PDE and Applied Mathematics Seminar[ Edit ]
We study global solutions $u:{\mathbb R}^3\to{\mathbb R}^2$ of the GinzburgLandau equation $\Delta u=(1u^2)u$ which are local minimizers in the sense of De Giorgi. We prove that a local minimizer satisfying the condition $\liminf_{R\to\infty}\frac{E(u;B_R)}{R\ln R}<2\pi$ must be constant. The main tool is a new sharp $\eta$ellipticity result for minimizers in dimension three that might be of independent interest. This is a joint work with Etienne Sandier (Universit\'e ParisEst).
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Small energy GinzburgLandau minimizers in ${\mathbb R}^3$ 
Speaker:  Itai Shafrir, Technion 
Place:  Amado 814, Technion 
Abstract:  
We study global solutions $u:{\mathbb R}^3\to{\mathbb R}^2$ of the GinzburgLandau equation $\Delta u=(1u^2)u$ which are local minimizers in the sense of De Giorgi. We prove that a local minimizer satisfying the condition $\liminf_{R\to\infty}\frac{E(u;B_R)}{R\ln R}<2\pi$ must be constant. The main tool is a new sharp $\eta$ellipticity result for minimizers in dimension three that might be of independent interest. This is a joint work with Etienne Sandier (Universit\'e ParisEst). 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 466 
Onedimensional Toeplitz words generalize periodic sequences and are therefore used as model for quasicrystals. They are constructed from periodic words with "holes" (that is, undetermined positions) by successively filling the holes with other periodic words. In this talk, the subclass of so called simple Toeplitz words is considered. We will discuss combinatorial properties of subshifts associated them. In addition to describing certain aspects of how ordered the word is, these properties are important tools for other questions as well. We will apply them to answer questions concerning the spectrum of Schrödinger operators and Jacobi operators on the subshift.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  On spectral properties of Schrödinger Operators on Simple Toeplitz Subshifts 
Speaker:  Daniel Sell, U Jena 
Place:  Amado 814, Technion 
Abstract:  
Onedimensional Toeplitz words generalize periodic sequences and are therefore used as model for quasicrystals. They are constructed from periodic words with "holes" (that is, undetermined positions) by successively filling the holes with other periodic words. In this talk, the subclass of so called simple Toeplitz words is considered. We will discuss combinatorial properties of subshifts associated them. In addition to describing certain aspects of how ordered the word is, these properties are important tools for other questions as well. We will apply them to answer questions concerning the spectrum of Schrödinger operators and Jacobi operators on the subshift. 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 457 
We consider a general class of sparse graphs which includes for example graphs that satisfy a strong isoperimetric inequality. First, we characterize these graphs in a functional analytic way by means of the form domain of Schrödinger operators. Furthermore, we study spectral bounds and characterize discreteness of the spectrum. As a particular consequence we obtain estimates on the eigenvalue asymptotics in this case. (This is joint work with Michel Bonnefont and Sylvain Golénia.)
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Schrödinger operators on sparse graphs 
Speaker:  Matthias Keller, University of Potsdam 
Place:  Amado 814, Technion 
Abstract:  
We consider a general class of sparse graphs which includes for example graphs that satisfy a strong isoperimetric inequality. First, we characterize these graphs in a functional analytic way by means of the form domain of Schrödinger operators. Furthermore, we study spectral bounds and characterize discreteness of the spectrum. As a particular consequence we obtain estimates on the eigenvalue asymptotics in this case. (This is joint work with Michel Bonnefont and Sylvain Golénia.) 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 437 
In the last 15 years, there has been much progress on higher dimensional solutions to the Einstein equation, much of it from the physics community. They are particularly interesting as, unlike 4 dimensional spacetimes, the horizon is no longer restricted to being diffeomorphic to the sphere, as demonstrated by the celebrated black ring solution of Emparan and Reall. Using the WeylPapapetrou coordinates and harmonic map, we show the existence of stationary solutions to the 5 dimensional vacuum Einstein equation, which are biaxisymmetric solutions with lens space horizons. This is a joint project with Marcus Khuri and Sumio Yamada.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  Biaxisymmetric stationary solutions to the vacuum Einstein equation with nonspherical horizons 
Speaker:  Gilbert Weinstein, Department of Mathematics and Department of Physics, Ariel University 
Place:  Amado 814, Technion 
Abstract:  
In the last 15 years, there has been much progress on higher dimensional solutions to the Einstein equation, much of it from the physics community. They are particularly interesting as, unlike 4 dimensional spacetimes, the horizon is no longer restricted to being diffeomorphic to the sphere, as demonstrated by the celebrated black ring solution of Emparan and Reall. Using the WeylPapapetrou coordinates and harmonic map, we show the existence of stationary solutions to the 5 dimensional vacuum Einstein equation, which are biaxisymmetric solutions with lens space horizons. This is a joint project with Marcus Khuri and Sumio Yamada. 

SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 465 
In his famous 1900 ICM address Hilbert proposed his famous list of problems for the 20th century. Among these was his 6th problem which was less clearly formulated than the others but dealt with a rigorous derivation of the macroscopic equations of continuum mechanics from the available microscopic theory of his time, i.e. statistical mechanics and specifically Boltzmann's kinetic theory of gases. The problem has drawn attention from analysts over the years and even Hilbert himself made a contribution. In this talk I will note how an exact summation of the ChapmanEnskog expansion for the Boltzmann equation due to Ilya Karlin ( ETH) and Alexander Gorban (Leicester) can be used to represent solutions of the Boltzmann equation and then show that these solutions CANNOT converge the classical balance laws of mass, momentum, and energy associated the Euler equation of compressible gas dynamics. Hence alas Hilbert's program (at least with respect to gas dynamics) has a negative outcome.
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  The problem with Hilbert's 6th problem 
Speaker:  Marshall Slemrod, University of WisconsinMadison 
Place:  Amado 814, Technion 
Abstract:  
In his famous 1900 ICM address Hilbert proposed his famous list of problems for the 20th century. Among these was his 6th problem which was less clearly formulated than the others but dealt with a rigorous derivation of the macroscopic equations of continuum mechanics from the available microscopic theory of his time, i.e. statistical mechanics and specifically Boltzmann's kinetic theory of gases. The problem has drawn attention from analysts over the years and even Hilbert himself made a contribution. In this talk I will note how an exact summation of the ChapmanEnskog expansion for the Boltzmann equation due to Ilya Karlin ( ETH) and Alexander Gorban (Leicester) can be used to represent solutions of the Boltzmann equation and then show that these solutions CANNOT converge the classical balance laws of mass, momentum, and energy associated the Euler equation of compressible gas dynamics. Hence alas Hilbert's program (at least with respect to gas dynamics) has a negative outcome.


SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 434 
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  TBA 
Speaker:  Eitan Tadmor, U Maryland  CSCAMM & ETH  Institute for Theoretical Studies 
Place:  Amado 814, Technion 
SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 458 
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  TBA 
Speaker:  Edriss S. Titi (The Weizmann Institute of Science and Texas A&M University) 
Place:  Amado 814, Technion 
Abstract:  


SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 456 
Type:  Seminar 

Name:  PDE and Applied Mathematics Seminar 
Title:  TBA 
Speaker:  Adi Ditkowski, Tel Aviv University 
Place:  Amado 814, Technion 
SubmittedBy:  Yehuda Pinchover, pincho@tx.technion.ac.il 
EventLink:  Event № 459 