15:00~16:00: Yasuo Ohno (Tohoku University)
"On special values of the multiple zeta functions of Arakawa-Kaneko type"
Arakawa-Kaneko's zeta function is a kind of generalization of the Riemann zeta function by using polylogarithms. I am planning to introduce two topics on combinatorics around its values at positive or negative integral points. This talk is based on joint work with N. Kawasaki.

16:20~17:20: Yuta Suzuki (Nagoya University)
"On relatively prime amicable pairs"
A famous Greek mathematician, Pythagoras tried to find symbolical meanings in numbers. One famous example of such symbolism in numbers is amicable pair, which was introduced as a symbol of friendship. A pair of positive integers $(M,N)$ is called an amicable pair if the sum of all divisors of $M$ except $M$ itself is equal to $N$ and the sum of all divisors of $M$ except $N$ itself is also equal to $M$. The smallest example is $(220,284)$.
Even amicable numbers are introduced more than 20 centuries ago, most of their properties are still unknown. For example, the infinitude of amicable pairs has not yet been proven. In this talk, we pick up a conjecture of Gmelin (1917), which claims that there is no relatively prime amicable pairs, and try to introduce some atmosphere of "modern elementary number theory". In particular, we improve Pollack's partial result (2015) on Gmelin's conjecture.

In the March RIKEN Day, we will have a talk with Ade Irma Suriajaya, a mathematician who is researching "prime numbers", on the theme of "the wonder of numbers".

See related links for details.

Multiscale modeling in biomedical engineering is gaining momentum because of progress in supercomputing, applied mathematics, and quantitative biomedical engineering.

For example, scientists in various disciplines have been advancing, slowly but steadily, the simulation of blood including its Olowing and the physiological properties of such components as red blood cells, white blood cells, and platelets. Platelet activation and aggregation stimulate blood clotting that results in heart attacks and strokes causing nearly 20 million deaths each year.

To reduce such deaths, we must discover new drugs. To discover new drugs, we must understand the mechanism of platelet activation and aggregation. To model platelets’ dynamics involves setting the basic space and time discretization in huge ranges of 5-6 orders of magnitudes, resulting from the relevant fundamental interactions at atomic, to molecular, to cell, to Oluid scales.

To achieve the desired accuracy at the minimal computational costs, we must select the correct physiological parameters in the force Oields such as the Morse potential and Hooke’s law as well as the spatial and temporal discretization, by machine learning.

We demonstrate our preliminary results of speeding up a multiscale two-platelet aggregation simulation, while maintaining sufOicient accuracy, by nearly one order of magnitude, compared with traditional algorithm that uses the smallest of all temporal and spatial scales in order to capture the Oinest details of the dynamics. We present our analyses of the accuracies and efOiciencies of the representative modeling. We will also outline the general methodologies of multiscale modeling of cells at atomic resolutions.

Prof. Kohji Matsumoto (Nagoya University)
"An overview of the theory of multiple zeta-functions"
Multiple zeta-functions are generalizations of the Riemann zeta-function, and its theory has been rapidly developed in these decades. It is connected with various fields of mathematics and mathematical physics. In this talk I will give an overview of some part of recent developments, mainly from the analytic viewpoint.

Prof. Jörn Steuding (University of Würzburg, Germany)
"On the Infinite in Number Theory"
Beginning with two simple examples from elementary number theory (one of diophantine origin and one of arithmetical nature), we discuss the role of “infinity” in number theory. We touch upon topics like how to find good rational approximations to irrational quantities and the distribution of prime numbers. We conclude with a motivation of the big open question in this field, namely, the Riemann hypothesis (one of the six unsolved millennium problems) and the Langlands program.

March 22–26, 2019
Main Conference (invited talks, posters and a limited number of short contributed talks)

Welcome Reception: March 22, 2019 (18:00~20:00)
Conference Dinner: March 25, 2019 (18:30~21:00)

March 27, 2019 (9:30~17:00)
One-day Workshop (a series of short contributed talks by young researchers to facilitate active discussions)

ORGANIZING COMMITTEE
Ade Irma Suriajaya (RIKEN)
Yoshinosuke Hirakawa (Keio University)
Masataka Ono (Kyushu University)
Shin-ichiro Seki (Tohoku University)
Keiju Sono (Ehime University)
Shingo Sugiyama (Nihon University)
Yuta Suzuki (Nagoya University)

ADVISORY COMMITTEE
Tetsuo Hatsuda (RIKEN iTHEMS)
Kenichi Bannai (Keio University, RIKEN AIP Center)

Arithmer Inc. is a startup company providing with business solutions in the field of AI / machine learning / robotics, which emerged from Mathematical Science Dep., Univ. of Tokyo.
I will present our recent success stories and ambitious attempts in which applied mathematics is fully utilized, such as optical character recognition, automatic artificial tooth design, scoring driver's skill from movie, and image measurement of human body.

Speakers:
Takuya Ueda (Tohoku Univ. Hospital)
Noriaki Ogawa (RIKEN iTHEMS)
Takayuki Sakajo (Math. Dep., Kyoto Univ.)
Yoshiki Sugitani (AIMR, Tohoku Univ.)
Jun Seita (RIKEN MIH)
Tetsuro Sekine (Nippon Medical School Hospital)
Masato Taki (RIKEN iTHEMS)
Kenji Takizawa (Faculty of Sci. and Eng., Waseda U.)

Hosted by SUURI-COOL Sendai（iTHEMS-AIMR Mathematical Science Cooperative Lab.）
Co-hosted by iTHEMS, AIMR
Sponsored by CREST "New Challenges for Mathematical Modeling in Clinical Medicine"

Organizers: Hiroshi Suito (AIMR), Tetsuo Hatsuda (iTHEMS)

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector potential defined in momentum space. Inspired by developments in high-energy physics, where higher-form Kalb-Ramond gauge fields were introduced, I hereby explore the existence of "tensor Berry connections" in quantum matter. My approach consists in a general construction of effective gauge fields, which I ultimately relate to the components of Bloch states. I apply this formalism to various models of topological matter, and I investigate the topological invariants that result from generalized Berry connections. I introduce the 2D Zak phase of a tensor Berry connection, which I then relate to the more conventional first Chern number; I also reinterpret the winding number characterizing 3D topological insulators to a Dixmier-Douady invariant, which is associated with the curvature of a tensor connection. Besides, my approach identifies the Berry connection of tensor monopoles, which are found in 4D Weyl-type systems in ultracold atoms.

GRIPS (Graduate-level Research in Industrial Projects for Students)-Sendai program was held last summer (June 18 - Aug. 10, 2018) with the support of iTHEMS as well as other institutions and companies. Two industrial projects were launched under the suggestion of TOYOTA and NEC, and two teams composed of US and Japanese students have worked intensively to find solutions of these problems. See for the details of the GRIPS program and the summary of activities at GRIPS-Sendai 2018.

This year, GRIPS-Sendai program will be held from June 17 through Aug. 9, 2019 with a larger scale under the support of iTHEMS. Stay tuned for further information.