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SLE Processes and Bieberbach Coefficients: A Modern Perspective

Delve into the relation between Bieberbach conjecture and SLE processes, exploring Duplantier, Chi, Nga, and Zinsmeister's estimates at Fractals and Related Fields II, 2011.

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SLE Processes and Bieberbach Coefficients: A Modern Perspective

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  1. Coefficient estimates for whole-plane SLE. Bertrand Duplantier, Nguyen Thi Phuong Chi, Nguyen Thi Thuy Nga, Michel Zinsmeister Fractals and related Fields II, Porquerolles, June 2011

  2. Bieberbach conjecture: 1916 Proof of the conjecture: De Branges, 1985

  3. 1999: Oded Schramm, SLE (stochastic Löwner evolution). Aim of this talk: revisit Bieberbach conjecture in the framework of SLE processes.

  4. -I- Bieberbach, Loewner, Schramm.

  5. Koebe function:

  6. Return to the history of Bieberbach conjecture

  7. -II- Bieberbach coefficients and Lévy processes

  8. TH 1

  9. TH2:

  10. Löwner’s estimate (mu=0):

  11. NO Fekete-Szegö counterexample.

  12. -III- Computer experiments

  13. Computer program

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