## 関数解析セミナー

開催情報 水曜日　15:00～16:00　数理科学研究科棟(駒場) 370号室 中村 周

### 2012年02月20日(月)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Jan Philip SOLOVEJ 氏 (コペンハーゲン大学)
Microscopic derivation of the Ginzburg-Landau model (ENGLISH)
[ 講演概要 ]
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年04月13日(水)

15:00-17:00   数理科学研究科棟(駒場) 128号室
Alexander Pushnitski 氏 (King's College, London)
Spectral theory for functions of self-adjoint operators (ENGLISH)
[ 講演概要 ]
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年02月23日(水)

14:00-18:00   数理科学研究科棟(駒場) 118号室
Dimitri Yafaev 氏 (Univ. Rennes 1) 14:00-14:45
The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)
David Damanik 氏 (Rice University) 15:00-15:45
Uniform localization (ENGLISH)
Erik Skibsted 氏 (Aarhus University) 16:15-17:00
Global solutions to the eikonal equation (ENGLISH)
Christian Gerard 氏 (Univ. Paris Sud 11) 17:15-18:00
Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

### 2007年01月25日(木)

14:00-17:00   数理科学研究科棟(駒場) 370号室
Ivana Alexandrova 氏 (East Carolina University)
Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators

### 2006年09月13日(水)

13:00-16:45   数理科学研究科棟(駒場) 123号室
Nicolas Burq氏は9月7日から13日まで、Andre Martinez氏とVania Sordoni氏は、9月11日から22日まで、東京大学数理科学研究科に滞在の予定です。
Andre' Martinez 氏 (Bologna University) 13:00-14:00
On the determination of non-analytic resonances
(joint work with T.Ramond and J. Sjostrand)
Nicolas Burq 氏 (Université de Paris Sud) 14:15-15:15
Global existence for energy critical waves in 3-d domains
(joint work with G. Lebeau and F. Planchon)
[ 講演概要 ]
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 氏 (Bologna University) 15:45-16:45
On the Born-Oppenheimer approximation of wave-operators