Khovanov homology theory - an introduction to categorification

May 13 (Fri) at 14:00 - 16:30, 2022

Taketo Sano (Special Postdoctoral Researcher, iTHEMS)

Jones polynomial is a knot invariant discovered by V. F. R. Jones in 1984. Not only that it is a useful mathematical tool, the discovery led to opening up a new research area, quantum topology, which connects quantum mechanics and low-dimensional topology. In 2000, M. Khovanov introduced a “categorification of the Jones polynomial”, which is now called Khovanov homology, and made categorification one of the fundamental concept in knot theory. Now what does categorification mean, and what is it good for? In this talk, assuming that many of the audience are not familiar with abstract category theory, I will start from easy examples of categories and categorifications, for example categorification of natural numbers, and explain why they are something natural to think of. In the latter part, I will briefly explain the construction of Khovanov homology, and introduce several related topics.

Venue: Hybrid Format (Common Room 246-248 and Zoom)

Event Official Language: English

Classical and Quantum Chaos

May 12 (Thu) at 16:00 - 17:00, 2022

Akira Shudo (Professor, Department of Physics, Graduate School of Science, Tokyo Metropolitan University)

Classical and quantum mechanics in multi-dimensions are qualitatively different from those in one-dimension since they are no more integrable in general and chaos appears in the dynamics. This brings a great deal of complexity or even richness both in classical and quantum dynamics. Especially in generic nonintegrable systems which are neither completely integrable nor fully chaotic, phase space becomes a mixture of regular and chaotic components. Such an aspect is a source of inexhaustible questions not only in the past but in the future. We here overview classical and quantum chaos in Hamiltonian systems.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: Topological Superconductors and Quantum Computing

May 9 (Mon) at 14:00 - 15:30, 2022

Ching-Kai Chiu (Senior Research Scientist, iTHEMS)

Venue: via Zoom

Event Official Language: English

Diversity of Asgardarchaota and Theoretical verification of the endosymbiotic theory

April 28 (Thu) at 10:00 - 11:00, 2022

Daiki Kumakura (Ph.D. Student, Graduate School of Life Science, Hokkaido University)

How did intracellular symbiosis occur and give rise to eukaryotic ancestor? This question has been considered to the two theories as three-domain theory and eocyte theory. Here I present asgard archaea, the archaeon closest to eukaryotes. Asgard archaea is an archaeon found at a deep-sea sampling site called Loki's castle at between Greenland and Norway. So all the closely related species are named after Norse mythology (Loki-, Thor-, Odin-, Heimdall-, etc.). Unlike other archaea, asgard archaea has many eukaryotic-specific proteins and is considered to be the closest to eukaryotes. In 2020, one of the asgard archaea species was finally successfully cultured. This archaeon was cultured and found to take on a branch-like structure. It is then hypothesized that intracellular symbiosis between this archaeon and the ancestor of mitochondria resulted in the ancestor of today's eukaryotic cells. In this talk, I would like to discuss with you the explanation of how we arrived at this hypothesis and how to construct a mathematical model.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 4

April 27 (Wed) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

iTHEMS x academist Online Event "World of Mathematical Sciences 2022"

April 24 (Sun) at 10:00 - 16:30, 2022

Masaki Taniguchi (Special Postdoctoral Researcher, iTHEMS)
Hidetoshi Taya (Special Postdoctoral Researcher, iTHEMS)
Akira Harada (Special Postdoctoral Researcher, iTHEMS)
Yingying Xu (Special Postdoctoral Researcher, iTHEMS)
Euki Yazaki (Postdoctoral Researcher, iTHEMS)

Venue: via Zoom

Event Official Language: Japanese

Recurrence theorems for topological Markov chains

April 22 (Fri) at 17:00 - 19:00, 2022

Cédric Ho Thanh (Postdoctoral Researcher, Prediction Science Laboratory, RIKEN Cluster for Pioneering Research (CPR))

Recurrence theorems place conditions under which probabilistic systems, specifically Markov chains, are expected to visit certain states infinitely often. For example, a printer with its many moving parts and the random requests it receives, may be described as a probabilistic system, and recurrence of the "ready to print" state is desirable. Recurrence theorems in the case of finite Markov chains are widely known. In this talk, we are interested in generalization to the infinitary setting. As it turns out, some care has to be put in the definition of infinite Markov chains. Rather than simply infinite, the introduct topological Markov chains, and show how standard constructions can be naturally extended to thisframework: path spaces, cylinder sets, as well as the semantic of LTL and PCTL. With all these tools in hand, we finally state our recurrence theorems. This is work in progress in collaboration with Natsuki Urabe and Ichiro Hasuo. This seminar is hold in a hybrid style. If you want attend the seminar onsite, please contact to Keita Mikami.

