongside, same era.
Later among the works it cites.
W. Werner, Random planar curves and Schramm-Loewner evolutions,
2004
Later among the works it cites.
D. Zhan, Loewner evolution in doubly connected domains,
2004
Later among the works it cites.
M. Bauer, D. Bernard, J. Houdayer, Dipolar stochastic Loewner evolutions,
2005
Later among the works it cites.
J. Cardy, SLE for theoretical physicists,
2005
Later among the works it cites.
J. Garnett, D. Marshall, Harmonic measure, Cambridge University Press, New York, 2005
2005
Later among the works it cites.
G. Lawler, Conformally Invariant Processes in the Plane,
2005
Later among the works it cites.
D. Marshall, S. Rohde, The Loewner differential equation and slit mappings,
2005
Later among the works it cites.
S. Rohde, O. Schramm, Basic properties of SLE,
2005
Later among the works it cites.
O. Schramm, S. Sheffield, Harmonic explorer and its convergence to
2005
Later among the works it cites.
O. Schramm, D. Wilson, SLE coordinate changes,
2005
Later among the works it cites.
K. Stephenson, Introduction to circle packing. The theory of discrete analytic functions, Cambridge University Press, Cambridge, 2005
2005
Later among the works it cites.
W. Werner, Conformal restriction and related questions,
2005
Later among the works it cites.
M. Bauer, D. Bernard, 2D growth processes: SLE and Loewner chains,
2006
Later among the works it cites.
A. Bobenko, T. Hoffmann, B. Springborn, Minimal surfaces from circle patterns: geometry from combinatorics,
2006
Later among the works it cites.
M. Bonk, Quasiconformal geometry of fractals, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Z”urich (2006), 1349–1373
2006
Later among the works it cites.
J. Dubedat, Excursion decompositions for SLE and Watts crossing formula,
2006
Later among the works it cites.
F. Camia, C. Newman, Critical percolation exploration path and
2007
Later among the works it cites.
J. Le Gall, The topological structure of scaling limits of large planar maps,
2007
Later among the works it cites.
O. Schramm, Conformally invariant scaling limits: an overview and a collection of problems. In
2007
Later among the works it cites.
S. Sheffield, Gaussian free fields for mathematicians,
2007
Later among the works it cites.
S. Smirnov, Towards conformal invariance of 2D lattice models, In
2007
Later among the works it cites.
T. Alberts, S. Sheffield, Hausdorff Dimension of the SLE curve intersected with the real line,
2008
Later among the works it cites.
R. Bauer, R. Friedrich, Chordal and bilateral SLE in multiply connected domains,
2008
Later among the works it cites.
V. Beffara, The dimension of the SLE curves,
2008
Later among the works it cites.
J. Le Gall, F. Paulin, Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere,
2008
Later among the works it cites.
R. Rhodes, V. Vargas, KPZ formula for log-infinitely divisible multifractal random measures, 2008, arXiv:math.PR/0807.1036
2008
Later among the works it cites.
W. Werner, The conformally invariant measure on self-avoiding loops,
2008
Later among the works it cites.
D. Zhan, Reversibility of chordal SLE,
2008
Later among the works it cites.
D. Zhan, Duality of chordal SLE,
2008
Later among the works it cites.
I. Benjamini, O. Schramm, KPZ in one dimensional random geometry of multiplicative cascades,
2009
Later among the works it cites.
J. Dubedat, Duality of Schramm-Loewner Evolutions,
2009
Later among the works it cites.
J. Dubedat, SLE and the free field: partition functions and couplings,
2009
Later among the works it cites.
P. Nolin, W. Werner, Asymmetry of near-critical percolation interfaces,
2009
Later among the works it cites.
O. Schramm, S. Sheffield, Contour lines of the two-dimensional discrete Gaussian free field,
2009
Later among the works it cites.
O. Schramm, S. Sheffield, D. Wilson, Conformal radii for conformal loop ensembles,
2009
Later among the works it cites.
S. Sheffield, Exploration trees and conformal loop ensembles,
2009
Later among the works it cites.
O. Schramm, S. Sheffield, A contour line of the continuum Gaussian free field, preprint (2010)
2010
Closest in time.
O. Schramm, W. Zhou, Boundary proximity of SLE,
2010
Closest in time.