## Functional Analysis Seminar

Seminar information archive ～09/27｜Next seminar｜Future seminars 09/28～

Date, time & place | Wednesday 15:00 - 16:00 370Room #370 (Graduate School of Math. Sci. Bldg.) |
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**Seminar information archive**

### 2012/02/20

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Microscopic derivation of the Ginzburg-Landau model (ENGLISH)

**Jan Philip SOLOVEJ**(University of Copenhagen)Microscopic derivation of the Ginzburg-Landau model (ENGLISH)

[ Abstract ]

I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

### 2011/04/13

15:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Spectral theory for functions of self-adjoint operators (ENGLISH)

**Alexander Pushnitski**(King's College, London)Spectral theory for functions of self-adjoint operators (ENGLISH)

[ Abstract ]

Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

### 2011/02/23

14:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)

Uniform localization (ENGLISH)

Global solutions to the eikonal equation (ENGLISH)

Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

**Dimitri Yafaev**(Univ. Rennes 1) 14:00-14:45The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)

**David Damanik**(Rice University) 15:00-15:45Uniform localization (ENGLISH)

**Erik Skibsted**(Aarhus University) 16:15-17:00Global solutions to the eikonal equation (ENGLISH)

**Christian Gerard**(Univ. Paris Sud 11) 17:15-18:00Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

### 2007/01/25

14:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators

**Ivana Alexandrova**(East Carolina University)Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators

### 2006/09/13

13:00-16:45 Room #123 (Graduate School of Math. Sci. Bldg.)

On the determination of non-analytic resonances

(joint work with T.Ramond and J. Sjostrand)

Global existence for energy critical waves in 3-d domains

(joint work with G. Lebeau and F. Planchon)

On the Born-Oppenheimer approximation of wave-operators

**Andre' Martinez**(Bologna University) 13:00-14:00On the determination of non-analytic resonances

(joint work with T.Ramond and J. Sjostrand)

**Nicolas Burq**(Université de Paris Sud) 14:15-15:15Global existence for energy critical waves in 3-d domains

(joint work with G. Lebeau and F. Planchon)

[ Abstract ]

I will present some recent results obtained recently with G. Lebeau and F. Planchon. We prove that the energy critical (quintic) non linear wave equation in 3-d domains with Dirichlet boundary conditions is globally well posed for any initial data (with finite energy). I will give some hints about the proof of this result which is based on some recent results by Smith and Sogge on $L^p$ estimates for spectral projectors and a carefull study of the boundary value problem.

I will present some recent results obtained recently with G. Lebeau and F. Planchon. We prove that the energy critical (quintic) non linear wave equation in 3-d domains with Dirichlet boundary conditions is globally well posed for any initial data (with finite energy). I will give some hints about the proof of this result which is based on some recent results by Smith and Sogge on $L^p$ estimates for spectral projectors and a carefull study of the boundary value problem.

**Vania Sordoni**(Bologna University) 15:45-16:45On the Born-Oppenheimer approximation of wave-operators