Quantum field theories (QFTs) describe a lot of physical phenomena in our world. And giving a mathematical definition of QFTs is a long-standing problem. There are several mathematical formulations: Wightman formulation, Osterwalder–Schrader formulation and Atiyah-Segal formulation. And each of them cover different aspects of QFTs.
Recently, Costello and their collabolators formulate QFTs by using prefactorization algbras. This formulaion cover a lot of classes of QFTs: TQFTs, 2d CFTs and perturbative QFTs. And they reproduce various results such as asymptotic freedom in non-Abelian gauge theories.
Prefactorization algbras can be given by Batalin–Vilkovisky quantization (BV quantization) of the Lagrangian. However the original BV quantizations are perturbative and they do not have non-perturbative effects like instantons. In this talk, we propose the way to include Abelian-instanton effects. In modern language, it is the same as ℤgauging.

Approximately 200,000 corneal transplantations are performed worldwide yearly, and more than half of them are applied to patients with corneal endothelial dysfunction. Recently, the restoration of functional corneas by injecting culture-expanded cells has developed in contrast to the conventional transplantation which relies on a limited number of donors’ corneas. This novel treatment opens up the potential to cure more patients with less surgical invasion and allows the utilization of cells with consistent and controlled quality. In this talk, I will introduce a unified physical biomarker for the quality assessment of corneal endothelial cells in in vitro culture and the predictive diagnosis of in vivo tissues using a single equation based on the collective order of cells. Taking an analogy to the two-dimensional colloidal assembly, the spatial arrangement of cells is generalized in terms of many-body interactions, and the “spring constant” of the underlying interaction potential is calculated from microscopy images. I also would like to discuss our recent approach to characterize the local structure of the arrangement of cells based on the topological data analysis.

Particle cosmology is a discipline seeking a fundamental understanding of the Universe based on particle physics. Five mysteries drive our research today: cosmic inflation, baryon asymmetry, neutrino properties, dark matter, and dark energy.
Resolving any of the five mysteries will revolutionize our picture of the Universe. Numerous interesting theoretical hypotheses have been proposed to this end. Many require new scalar quantum fields, such as inflatons, axions, supersymmetric particles, etc. They are, in a sense, an attempt to expand the role of the vacuum. Since we have not found such spin-zero fields yet, we shall invent new eyes to make an experimental or observational breakthrough.
The International Center for Quantum-field Measurement Systems for Studies of the Universe and Particles (QUP) was established in December 2021 at KEK under the WPI program of MEXT and JSPS. With its tagline of "bring new eyes to humanity," one of the primary missions of QUP is inventing and developing such new eyes for particle cosmology. In this seminar, after briefly introducing QUP, I focus on research topics I have contributed, including the LiteBIRD satellite to study inflatons and light scalar quantum field searches with novel methods using quantum sensing techniques.

Thanks to intensive research efforts, topology has been established as a fundamental concept in physics. For closed quantum systems, the classification of gapped topological phases has matured. Moreover, the importance of topology is not limited to isolated quantum systems. Recently, the topology of non-Hermitian Hamiltonians, which effectively describe systems with dissipation, has attracted much attention worldwide. This fascination is exemplified by topological phases and topological phenomena unique to non-Hermitian systems.

Against this background, the primary purpose of this workshop is to bring together researchers working on topological phases and to discuss (i) open questions in topological phases of closed quantum systems and (ii) the role of topology in open quantum systems and measurements.

Disease is caused by genetic factors and environmental factors. Genome-wide association study (GWAS) is a powerful method to find genetic factors associated with disease and human complex traits. One conceptual finding GWAS revealed is that many common diseases are caused by a combination of multiple genetic factors (polygenic), rather than a single causal mutation (monogenic). I have been working on finding genetic factors causing polygenic diseases by developing software that accurately finds sequence insertions and deletions from human population-scale sequencing datasets. In this talk, first, I will introduce some examples of disease-causing variants we recently discovered. Next I will also introduce my current research theme aiming to untangle how multiple genetic factors coordinately change cellular homeostasis, which I would like to have a collaboration with mathematical scientists.

I will start my talk with a brief overview of the standard reheating scenario. Then, I will discuss reheating through the evaporation of primordial black holes (PBHs) if one assumes PBHs are formed during the phase of reheating. Depending on their initial mass, abundance, and inflaton coupling with the radiation, I discuss two physically distinct possibilities of reheating the universe. In one possibility, the thermal bath is solely obtained from the decay of PBHs, while inflaton plays the role of the dominant energy component in the entire process. In the other possibility, PBHs dominate the total energy budget of the universe during evolution, and then their subsequent evaporation leads to a radiation-dominated universe. Furthermore, I will discuss the impact of both monochromatic and extended PBH mass functions and estimate the detailed parameter ranges for which those distinct reheating histories are realized. The evaporation of PBHs is also responsible for the production of DM. I will show its parameters in the background of reheating obtained from two chief systems in the early universe: the inflaton and the primordial black holes (PBHs). Then, I will move my discussion towards stable PBHs and discuss the effects of the parameters describing the epoch of reheating on the abundance of PBHs and the fraction of cold dark matter that can be composed of PBHs. If PBHs are produced due to the enhancement of the primordial scalar power spectrum on small scales, such primordial spectra also inevitably lead to strong amplification of the scalar-induced secondary gravitational waves (GWs) at higher frequencies. I will show how the recent detection of the stochastic gravitational wave background (SGWB) by the pulsar timing arrays (PTAs) has opened up the possibility of directly probing the very early universe through the scalar-induced secondary gravitational waves. Finally, I will conclude my talk by elaborating on the effect of quantum correction on the Hawking radiation for ultra-light PBHs and its observational signature through dark matter and gravitational waves.