RIKEN iTHEMS and the SACRA Interdisciplinary Research Division of the Graduate School of Science, Kyoto University signed a joint research agreement on the task "Creation of new fields and solution of various problems in science using mathematical-based interdisciplinary methods", which started in 2018, and the two institutions have been strengthening collaboration over the past five years. During this period, various collaborative activities in both research and education have been carried out and results have been achieved, including the holding of research symposia, joint lectures across universities, the establishment of visiting lectures, and educational activities in the MACS Study Group. At this forum, we would like to present the results of these five years of joint research and to link them to the start of further collaboration in the future. In particular, many undergraduate and graduate students have participated in the "MACS Study Group 2022-SG5 Pipeline Connecting RIKEN and MACS", and have been actively engaged in research activities with RIKEN researchers. The results of these SG5 activities will be presented by the students.

In the first half of my talk, I will review quantum groups at roots of unity and their representation theory. In the second half, I will explain a construction of new quantum groups using cohomology theories from topology. The construction uses the so-called cohomological Hall algebra associated to a quiver and an oriented cohomology theory. In examples, we obtain the Yangian, quantum loop algebra and elliptic quantum group, when the cohomology theories are the cohomology, K-theory, and elliptic cohomology respectively.

This talk aims to illustrate symmetries in geometry. The first half surveys a few examples of parametrizing coherent sheaves on a variety and how quantum groups control the symmetry of parametrization space. The second half aims to illustrate some special cases when the variety is a local toric 3-Calabi-Yau.

How does the nucleon get its mass? Certainly not from the Higgs -- the rest masses of the quarks it contains add up to only one percent of the nucleon mass. Rather the remaining 99% comes from the zero-point energy of the quarks, antiquarks and gluons localized in the nucleon. How do nuclei differ from being a simple collection of nucleons? How are the gluons, for example, distributed in nuclei? Do they stick out, or are they clumped towards the center of the nucleon? Gluons, like dark matter unseen but playing the crucial role in gluing matter together, are strongly interacting. Do such gluons form new emergent quantum states in nuclei, as in condensed matter physics? And how is the spin of the proton -- the key to NMR imaging -- put together from the spin and orbital motion of the quarks and gluons in the proton?

Note: Due to unexpected trouble, we have made the decision to postpone the seminar scheduled for February 21 to May 30. Sorry for the trouble.

Abstract:
The Sachdev-Ye-Kitaev (SYK) model, proposed in 2015, is a quantum mechanical model of N Majorana or complex fermions with all-to-all random four-body interactions. The model has attracted significant attention over the years due to its features such as the existence of the large-N solution with maximally chaotic behavior at low temperatures and holographic correspondence to low-dimensional gravity.
The sparse version of the SYK model reproduces essential features of the original model for reduced numbers of disorder parameters. We recently proposed [1] a further simplification, where we set the nonzero couplings to be +1 or -1 rather than sampling from a continuous distribution such as Gaussian. This binary-coupling model exhibits strong correlations in the spectrum, as observed in the spectral form factor, more efficiently in terms of the number of nonzero terms than in the Gaussian distribution case. We also discuss the scrambling dynamics with the binary-coupling sparse SYK model, comparing the model with the original model as well as the SYK model with random two-body terms [2], where the localization of the many-body eigenstates in the Fock space has been quantitatively studied [3,4].

In this talk, I will discuss the construction of the boundary symmetry algebra for BF-like theories in 3D and 4D. In the 3D case, the theory corresponds to (an extension of) 3D gravity allowing for a source of curvature and torsion. I will show how the study of the current algebra and its associated Sugawara construction allows for two notions of quadratic charges (the usual diffeomorphism and its "dual") independently of boundary conditions. I will discuss their resulting algebra and its relation with the usual construction of the asymptotic boundary algebra. In the 4D case, a similar yet fundamentally different construction is possible, similarly resulting in multiple quadratic charges. I will discuss their constructions and their possible relations to 4D gravity.

Within the holographic correspondence, boundary conditions play a fundamental role in determining the nature of the dual field theory. In this talk, I will show how to exploit mixed boundary conditions to obtain dynamical electromagnetism in the boundary theory. This is necessary to apply AdS-CFT to many real-world applications, e.g., magnetohydrodynamics, plasma physics, superconductors, etc. where dynamical gauge fields and Coulomb interactions are fundamental. As a proof of concept, I will show two emblematic cases. First, I will prove that the results from the 4-dimensional Einstein-Maxwell bulk theory with these deformed boundary conditions are in perfect agreement with relativistic magneto-hydrodynamics in 2+1 dimensions. Second, I will discuss the collective excitations of a bona-fide holographic superconductor and prove the existence of the Anderson-Higgs mechanism therein.

Ultra high-energy (UHE) cosmic rays (CRs) from distant sources interact with intergalactic radiation fields, leading to their spallation and attenuation through photo-hadronic processes. Their deflection and diffusion in large scale intergalactic magnetic fields (IGMFs), in particular those associated with Mpc-scale structures, alter the cumulative cooling and interactions of a CR ensemble to modify their spectral shape and composition observed on Earth. In this talk, I will demonstrate the extent to which IGMFs can affect observed UHE CRs, and show that source population models are degenerate with IGMF properties. Interpretation of observations, including the endorsement or rejection of any particular UHE CR source classes, needs careful consideration of the structural properties and evolution of IGMFs. Future observations providing tighter constraints on IGMF properties will significantly improve confidence in assessing UHE CR sources and their intrinsic CR production properties.

The Workshop on Virus Dynamics is an international meeting held every 2 years. It brings virologists, immunologists, and microbiologists together with mathematical and computational modellers, bioinformaticians, bioengineers, virophysicists, and systems biologists to discuss current approaches and challenges in modelling and analyzing different aspects of virus and immune system dynamics, and associated vaccines and therapeutics. This 6th version of the workshop builds on the success of previous ones held in Frankfurt (2013), Toronto (2015), Heidelberg (2017), Paris (2019) and virtually (2021). It is supported by the Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) program at RIKEN, by Nagoya University, and by the Japan Science and Technology Agency. Up-to-date information and registration is available via the website. The workshop is for in-person participation only (no virtual or hybrid option).