Spatially localized dissipative structures are observed in various fields, such as neural signaling, chemical reactions, discharge patterns, granular materials, vegetated landscapes, binary convection and block copolymer nanoparticles. These patterns are much simpler than single living cells, however they seem to inherit several characteristic “living state” features, such as generation of new patterns, self-replication, switching to new dynamics via collisions and adaptive morphological changes to environments. These behaviors stem from an interplay between the intrinsic instability of each localized pattern and the strength of external signals. To understand such an interplay, we explore the global geometric interrelation amongst all relevant solution branches of a corresponding system with approximate unfolding parameters. For instance, it has been uncovered that large deformation via strong collision is mapped into the network of unstable patterns in infinite dimensional space, and that an organizing center for 1D pulse generators is a double homoclinicity of butterfly type. Large deformation of patterns is unavoidable so that a global geometric structure formed by all relevant solution branches gives us much more insight rather than conventional PDE approaches. We illustrate the impact of this approach for the case of pulse generators. We also report on the recent exciting finding, namely the formation of exotic 3D nanoparticles of block copolymers caused by the interplay between internal repulsion and affinity to external solvent, which is consistent with experimental results.

The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and U(1) charge conservation are both preserved. In this talk, we discuss the generalization of the Lieb-Schultz-Mattis theorem to systems with higher-form symmetries, which act on extended objects of dimension n > 0. The prototypical lattice system with higher-form symmetry is the pure abelian lattice gauge theory whose action consists only of the field strength. We first construct the higher-form generalization of the Lieb-Schultz-Mattis theorem with a proof. We then apply it to the U(1) lattice gauge theory description of the quantum dimer model on bipartite lattices. Finally, using the continuum field theory description in the vicinity of the Rokhsar-Kivelson point of the quantum dimer model, we diagnose and compute the mixed ’t Hooft anomaly corresponding to the higher-form Lieb-Schultz-Mattis theorem.

Please note that the date and time of the 2nd lecture has been changed from May 21 10:30 to June 21 15:30.

Lecture 1 (10:00-11:30)
An introduction of Groebner bases of polynomial rings

Lecture 2 (13:00-14:30)
Groebner bases theory in design of experiments

Lecture 3 (15:00-16:30)
Groebner bases theory in sampling problems of contingency tables

This introductory lecture is about statistical theory from the point of view of the computational algebraic statistics, in particular the applications of Groebner bases. The statistical theory is a fundamental tool in natural science, social science and humanities, and the Groebner basis is a topic related to multi-variable polynomials. The Lecture will start from an introduction to the Groebner basis which would have wide applications in mathematics, physics, biology, chemistry, engineering, information science and computer science. Therefore, we welcome scientists in any field who are interested in this subject.

The event official language is Japanese (slides and writing are in English).

Rhythmic phenomena occur at all levels of biological organization, with periods ranging from milliseconds to years. Among biological rhythms, circadian clocks, of a period close to 24h, play a key role as they allow the adaptation of living organisms to the alternation of day and night. Biological rhythms represent a phenomenon of temporal self-organization in the form of sustained oscillations of the limit cycle type. Mathematical models show how the emergent property of oscillatory behavior arises from molecular interactions in cellular regulatory networks, which explains why cellular rhythms represent a major research topic in systems biology. After providing an introduction to biological rhythms and their modeling, I will focus on mathematical models for two major examples of rhythmic behavior at the cellular level : the circadian clock and the cell cycle. The coupling of these rhythms allows for their synchronization and for the occurrence of more complex patterns of oscillatory behavior. I will discuss the reasons why models for cellular rhythms tend to become more complex, upon incorporating new experimental observations. The case of cellular rhythms allows us to compare the merits of simple versus complex models for the dynamics of biological systems.

iTHEMS-CEMS Joint Colloquium.

Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics.

Abstract:
One of the most surprising aspects of quantum mechanics is that under certain circumstances it does not allow individual physical systems, even when isolated, to possess properties in their own right. This feature, first clearly appreciated by John Bell in 1964, has over the last half-century been tested experimentally and found (in most people's opinion) to be spectacularly confirmed. More recently it has been realized that it permits various operations which are classically impossible, such as "teleportation" and secure-in-principle cryptography.
This talk is a very basic introduction to the subject, which requires only elementary quantum mechanics.