Seminar

On special values of the multiple zeta functions of Arakawa-Kaneko type

March 16 (Sat) at 15:00 - 17:30, 2019

Yasuo Ohno (Professor, Mathematical Institute, Tohoku University)
Yuta Suzuki (JSPS Research Fellow, Graduate School of Mathematics, Nagoya University)

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.

Venue: Seminar Room #160

Event Official Language: English

Joint value distribution of quadratic L-functions (joint work with Hirofumi Nagoshi)

February 25 (Mon) at 16:20 - 17:20, 2019

Hidehiko Mishou (Tokyo Denki University)

In 1975, Voronin established the universality theorem for the Riemann zeta function. Roughly speaking this theorem asserts that any holomorphic function on 1/2

Venue: Seminar Room #160

Event Official Language: English

Symmetric Tornheim double zeta functions

February 25 (Mon) at 15:00 - 16:00, 2019

Takashi Nakamura (Tokyo University of Science)

Let $s,t,u \in {\mathbb{C}}$ and $T(s,t,u)$ be the Tornheim double zeta function. We investigate some properties of symmetric Tornheim double zeta functions. As a corollary, we give explicit evaluation formulas for $T(s,t,u)$ in terms of series of the gamma function and Riemann zeta function.

Venue: Seminar Room #160

Event Official Language: English

Biology Seminar

December 13 (Thu) at 14:00 - 16:00, 2018

Yusuke Kazama (Team Leader, Plant Genome Evolution Research Team, RIKEN Nishina Center for Accelerator-Based Science (RNC))
Jeffrey Fawcett (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

Speaker: Jeffrey Fawcett (iTHEMS) Title: Introduction to Genomics Abstract: The genetic information, or the genome, of almost all species are determined by the order (i.e. the "sequence") of millions of nucleotides represented by A, G, C, and T. I will first outline what we already know about the genome, how they differ across species and individuals, and how we can study them. I will then briefly introduce "3D Genomics", a topic that is becoming quite hot in biology now: the genome is not only a one dimensional "sequence" information but the chromosomes must be folded up to fit into the cell nuclei, and this 3D structure of the chromosome and the spatial positioning of the genes might be important for the biology of each species. Speaker: Yusuke Kazama (Nishina Center) Title: 大きな玉ほど大きく壊す：シロイヌナズナを用いて明らかにした重イオンビーム変異の特徴 Abstract: 重イオンビームはγ線やX線よりも線エネルギー付与（LET)が高いことで知られ、核種やビームの速度を選択することによりLETを調節して照射することもできる。私たちは、モデル植物シロイヌナズナを用いてLETが変異誘発に与える影響を調べ、変異率が最大となるLET＝30.0 keV/μm(LETmax)を発見した。突然変異体の全ゲノム解析を行ない、LETmaxでは塩基置換や小さい欠失が多いのに対し、LET=290 keV/μmでは大きな欠失や染色体再編成の頻度が高いことを明らかにした。目的や材料に合わせて「高効率で1遺伝子を破壊するにはLETmax照射」を、「2遺伝子以上の破壊や染色体再編成の誘発には高LET照射」を行うオンデマンド照射技術を確立した。今後は、染色体再編成が植物の形質に与える影響を、3Dゲノム構造の変化、クロマチン構造の変化、遺伝子発現の変化に注目して研究していきたい。

Venue: Seminar Room #160

Event Official Language: English

Cosmic-ray air showers: new arrays for searching origins and link to the collider physics

December 7 (Fri) at 14:00 - 15:00, 2018

Takashi Sako (Institute for Cosmic Ray Research (ICRR), The University of Tokyo)

Venue: Seminar Room #160

Event Official Language: English

Probability density functions attached to zeta functions

December 6 (Thu) at 16:00 - 17:00, 2018

Masahiro Mine (Tokyo Institute of Technology)

The study of the value-distribution of the Riemann zeta function is a classical topic in analytic number theory. In 1930s, Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. After Bohr and Jessen, similar results were proved for many other zeta functions. In this talk, I'll talk about density functions of such probabilities attached to the value-distributions of zeta functions. The density functions, which were named M-functions'' by Ihara, are connected with mean values of zeta functions, distributions of zeros of zeta functions, and so on.

