State-of-the-art acquisition devices produce surface representations of increasingly high resolution. While these detailed representations are important for production, they are problematic e.g. when exchanging drafts via the internet or when a quick rendering for comparison is necessary. In the first part of the talk, I will present results and further research questions from a paper I recently co-authored on 'Variational Shape Approximation'. This approach aims at linearizing the input surface and representing it via a set of localized planar segments. In the second part of the talk, I will present some ongoing research on surface representations via balls. This work started with constructions from spherical neodym magnets and provided a set of mathematical questions. These investigations are joint work with FU Berlin and OIST.

For identification of the dark matter, various methodologies are required. Especially, the direct detection is one of the most important goals to directly understand itself. Now, there are various technologies for direct detection, but almost all detectors have no direction sensitivity. We can obtain essential information such as dependence of motion between the earth and the dark matter, velocity distribution and background from direction information, therefore that becomes a very important methodology to identify the dark matter for future as long as we consider "particle dark matter". In this seminar, I report about the potential of direction sensitive dark matter search and current experimental effort.

The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been a paradigmatic model in nonequilibrium statistical physics. In particular, it in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.

量子コンピュータは古典コンピュータとは異なる原理に基づいて動いており、自然科学を含む様々な分野において大きな変化をもたらすと考えられている。特にこの数年の進展は著しく、量子計算の古典計算に対する優位性が実験的に初めて示されるなど、期待されているマイルストーンが着実に達成されていっている。一方で量子コンピュータの発展において常に障害となっているのがノイズである。量子状態はノイズの影響を受けやすく、現在の量子コンピュータにおいては量子ゲート操作を行うごとに状態の精度が減衰していってしまう。そのため、量子コンピュータにかける負担をできるだけ減らすようなアルゴリズムの開発や、計算結果からエラーを取り除く方法、観測回数をできるだけ減らす方法等、様々な研究が行われている。本講義ではこれら量子コンピュータの実用化に向けた最近の研究と今後の課題について話す。

–From the latest theories and observations to the explanation of the Nobel Prize in Physics! An introduction to black holes from active physicists–

The 2020 Nobel Prize in Physics was awarded to Sir Roger Penrose, Prof. Dr. Reinhard Genzel and Prof. Andrea Ghez for their contributions to the theory and observation of black holes. Black holes have continued to provide hot topics in recent years, such as gravitational waves from black hole coalescence and black hole imaging, but do you really know what black holes are? Three cutting-edge black hole researchers will explain its identity and mystery.

Levinson’s theorem is a surprising result in quantum scattering theory, which relates the number of bound states and the scattering part of the underlying quantum system. For the last about ten years, it has been proved for several models that once recast in an operator algebraic framework this relation can be understood as an index theorem for the Møller wave operators. Resulting index theorems are called topological version of Levinson’s theorem or shortly topological Levinson’s theorem. In this talk, we first review the background and the framework of our investigation. New analytical and topological results are provided for Schrödinger operators on the half-line. This talk is based on my Ph.D thesis.

December 14 at 10:00-11:30, 2020 (JST)
December 13 at 20:00-21:30, 2020 (EST)

In the history of mathematical study in pattern formation, the effect of domain has been considered as an important factor that can regulate spatial patterning. However, it is still unknown in biology how the geometry of the domain such as nuclear or cellular shapes can directly regulate the cell fate. In this talk, I will introduce two studies of spatial reorganization in chromatin and cellular dynamics and show that the domain is likely to play a critical role in determining the cell function.