Seminar

Several identities related to the degenerate Bernoulli polynomials and numbers

February 24 (Sat) at 16:00 - 17:00, 2018

Takao Komatsu (Professor, Wuhan University, China)

In this talk we demonstrate some relations in degenerate Bernoulli polynomials, which may be expressed as a general convolution identity. We also show some properties of hypergeometric degenerate Bernoulli polynomials and numbers.

Venue: Seminar Room #160

Event Official Language: English

Diophantine Frobenius Problems — counting theory, generating function and zeta functions

February 23 (Fri) at 16:00 - 17:00, 2018

Takao Komatsu (Professor, Wuhan University, China)

When a_1, ...,a_m are relatively prime positive integers, the number of solutions of the linear Diophantine equation a_1 x_1 + … + a_m x_m = b in non-negative integers x_1, ...,x_m, for any integer b, is our concern. We show several formulas to give the largest integer b without solution. Then we discuss the generating function of the number of solutions. Finally, we derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies a set of new identities for the Hurwitz zeta function.

Venue: Seminar Room #160

Event Official Language: English

Statistical mechanics of tissue homeostasis

January 22 (Mon) at 14:00 - 15:00, 2018

Kyogo Kawaguchi (The University of Tokyo)

Adult tissues undergo rapid turnover as mature cells are continuously lost and new cells arise through cell division. The balance between the gain and loss of cells must be finely orchestrated to maintain tissues, but how this balance is achieved remains largely unknown. Previous works [1] have used universal scaling laws to claim that the fate choice of stem cells (division or differentiation) are made strictly cell-autonomously. However, we recently recorded every stem cell fate choice within the mouse skin epidermal regions over one week and found that, far from being cell-autonomous, stem cell loss by differentiation is compensated by direct neighboring division [2]. In this talk, I will describe a model of tissue homeostasis using a macroscopic nonequilibrium setup, and explain how the coarse-graining of this model will lead to the effective dynamics of the voter model (DP2). I will show how we can use the property of dynamical crossover in the model -from the cell-autonomous regime (critical birth-death model) to the fate-coordinated regime (voter model)- to measure the length and time scales of stem cell coordination. I will then explain the pitfall in two-dimensions of using scaling relations for the clonal fate trace of cells, and present the workaround we used in the data analysis to definitively show the existence of cell-to-cell fate correlation.

Venue: Common Room #246-248

Event Official Language: English

Compact-star phenomena and equation of state

December 28 (Thu) at 10:30 - 11:30, 2017

Shun Furusawa (Special Postdoctoral Researcher, iTHEMS)

Venue: SUURI-COOL (Kyoto)

Event Official Language: English

Theoretical study on the universality in biological clock and its species-specificity

December 27 (Wed) at 16:00 - 17:00, 2017

Gen Kurosawa (Research Scientist, iTHEMS / Research Scientist, Theoretical Biology Laboratory, RIKEN)

Venue: SUURI-COOL (Kyoto)

Event Official Language: English

Mathematical Modeling of Retinal Cellular Mosaic Pattern Formation

December 27 (Wed) at 13:30 - 14:30, 2017

Noriaki Ogawa (Postdoctoral Researcher, Interdisciplinary Theoretical Science Research Group (iTHES), RIKEN)

Venue: SUURI-COOL (Kyoto)

Event Official Language: English

Topology of linear operators and topological insulators

December 27 (Wed) at 10:30 - 11:30, 2017

Yosuke Kubota (Research Scientist, iTHEMS)

Venue: SUURI-COOL (Kyoto)

Event Official Language: English

Chiral Phases in Frustrated 2D Antiferromagnets and Fractional Chern Insulators

December 21 (Thu) at 11:00 - 12:00, 2017

Eduardo Fradkin (University of Illinois, USA)

Venue: #535-537, 5F, Main Research Building

Event Official Language: English

Baryon Asymmetry of the Universe generated by Helical Hypermagnetic fields through chiral anomaly

