Turkish Version

VARGA KALANTAROV 60th Birthday Conference

 

5 November 2010

Koc University

 

Speakers

Okay Celebi

 

Yeditepe University

Alp Eden

 

Bogazici University

Gregory Seregin

 

Oxford University

Mete Soner

 

ETH - Zurich

Edriss Titi

 

UC Irvine – Weizmann Inst.

Ali Ulger

 

Koc University

                                  

The conference is supported by Koc University, and TUBITAK Project No: 107T896.

For more information, please send an e-mail to kalantarov60@gmail.com

                                  

Program

 9:30

Opening Talks

 

 9:45

Okay Celebi

Varga’yi ne kadar taniyorsunuz?

10:30

Break

 

11:00

Ali Ulger

Turkiye’de Matematik Nicin Gelisemedi?

11:45

Break

 

12:00

Alp Eden

Remarks on the asymptotic behavior of the solutions of non-linear PDEs

12:45

Lunch

 

14:00

Gregory Seregin

Local Regularity Theory for the Navier-Stokes Equations

15:00

Break

 

15:30

Edriss Titi

On the Loss of Regularity for the Three-Dimensional Euler Equations

16:30

Break

 

17:00

Mete Soner

Discrete approximations of nonlinear parabolic equations from finance

18:00

Conference Dinner

 

Talks

Okay CelebiVarga’yi ne kadar taniyorsunuz?

 

Ali Ulger - Türkiye’de Matematik Nicin Gelisemedi?

 

Alp Eden - Remarks on the asymptotic behavior of the solutions of non-linear PDEs

TBA

 

Gregory Seregin - Local Regularity Theory for the Navier-Stokes Equations

In the talk, I am going to discuss recent regularity results for suitable weak solutions to the Navier-Stokes equations.

 

Edriss Titi - On the Loss of Regularity for the Three-Dimensional Euler Equations

A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of solutions of Euler equations may, in some cases, fail to be a solution of Euler equations. We use this shear flow example to provide non-generic, yet nontrivial, examples concerning the loss of smoothness of solutions of the three-dimensional Euler equations, for initial data that do not belong to $C^{1,\alpha}$. Moreover, we show by means of this shear flow example the existence of weak solutions for the three-dimensional Euler equations with vorticity that is having a nontrivial density concentrated on non-smooth surface. This is very different from what has been proven for the two-dimensional Kelvin-Helmholtz problem where a minimal regularity implies the real analyticity of the interface.  Eventually, we use this shear flow to provide explicit examples of non-regular solutions of the three-dimensional Euler equations that conserve the energy, an issue which is related to the Onsager conjecture.

 

Mete Soner - Discrete approximations of nonlinear parabolic equations from finance

It is known that scalar, parabolic, semi-linear partial differential equations have several probabilistic representations. Also "recently" we were able to obtain a representation for fully nonlinear equations and geometric equations as well. Reversely, one can derive these equations as pricing equations for some financial models. One such occasion is a liquidity model which yields a quadratic nonlinearity of the Hessian. In joint work with Selim Gokay, we used this model to understand the discretization properties of such representations. In this talk, I will describe this simple discrete financial model and the convergence proof.

Transportation to Koc University