Venue: Seminar Room #160

Event Official Language: English

On A_2-liftings of sum formulas and Bowman-Bradley type formulas for finite multiple zeta values

November 22 (Thu) at 11:40 - 12:40, 2018

Shin-ichiro Seki (Tohoku University)

Both the sum formula and Bowman-Bradley's theorem for multiple zeta values are well known. Recently, Saito and Wakabayashi proved counterparts of these two formulas for A-finite multiple zeta values. In this talk, I will explain that A_2-liftings of some parts of Saito-Wakabayashi's results have simple forms using Seki-Bernoulli numbers. The first part of this talk is a joint work with Shuji Yamamoto. The second part is a joint work with Hideki Murahara and Tomokazu Onozuka.

Venue: Seminar Room #160

Event Official Language: English

Generating functions of CM & RM values

November 22 (Thu) at 10:30 - 11:30, 2018

Toshiki Matsusaka (Kyushu University)

The special values of the elliptic modular j function j(z) at imaginary quadratic points are known as singular moduli (CM values), and play important roles in algebraic number theory. As a real quadratic analogue, Kaneko (2009) defined the `values’ of j(z) at real quadratic points (RM values). In 2011, Duke-Imamoglu-Toth showed that the generating function of the traces of these CM & RM values becomes a harmonic Maass form of weight 1/2. In this talk, I shall introduce a new class called polyharmonic weak Maass forms, inspired by works of Lagarias-Rhoades on the Kronecker limit formula, and give a generalization of Duke-Imamoglu-Toth’s work for any polyharmonic weak Maass form.

Venue: Seminar Room #160

Event Official Language: English

Study of density dependent nuclear symmetry energy by using heavy RI collisions at RIKEN-RIBF

November 16 (Fri) at 14:00 - 16:00, 2018

Tada-aki Isobe (Senior Research Scientist, Radioactive Isotope Physics Laboratory, RIKEN Nishina Center for Accelerator-Based Science (RNC))

The nuclear Equation of State (EoS) is a fundamental property of nuclear matter. An international collaboration, named SPiRIT, to study the density dependence of asymmetry term in nuclear EoS has been formed since 2009. The main aim of this collaboration is to make the constraint on the asymmetry term of nuclear EoS for higher dense region($\rho>\rho_0$). In this talk, the conceptual idea of the project will be given in addition to some result of data analysis for the physics run performed at 2016 spring.

Venue: Seminar Room #160

Event Official Language: English

Spintronics in Non-Inertial Frames

November 15 (Thu) at 13:00 - 18:00, 2018

Mamoru Matsuo (University of Chinese Academy of Sciences, China)

Venue: Seminar Room #160

Event Official Language: Japanese

New Venues in Formation and Detection of Primordial Black Hole Dark Matter

November 12 (Mon) at 14:00 - 15:00, 2018

Volodymyr Takhistov

Abstract: Primordial black holes (PBH) provide an attractive non-particle dark matter (DM) candidate. I will discuss a novel PBH production mechanism that can appear generically in models with scalar fields. Recent re-evaluations of PBH constraints suggest that the open parameter space for PBHs to constitute all of dark matter is appreciably larger than previously thought. I will show how compact stars can serve as laboratories for probing it. The variety of resulting novel astrophysical signals are of particular interest to the vibrant field of multi-messenger astronomy. More-so, PBH-star interactions suggest an elegant resolution to some of the most puzzling questions in astrophysics, such as the origin of gold and other heavy elements.

Venue: Seminar Room #160

Event Official Language: English

The 28th QCD Club

November 9 (Fri) at 15:00 - 17:00, 2018

Title: Application of a gradient flow method to thermodynamics of QCD with dynamical quarks Language: Japanese or English

Event Official Language: English

Population genetics of duplicated genes

November 1 (Thu) at 15:30 - 18:00, 2018

Hideki Innan (The Graduate University for Advanced Studies (SOKENDAI))

Venue: Seminar Room #160

Event Official Language: English

Assembly rules and a theory for invasion and extinction in minimal food webs

October 29 (Mon) at 15:00 - 18:00, 2018

Namiko Mitarai (Associate Professor, Niels Bohr Institute, University of Copenhagen, Denmark)

We propose a theory of the evolution of a minimal food web by sequential invasion of new species [1]. Our theory is based on the standard generalized Lotka-Volterra equations, where basal species compete through resource depletion [2]. The considered food webs are “minimal”, as each species only feeds on a single resource, leading to a hierarchical, tree-like food web [1,3]. We prove that at each invasion step there is one uniquely determined outcome: either the invader peacefully coexists with the residents and resources are re-distributed; the invader is eliminated; or one or several of the resident species are removed in a uniquely defined extinction cascade. At the end of either of these processes the resulting food web relaxes to a globally stable (and feasible) steady state. We break down the essence of our theory in the conceptual “invasion extinction model” (IEM), which allows us to analytically compute the persistence time and the extinction size distribution.

