In this talk, I will introduce the topic of thermodynamic inequalities. One motivation for studying inequalities is that they can provide universal constraints on what can and cannot happen in physical systems. From a more practical point of view, they can be used to estimate physical observables even in situations where no equality is available. I will highlight a few recent examples of thermodynamic inequalities in the form of uncertainty relations and speed limits.

In the main part of the talk, I will explain a general technique for deriving new inequalities, by starting from information-theoretic bounds and considering “virtual perturbations” of a physical system. I will show how this method can be used to derive and generalize the so-called “thermodynamic uncertainty relation”. An interesting application of such uncertainty relations is to estimate the dissipation in biological systems such as molecular motors.

The second main topic is how to relate inequalities to equalities. When using inequalities to estimate physical quantities, it is crucial to understand the conditions under which the inequality can be tight. One way to achieve this is to “promote” the inequality into an equality via a variational principle. On the one hand, this provides conditions for obtaining a tight bound. On the other hand, variational expressions can also serve as a starting point to derive new inequalities.

Despite its weakness, gravity is the primordial source of particle production in the early Universe. All the particles, including dark matter, can inevitably be created after the end of inflation through gravity. To study this production channel, two different approaches have commonly been considered, one of which is based on the Boltzmann equation, and the other is based on the Bogoliubov transformation. The former approach has widely been used in phenomenological studies of dark matter, while the latter has been developed to describe particle production in curved spacetime. I will discuss when these two approaches are equivalent and when they are not by considering the pure gravitational production of a scalar particle.

The elasticity of population growth to a demographic parameter quantifies the proportional sensitivity of population growth to such parameter. In this talk, I will illustrate some cases where elasticities of population growth to demographic parameters acquire a special importance to evolutionary biology. In particular, I will discuss the relevance of these elasticities in studying the evolution of aging, their role in the computation of the generation time and their relationship to some trade-offs organisms may face as they optimise their fitness.

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?

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).