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Geometry and Quantization, Travaux Mathematiques 19 (2011) Dedicated to the Lectures of the school Geoquant 2009, September 2009 at the University of Luxembourg.

[1] Martin Schlichenmaier: Almost-graded central extensions of Lax operator algebras.

[2] Fernando Pérez-Conzález, Jouni Rättyä, Jari Taskinen: Lipschitz continuous and compact composition operators in hyperbolic classes.

[3] Irina Markina and Alexander Vasiliev: Evolution of smooth shapes and integrable systems.

[4] A. Blokh, D. Childers, G. Levin, L. Oversteegen, and D. Schleicher: An extended Fatou-Shishikura inequality and wandering branch continua for polynomials.

[5] Markus Müller and Dierk Schleicher: How to add a noninteger number of terms: from axioms to new identities.

[6] D. Dudko and Dierk Schleicher: Homeomorphisms between limbs of the Mandelbrot set.

[7] B. Bollobás, M. Lackmann and Dierk Schleicher: A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton's method.

[8] Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk: Loewner theory in annulus I: evolution families and differential equations.

[9] Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk: Loewner theory in annulus II: Loewner chains.

[10] Björn Gustafsson and Vladimir G. Tkachev: On the exponential transform of multi-sheeted algebraic domains.

[11] Mark Elin and David Shoikhet: Boundary behavior and rigidity of semigroups of holomorphic mappings.

[12] Dierk Schleicher: On the efficient global dynamics of Newton's method for complex polynomials.

[13] Philipp Meerkamp and Dierk Schleicher: Hausdorff dimension and biaccessibility for polynomial Julia sets.

[14] Stephen J. Gardiner: Coincidence of harmonic and finely harmonic functions.

[15] Martin Schlichenmaier: An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module.

[16] Erlend Grong, Irina Markina and Alexander Vasiliev: Sub-Riemannian structures corresponding to Kählerian metrics on the universal Teichmueller space and curve.

[17] Erlend Grong, Irina Markina and Alexander Vasiliev: Sub-Riemannian geometry on infinite-dimenasional manifolds.

[18] Georgy Ivanov and Alexander Vasiliev: Loewner evolution driven by a stochastic boundary point.

[19] Björn Gustafsson and Yu-Lin Lin: On the dynamics of roots and poles for solutions of the Polubarinova-Galin equation.

[20] Björn Gustafsson and Makoto Sakai: On the curvature of some free boundaries in higher dimensions.


[1] Stephen J. Gardiner and Marius Ghergu: Champagne subregions of the unit ball with unavoidable bubbles.

[2] Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk: Geometry behind chordal Loewner chains.

[3] Manuel D. Contreras, Chiara de Fabritiis, Santiago Díaz-Madrigal: Semigroups of holomorphic functions in the polydisk.

[4] Alexander Borichev, Mikhail Sodin: Weighted exponential approximation and non-classical orthogonal spectral measures.- arXiv: 1004.1795v1.

[5] F. Le Roux, A. G. O’Farrell, M. Roginskaya and I. Short: Flowability of plane homeomorphisms.

[6] Pamela Gorkin and Anthony G. O’Farrell: Pervasive algebras and maximal subalgebras.

[7] Marius Ghergu: Lane-Emden systems with negative exponents, J. Functional Analyis 258(2010) 3295-3318.

[8] Stephen J. Gardiner: Sets of determination for the Nevanlinna class.

[9] Jürgen Grahl and Shahar Nevo: On a result of Singh and Singh concerning shared values and normality.

[10] Daniel Alpay, Olga Timoshenko, Prasad Vegulla and Dan Volok: Generalized Schur functions and felated de Branges-Rovnyak fpaces in the Banach space setting.

[11] Uri Srebro and Eduard Yakubov: µ-homeomorphisms with a prescribed singular set.

[12] Shahar Nevo and Lawrence Zalcman: Completely irreducible sequences of meromorphic functions.

[13] Jürgen Grahl and Shahar Nevo: Differential polynomials and shared values.

[14] Mark L. Agranovsky: Holomorphic extension from the unit sphere in C^n into complex lines passing through a finite set.

[15] Mark L. Agranovsky: Characterization of polyanalytic functions by meromorphic extensions into chains of circles.