December 20 (Wed) at 11:00 - 12:00, 2017

Kohei Kamada (Center for Theoretical Physics of the Universe, Institute for Basic Science, Republic of Korea)

Recent observations of TeV blazars by Fermi identified deficits of secondary GeV cascade photons.These observations can be explained by intergalactic magnetic fields, which may have a primordial origin.If the magnetic fields are helical and generated before the electroweak symmetry breaking,nontrivial interaction between (hyper)magnetic fields and other particles can cause some interestingand non negligible phenomena in the early Universe. In this talk, I will show that the baryon asymmetry can be generated by the chiral anomaly and this mechanism might be responsible for the present baryon asymmetry of the Universe. The intergalactic magnetic fields are its smoking-gun. If this mechanism is responsible for the present Universe,the BSM physics is needed for the generation of (hyper)magnetic fields but not for the baryogenesis.

Venue: Seminar Room #160

Event Official Language: English

A New Look at Matrix Models for QCD3

November 24 (Fri) at 16:30 - 18:00, 2017

Takuya Kanazawa

Non-chiral random matrix models for QCD in 2+1 dimensions and their new generalizations will be discussed.

Venue: Seminar Room #160

Event Official Language: English

The Riemann-Roch theorem

September 26 (Tue) at 14:00 - 15:00, 2017

Yosuke Kubota (Research Scientist, iTHEMS)

In the mid- 19th century, B. Riemann introduced the notion of Riemann surface in his Ph.D thesis on complex analysis. Together with non-Euclidean geometry, the theory of Riemann surface is a germination of modern geometry in both algebraic and analytic sense. In this talk, I will give an introduction of the theory of Riemann surface centering around the Riemann-Roch theorem. It is an important prototype of the Atiyah-Singer index theorem, the starting point of my research field.

Venue: Seminar Room #160

Event Official Language: English

Connections of Pair Correlations to Equidistribution and Additive Energy

August 31 (Thu) at 13:30 - 15:00, 2017

Thomas Lachmann (Graz University of Technology, Austria)

Venue: Common Room #246-248

Event Official Language: English

Pulsar Winds: Ultimate Relativistic Outflows

August 29 (Tue) at 13:30 - 14:30, 2017

Dmitry Khangulyan (Rikkyo University)

A highest density body that features the strongest magnetic field launches, no surprise, an ultimate outflow -- pulsar wind. Despite their relativistic nature and complexity, a few simple analogies can help us to understand the essence of pulsar physics. I will present several links connecting basic mechanics and electrodynamics, every-day thermodynamics and hydrodynamics to the processes taking place in the vicinity of pulsars. These fundamental relations not only provide a simple mental image for the pulsar physics but also have their imprint in high-energy data obtained from pulsars and pulsar wind nebulae.

Venue: #433, Main Research Building

Event Official Language: English

Joint Seminar with Condensed Matter Theory Laboratory

July 20 (Thu) at 13:30 - 15:00, 2017

Shinsei Ryu (Associate Professor, Department of Physics and the College, The University of Chicago, USA)

Venue: #435-437, Main Research Building

Event Official Language: English

An invitation to number theory

July 10 (Mon) at 13:30 - 14:30, 2017

Hiroyasu Miyazaki

The goal of number theory is to reveal the mystery of natural numbers 1,2,3…. It has a long history, and it is still developing by exchanging ideas with many other branches of mathematics. In the long history, number theory had been thought of as a pure mathematics with no direct application outside mathematics. However, the rapid development of computer science changed the situation: the theory of prime numbers has been applied to code theory, cryptography, random number generation etc. It seems that there are several researches in physics and biology using the method of number theory, too. The aim of this talk is to give a beginner-friendly introduction to number theory. Among many topics, I will focus on very fundamental and important concepts: the “p-adic numbers” and the “finite fields.” I hope that this talk will motivate you to relate your research to number theory.