Venue: Seminar Room #160

Event Official Language: English

Relations between fractal dimensions and arithmetic progressions

October 23 (Tue) at 11:35 - 12:35, 2018

Kota Saito (Nagoya University)

In this talk we give estimates for the dimensions of sets in real numbers which uniformly avoid finite arithmetic progressions. More precisely, we say that $F$ uniformly avoids arithmetic progressions of length $k\geq 3$ if there is an $\epsilon>0$ such that one cannot find an arithmetic progression of length $k$ and gap length $\Delta>0$ inside the $\epsilon\Delta$ neighbourhood of $F$. Our main result is an explicit upper bound for the Assouad (and thus Hausdorff) dimension of such sets in terms of $k$ and $\epsilon$. In the other direction, we give examples of sets which uniformly avoid arithmetic progressions of a given length. We also consider higher dimensional analogues of these problems, where arithmetic progressions are replaced with arithmetic patches lying in a hyperplane. As a consequence, we obtain a discretised version of a `reverse Kakeya problem': we show that if the dimension of a set in $\mathbb{R}^d$ is sufficiently large, then it closely approximates arithmetic progressions in every direction. The above is a joint work with Fraser and Yu. Finally we show that the converse of `reverse Kakeya problem' does not hold. This is a single-author work.

Venue: Large Meeting Room, 2F Welfare and Conference Building (Cafeteria)

Event Official Language: English

Generalized Erdös and Obláth theorem for polynomial-factorial Diophantine equations

October 23 (Tue) at 10:30 - 11:30, 2018

Wataru Takeda (Nagoya University)

Diophantine equations are equations where only integer solutions are accepted. There are many types of Diophantine equations and many results are known. Our Diophantine equation is of the form x^n+y^n=m!. Erdös and Obláth showed that the Diophantine equation x^2+y^2=m! has only two positive integer solutions (x,y,m)=(1,1,2),(12,24,6). In this talk, the factorial function m! is replaced with a generalized factorial function Π(m) over number fields. Then whether there are infinitely many solutions or not depends on the number field. We give necessary and sufficient condition for existence of infinitely many solutions of x^2+y^2=Π(m). More generally, we introduce an observation for higher degree equation x^n+y^n=Π(m).

Venue: Large Meeting Room, 2F Welfare and Conference Building (Cafeteria)

Event Official Language: English

Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser

September 28 (Fri) at 13:30 - 17:00, 2018

Ryo Hanai (Osaka University)

Venue: Seminar Room #160

Event Official Language: Japanese

Number Theory Seminar: 3 Talks

July 24 (Tue) at 10:00 - 12:35, 2018

Masataka Ono (Keio University)
Shingo Sugiyama (Nihon University)
Yoshinosuke Hirakawa (Keio University)

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.

Venue: Seminar Room #160

Event Official Language: English

Introduction to topological band structure

July 6 (Fri) at 10:30 - 17:30, 2018

Tomoki Ozawa (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

In this seminar, I give an introduction to topological band structures. Topological band structure is the fundamental idea to understand phenomena such as the quantum Hall effect, topological insulators, and topological superconductors. Although originally found in fermionic electron systems, topological band structure is essentially a single-particle property, and thus the same phenomenon can arise also in bosonic systems. In fact, topological band structure does not even need quantum mechanics; topological band structure can arise in classical waves inside a periodic medium, such as electromagnetic waves or classical mechanical waves. In this seminar, I first give a brief introduction to key concepts in topological band structures, such as Berry curvature, Chern number, bulk-edge correspondence, and ten-fold way classification of topological insulators. I then explain how topological band structure can arise in classical systems, giving a brief introduction to the field of topological photonics and topological mechanics.

Venue: Seminar Room #160

Event Official Language: Japanese

Topological Photonics and the four-dimensional quantum Hall effect

July 3 (Tue) at 15:00 - 17:00, 2018

Tomoki Ozawa (Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS))

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.

Venue: 1F Meeting Room, AIMR Main Building

Event Official Language: English