[16] M.Agranovsky, D.Khavinson, and H.S.Shapiro: Malmheden's theorem revisited.

[17] Mark Elin, Dmitry Khavinson, Simeon Reich, David Shoikhet: Linearization models for parabolic dynamical systems via Abel’s functional equation.

[18] Mark Elin, David Shoikhet and Nikolay Tarkhanov: Separation of boundary singularities for holomorphic generators.

[19] Anna Korolko, Irina Markina: Nonholonomic semi-Riemannian geometry.

[20] Mauricio Godoy Molina, Irina Markina: Sub-Riemannian geodesics and heat operator on odd dimensional spheres.

[21] Anna Korolko, Irina Markina: Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation.

[22] Mauricio Godoy Molina, Erlend Grong, Irina Markina, Fátima Silva Leite: Intrinsic rolling of manifolds.

[23] Mauricio Godoy Molina, Erlend Grong, Irina Markina, Fátima Silva Leite: An intrinsic formulation rolling of the manifolds problem.

[24] Zoltan M. Balogh, Roberto Monti, Jeremy T. Tyson: Frequency of Sobolev and quasiconformal dimension distortion.

[25] Zoltan M. Balogh, Cornel Pintea, Heiner Rohner: Size of tangencies to non-involutive distributions.

[26] Zoltan M. Balogh, Katrin Fässler, Ioannis D. Platis: Modulus of curve families and extremality of spiral-stretch maps.


[1] Filippo Bracci, Mark Elin, and David Shoikhet: Normal forms and linearization of holomorphic dilation type semigroups in several variables.

[2] Björn Gustafsson and Vladimir Tkachev: On the Jacobian of the harmonic moment map.

[3] Björn Gustafsson, Mihai Putinar, Edward B. Saff, and Nikos Stylianopoulos: Begman polynomials on an archipelago: estimates, zeros and shape reconstruction.

[4] Manuela Basallote, Manuel D. Contreras, Carmen Hernándes-Mancera: Commuting finite Blaschke products with no fixed points in the unit disk.

[5] Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal: Evolution families and the Loewner equation II: complex hyperbolic manifolds.

[6] Manuel D. Contreras, Santiago Díaz-Madrigal, Pavel Gumenyuk: Loewner chains in the unit disk.

[7] Zoltán M. Balogh, Katrin Fässler, Kirsi Peltonen: Uniformly quasiregular maps on the compactified Heisenberg group.

[8]  Zoltán M. Balogh, Alexandre Engoulatov, Lars Hunziker, Outi Elina Maasalo: Functional inequalities and Hamilton-Jacobi equations in geodesic spaces.

[9] Irina Markina, Alexander Vasil'ev: Conformal field theory and Loewner-Kufarev evolution.

[10] Anna Korolko, Irina Markina: Semi-Riemannian geometry with non-holonomic constraints.

[11] Mauricio Godoy Molina, Irina Markina: Sub-Riemannian geometry of parallelizable spheres.

[12] José San Martín, Anthony O'Farrell: A controllability criterion for switched linear systems, ArXiv: 0905.0650 [math.OC], 2009.

[13] Anthony O'Farrell, Maria Roginskaya: Conjugacy of real diffeomorphisms. A survey.

[14] Nick Gill, Anthony O'Farrell, Ian Short: Reversibility in the group of homeomorphisms of the circle.

[15] Mark Elin, Dmitry Khavinson, Simeon Reich, David Shoikhet: Linearization models for paraboloc dinamical systems via Abel's functional equation.

[16] Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal: Semigroups versus evolution families in the Loewner theory. ArXiv: 0907.4324 [math.CV], 2009.

[17] Rubén A. Hidalgo, Mauricio Godoy: Navier-Stokes equations on graphs.

[18] Stephen J. Gardiner and Tomas Sjödin: Potential theory in Denjoy domains.

[19] Zoltan M. Balogh, Reto Berger, Roberto Monti, and Jeremy T. Tyson: Exceptional sets for self-similar fractals in Carnot groups.

[20] Stephen J. Gardiner: Potential theory in the exterior of a cylindrical set.

[21] Stephen J. Gardiner: Finely continuously differentiable functions.

