A macroscopic theory for adaptive changes of cells is presented, based on consistency between cellular growth and molecular replication, as well as robustness of fitted phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes are shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states is derived, as is confirmed by adaptation experiments of bacteria under stress. The theory is extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and by environmental adaptation, which also explains the evolutionary fluctuation-response relationship previously uncovered. Relevance of statistical-physics and dynamical-systems approach is discussed.

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.

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.

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.

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).