In this talk, we will review the history and the latest trends in artificial intelligence (AI) and mathematical technologies in recent years. We will also introduce various real-world problem-solving efforts that utilize state-of-the-art mathematics and artificial intelligence technology. Additionally, we will explore the role of mathematical and AI technologies and the social value they bring, while providing examples of their applications in a wide range of fields, such as manufacturing, disaster prevention, medical care, and institutional design in society. Furthermore, we will consider the thinking and skills required to address industrial and social issues using mathematical and AI technologies. The technologies that will be discussed in this talk include the following keywords: mathematical modeling, simulation, optimization, deep learning, topological data analysis, causal discovery, game theory, matching theory, and social mathematics.

Tropical geometry is a field of mathematics that naturally emerges when considering the limits of spaces with respect to some parameters. One of the motivations to study tropical geometry is to describe the behaviors of the spaces under the limit. In this math seminar, starting with a brief introduction to tropical geometry, we discuss its application to computation of period integrals, which are one of the most fundamental quantities of complex manifolds. The goal is to compute asymtptotics of period integrals for complex hypersurfaces in toric varieties using tropical geometry, and observe that the Riemann zeta values (or the gamma classes) appear in the result of the computation.
The first half of the talk will be a brief introduction to tropical geometry for non-experts including those who are working outside mathematics, and everyone will be welcome.

Organisms have diverse biological clocks synchronized with environmental cycles　depending on their habitats. The change in endogenous rhythms could contribute to range expansion in a novel rhythmic environment. For example, the Anticipation of tidal changes has driven the evolution of circatidal rhythms in some marine species. I am interested in the genetic and non-genetic changes in the biological rhythms and adaptation to tidal environments in the freshwater snail, Semisulcospira reiniana. Chronobiological analyses of behavior and gene expression revealed that snails had habitat-specific endogenous rhythms: individuals in a nontidal population showed the circadian rhythm while those in a tidal population showed the circadian and circatidal rhythms. The entrainment to the simulated tidal cycles increased the strength of circatidal activity only in snails in a tidal population. Although the circatidal rhythms in the transcriptome were clearer in individuals entrained to tidal cycles, the number of circatidal rhythmic transcripts was greater in a tidal population than in a nontidal population. These results suggest biological rhythms in the snails plastically change at the molecular level, but the strength of circatidal rhythm is different between populations. Finally, transcriptome-wide population genetic analysis revealed that these two populations can be clearly distinguished genetically, though the genetic distance was very small. Thus, genetic differentiation in biological rhythms could result from the evolution of a small number of genes. These findings suggest that adaptive plasticity and genetic changes in the biological rhythms play an important role in coping with tidal environments.

Fractonic phases are emergent quantum phases of matter that host excitations with restricted mobility. Although these phases have been considered to be of “beyond Landau” order, we show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of generalized symmetries. The corresponding symmetries are continuous higher-form symmetries whose conserved charges do not commute with spatial translations, and we refer to them as nonuniform higher-form symmetries. For a given set of nonuniform symmetries, the effective theory associated with the spontaneous breaking of them can be constructed. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu–Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. In this formulation, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

Field: condensed matter physics
Keywords: fractonic phases, higher-form symmetries, Nambu-Goldstone modes, Higgs mechanism, gauge theories

Note for participants:
For on-site participants, please register via the registration form.
For online participants finding the Zoom link, you can get it after filling the registration form.

Program:
13:30-15:00 Lecture 1
15:00-15:30 Coffee break
15:30-17:00 Lecture 2

Abstract:
In this talk, I will give an overview of the recent rapid progress of cold-atom quantum computers. In a cold-atom quantum computer, a laser-cooled atomic gas in a vacuum chamber is captured with a two-dimensional trap array called an optical tweezers array, which is an array of tightly focused laser beams. An array of cold single atoms thus created is initialized, gate operated, and readout with other laser beams. Because of its controllability and scalability, the cold-atom quantum computer has been attracting much attention, as one of the most promising candidates in the race to develop quantum-computer hardware. I will describe the characteristics and development trends of the cold-atom hardware, as well as the development of a cold-atom quantum computer at Institute for Molecular Science including the realization of an ultrafast quantum gate using ultrashort laser pulses.