[22] Stephen J. Gardiner and Tomas Sjödin: Partial balayage and the exterior inverse problem of potential theory.

[23] Marius Ghergu and Joanna Pres: Positive harmonic functions that vanish on a subset of a cylindrical surface.

[24] Erlend Grong and Alexander Vasil'ev: Sub-Riemannian and sub-Lorentzian geometry on SU(1,1) and on its universal cover. arXiv: 0910.0945 [math.DG], 39 pp.

[25] Tiziano Casavecchia and Santiago Díaz-Madrigal: Non-autonomous version of the Denjoy-Wolff theorem, 26 pp.


[1] Walter Bergweiler, Alastair Fletcher, Janis Meyer and Jim Langley: The escaping set of a quasiregular mapping.

[2] D.-Ch. Chang, I. Markina, A.Vasil'ev: Sub-Lorentzian geometry on anti-de Sitter space.-J. Math. Pures Appl. (to appear) arXiv: 0708.0879v1 [math.DG], 2007, 31 pp.

[3] I.Markina, A.Vasil'ev: Virasoro algebra in Loewner-Kufarev contour dynamics.- arXiv: 0801.2334v2 [math-ph], 2008, 23 pp.

[4] D.-Ch. Chang, I. Markina, A.Vasil'ev: Sub-Riemannian geodesics on the 3-D sphere.- Compl. Anal. Oper. Theory (2008) (to appear); arXiv: 0804.1695v2 [math.DG], 13 pp.

[5] A. Vasil'ev: From the Hele-Shaw Experiment to Integrable Systems: A Historical Overview.

[6] K. Gröchenig, G. Kutyniok, K. Seip: Landau's necessary density conditions for LCA groups.

[7] Yu.Lyubarskii, W.R.Madych: Irregular Poisson type  summation.-Sampling Theory in Signal and Image Processing, 7(2008), no.2, 173-186.

[8] Z.Balogh, J.T.Tyson, B.Warhurst: Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups.

[9] Z.Balogh, K.Fässler: Rectifiability and Lipschitz extensions into the Heisenberg group.

[10] K.Gröchenig, Yu.Lyubarskii: Gabor (super)frames with Hermite functions.

[11] D.-Ch. Chang, I. Markina, A.Vasil'ev: Modified action and differential operators on the 3-D sub-Riemannian sphere.

[13] P.Galanopulos, D.Girela, J.A.Peláez: Multipliers and integration operators on Dirichlet spaces.

[14] E.Grong, P.Gumenyuk, A.Vasil'ev: Matching univalent functions and conformal welding.

[15] D.Prokhorov, A.Vasil'ev: Singular solutions to the Loewner equation.

[16] G.Ascensi, Yu.Lyubarskii, K.Seip: Phase space distribution of Gabor expansions.

[17] F.Bracci, M.D.Contreras, S.Díaz-Madrigal: Evolution families and the Loewner equation I: the unit disk.

[18] F.Bracci, M.D.Contreras, S.Díaz-Madrigal: Evolution families and the Loewner equation II: complex hyperbolic manifolds.

[19] Walter Bergweiler, Alexandre Eremenko, Meromorphic functions with linearly distributedvalues and Julia sets of rational functions, arXiv:0808.3800

[20] Walter Bergweiler, Boguslawa Karpinska, Gwyneth M. Stallard, The growth rate of an entire function and the Hausdorff dimension of its Julia set, arXiv:0807.2363

[21] Zheng Jian-Hua,  Dynamics of hyperbolic meromorphic functions.

[22] Patrick Ahern, Anthony G. O’Farrell, Reversible Biholomorphic Germs.

[23] Anna Korolko, Irina Markina: Nonholonomic Lorentzian geometry on some H groups. arXiv:0809.4450.
[24] Bastian Laubner, Dierk Schleicher and Vlad Vicol: A combinatorial classification of postsingularly finite complex exponential maps, Discrete and Continuous Dynam. Sys. 22 (2008), no. 3.

[25] Markus Förster and Dierk Schleicher: Parameter rays in the space of exponential maps, Ergod. Th. & Dynam. Sys. (2008)

[26] John Hubbard, Dierk Schleicher and Mitsuhiro Shishikura: Exponential Thurston maps and limits of quadratic differentials, J. Amer. Math. Soc.

