Vietnam National University (VNU) College of Science Department of Mathematics

2 = Summer Seminar Real and complex analysis July 19, 2014, Room 405, Building T3 Schedule 7h00 - 7h50

Coffee and Registration

7h50 - 8h00

Welcome speech

8h00 - 8h50

Cung The Anh (Hanoi University of Education) TBA

8h50 - 9h00

Tea break

9h00 - 9h50

Tran Vu Khanh (National University of Singapore) The Kohn-Laplacian equation on CR manifolds

9h50 - 10h00

Tea break

10h00 - 10h50

Phan Thanh Nam (Institute of Science and Technology, Austria) How many extra electrons that a neutral atom can bind?

10h50 - 11h00

Tea break

11h00 - 11h50

Tran Minh Binh (Basque Center for Applied Mathematics, Spain) Convergence to equilibrium of the quantum boltzmann equation.

11h50 - 12h00

Tea break

12h00 - 12h25

Trinh Tuan Phong (University of Paris 13, France) Decorrelation estimates for a 1D random model in the localized regime.

12h25

End of Program

12h30

Workshop Reception

Title and abstract Long-time behavior of solutions to some equations in fluid mechanics Cung The Anh Hanoi National University of Education [email protected] The aim of this talk is twofold. First, we will briefly introduce the theory of pullback attractors that has been developed recently and has shown to be very useful in the understanding of the dynamics of non-autonomous dynamical systems. Second, we will present some recent results on the existence and fractal dimension estimates of pullback attractors for some nonautonomous nonlinear partial differential equations arising in fluid mechanics.

Convergence to equilibrium of the quantum Boltzmann equation. Tran Minh Binh Basque Center for Applied Mathematics, Spain [email protected] We consider the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither bounded from below nor from above. We prove the existence and uniqueness of solutions that satisfy the conservation of the energy. We show that each of these solutions converge to the corresponding stationary state, algebraically as time tends to infinity. We also provide a constructive estimate of the coercivity constant of the linearised collision operator.

The Kohn-Laplacian equation on CR manifolds Tran Vu Khanh National University of Singapore [email protected] The complex Laplacian on CR manifolds is firstly defined by J.J. Kohn and called the KohnLaplacian. In this talk, we discuss about the existence, global and local regularity of the solution of the Kohn-Laplacian equation.

How many extra electrons that a neutral atom can bind? Phan Thanh Nam Institute of Science and Technology, Austria [email protected] It is conjectured that a neutral atom can bind at most one or two extra electrons. I will review some mathematical results on this ionization problem. I will also discuss some related open problems.

Decorrelation estimates for a 1D random model in the localized regime. Trinh Tuan Phong University of Paris 13, France [email protected] In this short talk, we would like to introduce decorrelation estimates for the eigen-values of a 1D discrete tight binding model near two distinct energies in the localized regime. Such estimates yield the asymptotic independence for local level statistics near n distinct energies for any n.

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