Quantum field theory (QFT) has been formulated as a theoretical tool to describe elementary particles and nuclei. However, after introducing the concept of "effective field theory," QFT has been providing a general and powerful theoretical framework for describing various universal phenomena in broader range of physical systems, including condensed matter physics and statistical physics.
In this lecture, we will explore the basic aspects of field theory by employing it to address quantum many-body problems in simple nonrelativistic systems.

The topics covered will include:

Lecture 1: Low-energy scattering and renormalization in quantum mechanics
Lecture 2: Effective field theory of low-energy scattering
Lecture 3: Spontaneous symmetry breaking in weakly-interacting bose gas
Lecture 4: Effective field theory of superfluid
Lecture 5: Introduction to in-medium potential
Lecture 6: Complex-valued in-medium potential between heavy impurities in ultracold atoms

The aim is to provide an introductory overview and explanation of basics concepts in field theory.

Schedule:

Wed., Dec. 27
10:00 - 11:30: Lecture 1
13:00 - 14:30: Lecture 2
15:00 - 16:30: Lecture 3

Thur., Dec. 28
10:00 - 11:30: Lecture 4
13:00 - 14:30: Lecture 5
15:00 - 16:30: Lecture 6

Inspired by the recent development in quantum computers, much efforts have been devoted to exploring their potential applications in lattice gauge theories. However, in contrast to condensed matter systems, we face many challenges in applications of quantum computations to lattice gauge theories, where one of the major obstructions lies in implementation of gauge symmetries in quantum computations. In this seminar, I talk about a possible solution to the problem based on a unitary modular tensor category, expressing the Hamiltonian of lattice gauge theories in terms of the so called F moves, and implementing the F moves on quantum computers.
References:
TH, Y. Hidaka, JHEP 09 (2023) 126; JHEP 09 (2023) 123.

Type-I X-ray bursts are rapidly brightening phenomena triggered by the nuclear burning of light elements near the surface of accreting neutron stars. Most of the X-ray bursters show irregular behavior of light curves. However, some X-ray bursters are somehow quite regular, i.e., constant recurrence time and constant shaper of light curves, and are often called Clocked bursters, which are powerful sites to probe uncertainties of many model parameters such as accretion rate, the composition of accreted matter, reaction rates, neutron star structure, and temperature. In this study, we focus on the uncertainties of the equation of states, which determines the latter two properties. Based on our numerical models covering whole areas of neutron stars, we will present their impact on X-ray burst light curves. Furthermore, we will discuss the possibility of constraining the equation of states from Clocked bursters such as GS 1826-24 and 1RXS J180408.9-342058.

The density functional theory (DFT) is one of the powerful methods to solve quantum many-body problems, which, in principle, gives the exact energy and density of the ground state. The accuracy of DFT is, in practice, determined by the accuracy of an energy density functional (EDF) since the exact EDF is still unknown. Currently, DFT has been used in many communities, including nuclear physics, quantum chemistry, and condensed matter physics, while the fundamental study of DFT, such as the first principle derivations of an accurate EDF and methods to calculate many observables from obtained densities and excited states. However, there has been little opportunity to have interdisciplinary communication.

On December 2022, we had the first workshop on this series (DFT2022) at Yukawa Institute for Theoretical Physics, Kyoto University, and several interdisiplinary discussions and collaborationd were started. To share such progresses and extend collaborations, we organize the second workshop. In this workshop, the current status and issues of each discipline will be shared towards solving these problems by meeting together among researchers in mathematics, nuclear physics, quantum chemistry, and condensed matter physics.

This workshop mainly comprises lectures/seminars on cutting-edge topics and discussion, while a half-day session composed of contributed talks is also planned.

This workshop is partially supported by iTHEMS-phys Study Group. This workshop is a part of the RIKEN Symposium Series.

The detailed information can be found in the workshop website.