[27] Dierk Schleicher: Hausdorff dimension, its properties, and its surprises.

[28] Johannes Rückert and Dierk Schleicher: On Newton's method for entire functions, J. London Math. Soc. (2) 75 (2007) 659–676.

[29] Dierk Schleicher: Newton’s method as a dynamical system: efficient root finding of polynomials and the Riemann ζ function, Fields Institute Communications Volume 53, 2008.

[30] Günter Rottenfusser, Johannes Rückert, Lasse Rempe and Dierk Schleicher: Dynamic rays of bounded-type entire functions, ArXiv 0704.3213 [math.DS]

[31] Henk Bruin and Dierk Schleicher: Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials, Journal of the London Mathematical Society.

[32] Anthony G. O'Farrell and Ian Short: Reversibility in the diffeomorphism group of the real line.


[1] D.Prokhorov, A.Vasil'ev: Singular and tangent slit solutions to the Loewner equation.- arXiv: 0708.1048v1 [math.CV], 2007, 8 pp. 

[2] D.-Ch. Chang, I. Markina, A.Vasil'ev: Sub-Lorentzian geometry on anti-de Sitter space.- arXiv: 0708.0879v1 [math.DG], 2007, 31 pp.

[3] J.M.Anderson, A.Vasil'ev: Lower Schwarz-Pick estimates and angular derivatives.- Ann. Acad. Sci. Fenn. arXiv: CV/0608531, v2, 2006, 11 pp.

[4] R.Hidalgo, I.Markina, A.Vasil'ev: Finite dimensional grading of the Virasoro algebra.- Georgian Math. J. 14 (2007), no. 3, 419-434.

[5] M.D. Contreras, S. Diaz-Madrigal, A.Vasil'ev: Digons and angular derivatives of analytic self-maps of the unit disk.- Complex Variables and Elliptic Equations, 52 (2007), no.8, 685-691; arXiv: math.CV/0701272, v1, 2007, 8 pp.

[6] Der-Chen Chang, Irina Markina: Quaternion $H$-type group and differential operator $\Delta_{\lambda}$.- Science in China. Ser. A. (to appear)

[7] Der-Chen Chang, Irina Markina: Anisotropic quaternion Carnot groups: geometric analysis and Green's function. - Adv. Appl. Math. 39 (2007), 345-394.

[8] Ovidiu Calin, Der-Chen Chang, Irina Markina: Geometric analysis on $H$-type groups related to division algebras.

[9] Ovidiu Calin, Der-Chen Chang Irina Markina: Sub-Riemannian geometry on the sphere S3.- Canadian J. Math. (to appear)

[10] M. D. Contreras, S. Diaz-Madrigal, M. J. Martin, and D. Vukotic: Holomorphic self-maps of the disk intertwining with linear fractional maps.

[11] M.Dostanić, M.Jevtić, and D.Vukotić: Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type.

[12] A.Stray: Restrictions of the disk algebra described locally.

[13] P.Gumenyuk: Caratheodory convergence of immediate basins of attraction to a Siegel disk.- math/0608644v4 [math.CV], 2007, 26 pp.

[14] T.Bloom, N.Levenberg, and Yu.Lyubarskii: A Hilbert lemniscate theorem in C^2.

[15] A.Borichev, Yu.Lyubarskii: Uniqueness theorems for Korenblum type spaces.

[16] Yu.Lyubarskii, R.Vershinin: Uncertainty Principles and Vector Quantization.

[17] Stephen M. Buckley and Dragan Vukotic: Univalent interpolation in Besov spaces and superposition into Bergman spaces.

[18] B.Gustafsson and V. Tkachev: The resultant on compact Riemann surfaces.

[19] D.Girela, F.Pérez-González, J.A.Peláez and J.Rättyä: Carleson measures for the Bloch space.

[20]  D.Girela: Conformal mappings and spaces of analytic functions.

[21] Eero Saksman and Kristian Seip: Integral means and boundary limits of Dirichlet series.

[22] Walter Bergweiler: Newton's method and Bakers domains. arXiv:0710.1147v1 [math.CV]

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