Venue: Seminar Room #160

Event Official Language: English

Braids and topological mixing

June 26 (Mon) at 14:00 - 15:00, 2017

Eiko Kin (Osaka University)

In mathematics, the braids are important tools for the knot theory, hyperbolic geometry, and dynamical systems etc. In the last ten years, the braids have been used to study mixing in fluids. Various simple mixing devices (e.g. taffy machines) have been developed. These devices utilize a particular type of braid, so-called a pseudo-Anosov type. The notion of pseudo-Anosov braids comes from the Nielsen-Thurston theory on the surface automorphisms, and the theory says that the devices using pseudo-Anosov braids are "efficient" in some sense. In this lecture, I will give a quick introduction of the Nielsen-Thurston theory and the classification of braids. I will give a picture of the "complexity" forced by pseudo-Anosov braids. In particular, I will explain why pseudo-Anosov braids are useful and why they can be used to build interesting mixing devices. Cosponsored by RIKEN iTHEMS and AIP Mathematical Science Team

Venue: RIKEN Tokyo Liaison Office (Nihonbashi)

Event Official Language: English

Homological algebra, Renormalization and Transversality

June 26 (Mon) at 10:30 - 11:30, 2017

Kenji Fukaya (Permanent Member, Simons Center for Geometry and Physics, Stony Brook University, New York, USA)

Transversality is a basic concept of differential topology and theory of manifold. Homological algebra may be regarded as a method to approximate `spaces' by an algebra and is a basic concept in agebraic topology. I would like to explain in this talk how they are related to some basic problem of quantum field theory such as renormalization. Cosponsored by RIKEN iTHEMS and AIP Mathematical Science Team

Venue: RIKEN Tokyo Liaison Office (Nihonbashi)

Event Official Language: English

Galois representations and the Langlands correspondence

June 8 (Thu) at 13:30 - 14:30, 2017

Kazuki Tokimoto (Kyoto University)

The Langlands correspondence relates number-theoretic objects to completely different objects. While still largely conjectural, it has attracted interests of many mathematicians over the years. It is known that the local Langlands correspondence in a special case can be constructed in a geometric way (the non-abelian Lubin-Tate theory). In this talk, I will explain some basic concepts in mathematics (such as groups, representations and Galois groups) and then try to convey some flavor of my result related to the non-abelian Lubin-Tate theory.

Venue: Seminar Room #160

Event Official Language: English

Atypicality of most few-body observables

May 29 (Mon) at 13:30 - 14:30, 2017

Ryusuke Hamazaki (The University of Tokyo)

Understanding how isolated quantum systems thermalize has recently gathered renewed interest among theorists, thanks to the experimental realizations of such systems. The eigenstate thermalization hypothesis (ETH) is particularly investigated as a sufficient condition for the approach to thermal equilibrium. It states that diagonal matrix elements of an observable for the energy eigenstates are almost the same within a small energy shell. The ETH is justified for an observable and a Hamiltonian whose respective eigenbases are typically oriented to each other; i.e., for almost all unitary transformations of these two eigenbases with respect to the uniform Haar measure. In this seminar, we consider a Hamiltonian with few-body interactions and random observables without assuming the uniform Haar measure. These observables are chosen in an operational manner as random linear combinations of the operator basis of spins. We show that most few-body observables have atypical matrix elements when the energy width is not exponentially small with the system size. Namely, the maximum fluctuation for diagonal matrix elements is larger than that predicted by the uniform Haar measure.

Venue: #433, Main Research Building

Event Official Language: English

Guiding principles to develop tough polymer materials: An exactly solvable model

May 25 (Thu) at 10:30 - 11:30, 2017

Naoyuki Sakumichi (Project Assistant Professor, Soft Matter Center, Ochanomizu University)

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump [1-3], i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies [4] over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description [5]. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.

Venue: Seminar Room #160

Event Official Language: English