Atiyah-Floer conjecture concerns a relationship between Floer homology in Gauge theory and Lagrangian Floer homology. One of its difficulty is that the symplectic manifold on which we consider Lagrangian Floer homology is in general singular. In this talk I will explain that, by using relative and equivariant version of Lagrangian Floer homology, we can resolve this problem and can at least state the conjecture as rigorous mathematical conjecture.

Supported by RIKEN iTHEMS and Tuesday Seminar on Topology (Graduate School of Mathematical Sciences, The University of Tokyo).

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

10:30-12:30 Introduction to spin-boson model @DR3 (14th Building 213)
14:00-15:30 Kondo effect @DR7 (14th Building 217)
16:00-17:30 Detail of NIBA formalism @DR7 (14th Building 217)

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.

In this seminar, I will give an introduction to topological photonics, that is, the study of topological band structures and resulting topological phenomena in photonic systems. I will first review basic concepts of topological band structures, and then explain what it means to realize topological band structures in photonic systems. I will particularly emphasize some important differences with respect to solid-state electron systems. I then present some of my own works in topological photonics, such as the synthetic dimensions in photonic systems, which allows one to explore models and phenomena in high dimensions including the four-dimensional quantum Hall effect.

This is the first joint workshop between iCeMS (Kyoto Univ.) and iTHEMS (RIKEN). The WS is co-hosted by KUIAS (Kyoto Univ.), iTHEMS (RIKEN) and MACS Program (Kyoto Univ.). By exploring the forefront of experimental and mathematical biology, this workshop aims to stimulate novel research directions in these areas and strengthen the connection between Kyoto Univ. and RIKEN. Those who plan to attend the "get-together", please register before June 22 (Fri.) noon.

Co-hosted by
Kyoto University Institute for Advanced Study (KUIAS), Kyoto Univ.
Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN
MACS Program (MACS), Kyoto Univ.

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.

This seminar is aimed at scientists in general, not only to mathematicians.

10:00-10:45
Title: Multiple zeta functions associated with 2-colored rooted trees
Speaker: Dr. Masataka Ono (Keio University)
Abstract: In our recent work, we introduced a combinatorial object and finite sum associated with them which we call finite multiple zeta values associated with 2-colored rooted trees and gave a unified interpretation to some types of finite multiple zeta values. In this talk, we introduce multiple zeta function associated with 2-colored rooted tree and discuss its analytic properties, for example, the possible singularities and functional equations.

10:55-11:40
Title: Modular forms and trace formulas with applications to equidistributions of their Fourier coefficients
Speaker: Dr. Shingo Sugiyama (Nihon University)
Abstract: Modular forms are interesting objects in number theory as they are related to arithmetic problems. Trace formulas of Hecke operators acting on modular forms are very useful tools to study arithmetic invariants: Fourier coefficients, special values of L-functions, Hurwitz class numbers. We will start fundamental notions on modular forms and trace formulas of Hecke operators for non-experts, and introduce our results on a generalization of Serre’s vertical Sato-Tate law. Some results in this talk are based on a joint work with Masao Tsuzuki (Sophia University).

11:50-12:35
Title: On a generalization of Dobinski's formula
Speaker: Yoshinosuke Hirakawa (Keio University)
Abstract: Dobinski's formula is a very classical formula, which expresses the Bell number as an infinite series. Here, the Bell number is the number of partitions of a finite set. Such a "combinatorial-analytic" formula should lead us to more beautiful number theory. In this talk, we introduce a generalization of Dobinski's formula by means of a certain multiple generalization of the exponential function.

The International Symposium on Quantum Fluids and Solids (QFS) will be held at Ito International Research Center (IIRC) on Hongo campus of the University of Tokyo, Japan, from July 25 through 31, 2018. One of the sponsors of this conference is iTHEMS.

The QFS series started forty-three years ago making it one of the oldest series of international conferences in the field of low temperature physics. It has historically been focusing on physics of liquid and solid helium and hydrogen. But in this century its scope is expanding widely from laser cooled cold atoms to topological matters. At QFS2018 in Tokyo, this trend will be continued and with even more interdisciplinary aspects emphasized between the traditional subjects and those in broader physical systems.