## REPORTS

### Workshop

#### Workshop on "Avoided ? Crossing of Eigenvalue Curves" --- Non-commutative Harmonic Oscillator, Special Functions and Number Theory---

2012.03.11

Workshop on

"Avoided ? Crossing of Eigenvalue Curves"

-- Non-commutative Harmonic Oscillator, Special Functions and Number Theory--

Date: March 7 to 9, 2012.

Place: Inamori Center, Ito Campus, Kyushu University

Organized by:

Masao Hirokawa (Department of Mathematics, Okayama University)

Fumio Hiroshima (Faculty of Mathematics, Kyushu University)

Jinsung Park (School of Mathematics, KIAS)

Masato Wakayama(Institute of Mathematics for Industry, Kyushu University)

Program:

March 7

10:00-10:50 Masato Wakayama (Kyushu)

Number theoretical approach to spectrum for non-commutative harmonic oscillators

11:00-11:50 Setsuo Taniguchi (Kyushu)

A stochastic analytical approach to NCHO

13:40-14:30 Yoshitaka Watanabe (Kyushu)

Computer-assisted stability and instability proofs for the Orr-Sommerfeld problem with Poiseuille flow

Coffee break

15:10-16:00 Asao Arai (Hokkaido)

Quantum fields and analytic number theory

16:10-17:00 Jinsung Park (KIAS)

A generalization of the Dedekind eta function over Teichm"uller spaces

17:10-18:00 Roger E. Howe (Yale University.)

Iterated Pieri algebras,highest terms, and the Littlewood-Richardson Rule

March 8

10:00-10:50 Hiroyuki Ochiai (Kyushu)

Non-commutative harmonic oscillators and the connection problem for the Heun differential equation

11:00-11:50 Kouichi Takemura (Chuo)

On solutions of Heun's differential equation

13:30-14:20 Masao Hirokawa (Okayama)

Transition between the regimes of strong and ultra-strong couplings in circuit QED

Coffee break

15:00-15:50 Tsuyoshi Yamamoto (NEC)

Avoided crossings in superconducting qubits

16:00-16:50 Kouichi Semba (NTT)

Spectrum and dynamics observed in a quantum hybrid system

17:00-17:50 Valentin Zagrebnov (Marseille)

Quantum dynamics of cavity pumped by atomic beam

Banquet

March 9

10:00-10:50 Kazufumi Kimoto (Ryukyus)

Arithmetic structure of the non-commutative harmonic oscillator

Coffee break

11:30-12:20 Takashi Ichinose (Kanazawa)

On improved Sobolev embedding theorems for vector-valued functions

14:00-14:50 Klaus Schmidt (Vienna)

Mahler measure and entropy of algebraic group actions

15:00-15:50 Nobushige Kurokawa (TITech)

Euler's identity, Euler zeta functions and Euler characteristics