Time: 9:00 – 11:00, Monday 15 and Tuesday 16, December, 2014
Location: VIASM Lecture Hall C2.
Lecturer: Michel Zinsmeister, Professor of Mathematics, at MAPMO (Mathematics, Applications and Mathematics Physics, Orleans)
Abstract:
In 1916 Bieberbach observed that if f is holomorphic and injective in the disk and if f(0)=0, f’(0)=1 then, if we write f(z)=z+a_2z^2+a_3z^3+…, the modulus of a_2 is les or equal to 2. He also conjectured that the modulus of a_n is less than n for all n greater or equal to 2.
In 1923, Karl Loewner developed a theory of driven growth processes in the plane that allowed him to prove Bieberbach conjecture for n=3.
In 1999, Oded Schramm revisited Loewner theory by considering growth processes driven by Brownian motion, which lead him to create the rich theory of SLE.
In this talk I will revisit SLE theory from the Bieberbach viewpoint; some remarkable phenomena occur at some values of the SLE parameter, with consequences on the multifractal spectrum of SLE.
1) Planar growth processes.
Abstract: In this talk we will survey the different situations involving planar growth processes, from electro deposition to bacteria colonies ans growth of cities.
We will focus on Hele-Shaw flows and on the phD of Nguyen Thi Thuy Nga, former student of the master in HCMC, about growth of cities.
2) coefficient problem for SLE processes.
Abstract: The planar growth processes may be treated in a unified manner with the help of Loewner theory of planar growth.
Loewner developped his theory to solve Bieberbach conjecture. His theory was spectacularly revived by Oded Schramm in 1999 with his discovery of SLE (stochastic Loewner evolution.
In this talk we revisit Bieberbach coefficient problem in the frame work of SLE processes.
This is a joint work with B.Duplantier, Nguyen Thi Thuy Nga, Nguyen Thi Phuong Chi, Ho Xuan Hieu and Le Thanh Binh, former students of the HCMC master program.
Registration:
Please fill in the registration form below your contact information. Deadline for registration: 12/12/2014.