日時： 2026年 10月 17日 （土） 14:00 -- 16:30
場所： 学習院大学　南4号館2階 205号室

1. 14:00--15:00
講演者：吉田 尚矢 氏（立命館大学）

Title: Semiclassical shape resonances for magnetic Stark Hamiltonians

Abstract: We consider the two-dimensional semiclassical Schrödinger operator with a constant magnetic field and a constant electric field, whose scalar potential is a smooth perturbation V of the linear potential. For decaying V, the spectral picture is as follows. Without the electric field, the spectrum consists of the Landau levels, and V creates discrete eigenvalues outside them. Once the electric field is switched on, the spectrum becomes the whole real line and the operator has no embedded eigenvalues (Adachi-Tsujii). Hence V is expected to produce resonances rather than bound states. Previous works on magnetic Stark resonances treat the strong magnetic field limit (Wang; Dimassi-Petkov) or the weak electric field limit (Ferrari-Kovařík).
In this talk we fix both fields and, under an analyticity assumption on V near infinity, study shape resonances created by potential wells in the semiclassical limit. Resonances are defined as poles of the meromorphic continuation of the cutoff resolvent, and are characterized as discrete eigenvalues of the operator obtained by complex translation outside a compact set. We prove a one-to-one correspondence, including multiplicities, between resonances exponentially close to the real axis and eigenvalues of a reference operator whose potential is flattened outside the well. As consequences, we obtain the asymptotics of the real parts of the shape resonances near the bottom of a non-degenerate well via the Birkhoff normal form, and a resonance-free region separating them from the other resonances. We also discuss open problems, such as lower bounds on the resonance widths and their dependence on the magnetic field.
This talk is based on joint work with K. Kameoka (Ritsumeikan University).

2. 15:30--16:30
講演者：新國 裕昭 氏（前橋工科大学）

Title: δ型超曲面相互作用に従う重調和作用素のスペクトルについて

Abstract: 本講演では，Lipschitz 超曲面上に台を持つ δ型相互作用に従う重調和作用素について得られた成果を共有する．J.Behrndt, P. Exner, V. Lotoreichik が Schrödinger 作用素に対して2014年に導入した方法に倣って，対応する2次形式を通して超曲面上の δ型相互作用に従う重調和作用素を自己共役作用素として実現する．また，超曲面がコンパクトな場合の本質スペクトルに関する結果を述べる．さらに，相互作用の台が3次元 Euclid 空間内の球面である場合に，球面調和関数による部分波展開を用いることで負の固有値に関して得られた結果を紹介する．

日時： 2026年 6月 20日 （土） 14:00 -- 16:30
場所： 学習院大学　南4号館2階 205号室

1. 14:00--15:00
講演者：藤井 豪琉 氏（東京大学）

Title: Characterization of spacetime singularities for the Schrödinger equation

Abstract: We present a characterization of spacetime singularities of a solution to the Schrödinger equation with a time-dependent short-range perturbation. Spacetime singularities are described by a quasi-homogeneous wave front set due to Lascar (1977). We show that under the non-trapping condition, the quasi-homogeneous wave front set of a solution is determined by that of the free solution, and classical spatial high-energy scattering data. In the one dimensional case it further reduces to the homogeneous wave front set of its initial data.
The proof of the former result is inspired by Nakamura (2009), which considered spatial singularities. However, extended analysis is required to handle the spacetime classical flow and time-dependent coefficients. This talk is based on a joint work with Kenichi Ito (Kobe University).

2. 15:30--16:30
講演者：Christian Gérard 氏（オルセー数学研究所）

Title: Aspects of Quantum Field Theory on Curved Spacetimes

Abstract: Quantum Field Theory on curved spacetimes describes quantum fields in an external gravitational field, represented by the Lorentzian metric of the ambient spacetime. It is used in situations where both the quantum nature of the fields and the effect of gravitation are important, but the quantum nature of gravity can be neglected. Its most important areas of application are the study of phenomena occurring in the early universe and in the vicinity of black holes, and its most celebrated result is the discovery by Hawking that quantum particles are created near the horizon of a black hole.
We will give an introductory lecture aimed at non-experts to mathematical aspects of QFT on curved spacetimes. We will focus on Hadamard states, which are substitutes for the vacuum state when oneconsiders general spacetimes.

日時： 2026年 6月 13日 （土） 15:30 -- 16:30
場所： 学習院大学　南4号館2階 205号室

15:30--16:30
講演者：Gianluca Panati 氏（ローマ・サピエンツァ大学）

Title: The Localization Dichotomy for periodic and non-periodic insulators

Abstract: We aim at investigating the localization properties of (independent) electrons in solids, possibly including a periodic magnetic field, as e.g. in Chern insulators and in Quantum Hall systems. The dynamics of the electrons is modeled by a magnetic Schrödinger operator, or by its discrete analog, possibly with ergodic disorder.
In 2016, we proposed to describe the localization properties of the system by the decay of the Wannier Bases associated with the spectral projection below the Fermi energy, which is supposed to be in a spectral gap. In the periodic case, we proved the validity of a Localization Dichotomy, for dimension \( d \leq 3 \), stating the following: either there exist an exponentially localized Wannier Basis, and correspondingly the system is in a Chern-trivial topological phase with vanishing Hall conductivity, or the decay of any Wannier basis is such that the expectation value of the squared position operator, or equivalently of the Marzari-Vanderbilt localization functional, is infinite. In the latter case, the Chern number of the Fermi projector is non-zero.
While in the non-periodic (disordered) case the mathematical picture is still incomplete, several new results have been proved in the last few years, based on a variety of techniques.
The talk is based on joint works with D. Monaco, A. Pisante, and S. Teufel for the periodic setting, and with G.Marcelli, G. Moscolari, and V. Rossi for the non-periodic case.