Venue: Hybrid Format (Common Room 246-248 and Zoom) (Main Venue)

Event Official Language: English

How is turbulence born: Statistical mechanics and ecological collapse in transitional fluids

April 22 (Fri) at 15:00 - 16:30, 2022

Hong-Yan Shih (Assistant Research Fellow, Institute of Physics, Academia Sinica, Taiwan)

The onset of turbulence is ubiquitous in daily life and is important in various industrial applications, yet how fluids become turbulent has remained unsolved for more than a century. Recent experiments in pipe flow finally quantified this transition, showing that non-trivial statistics and spatiotemporal complexity develop as the flow velocity is increased. Combining numerical simulations of the hydrodynamics equations and an effective theory from statistical mechanics, we discovered the surprising fact that fluid behavior at the transition is governed by the emergent predator-prey dynamics, leading to the mathematical prediction that the laminar-turbulent transition is analogous to an ecosystem on the edge of extinction. This prediction demonstrates that the laminar-turbulent transition is a non-equilibrium phase transition in the directed percolation universality class, and provides a unified picture of transition to turbulence in various systems. I will also show our recent progresses on transitional turbulence, including how an extended ecological model with energy balance successfully recapitulates the spatiotemporal patterns beyond the critical point, and the determination of the critical behavior and an emergent novel phase under interactions in the experimental collaboration.

Venue: via Zoom

Event Official Language: English

Coherent emission from 3D relativistic shocks

April 22 (Fri) at 14:00 - 15:00, 2022

Masanori Iwamoto (Kyushu University)

The origin of fast radio bursts (FRBs; Lorimer et al. 2007) is one of the unsolved problems in astrophysics. Many observations of FRBs indicate that FRBs must be coherent emission in the sense that coherently moving electrons radiate electromagnetic waves. In relativistic shocks, it is well known that coherent electromagnetic waves are excited by synchrotron maser instability (SMI) in the shock transition (Hoshino & Arons 1991). The SMI is also known as the emission mechanism of coherent radio sources such as auroral kilometric radiation at Earth and Jovian decametric radiation. Recently, some models of fast radio burst based on the coherent emission from relativistic shock via the SMI have been proposed (e.g., Lyubarsky 2014; Beloborodov 2017; Plotnikov & Sironi 2019; Metzger et al. 2019) and the SMI in the context of relativistic shocks attracts more attention from astrophysics. In this study, by performing the world’s first three-dimensional (3D) particle-in-cell (PIC) simulation of relativistic shocks, we will demonstrate that large-amplitude electromagnetic waves are indeed excited by the SMI even in 3D and that the wave amplitude is significantly amplified and comparable to that in pair plasmas due to a positive feedback process associated with ion-electron coupling. Based on the simulation results, we will discuss the applicability of the SMI for FRBs in this talk.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 3

April 21 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Neurons are potential statisticians

April 21 (Thu) at 10:00 - 11:00, 2022

Takuya Isomura (Unit Leader, Brain Intelligence Theory Unit, RIKEN Center for Brain Science (CBS))

Humans and animals can predict what will happen in the future and act appropriately by inferring how the sensory inputs were generated from underlying hidden causes. The free-energy principle is a theory of the brain that can explain how these processes occur in a unified way. However, how the fundamental units of the brain, such as the neurons and synapses, implement this principle has yet to be fully established. Here, we have mathematically shown that neural networks that minimise a cost function implicitly follow the free-energy principle and actively perform statistical inference. We have reconstructed a biologically plausible cost function for neural networks based on the equation of neural activity and shown that the reconstructed cost function is identical to variational free energy, which is the cost function of the free-energy principle. This equivalence speaks to the free-energy principle as a universal characterisation of neural networks, implying that even at the level of the neurons and synapses, the neural networks can autonomously infer the underlying causes from the observed data, just as a statistician would. The proposed theory will advance our understanding of the neuronal basis of the free-energy principle, leading to future applications in the early diagnosis and treatment of psychiatric disorders, and in the development of brain-inspired artificial intelligence that can learn like humans.

Venue: via Zoom

Event Official Language: English

Light-matter control of quantum materials: From light-induced superconductivity to cavity materials

April 20 (Wed) at 15:30 - 17:00, 2022

Michael Sentef (Emmy Noether Research Group Leader, Max Planck Institute for the Structure and Dynamics of Matter, Germany)

In this talk I will discuss recent progress in controlling and inducing materials properties with light [1]. Specifically I will discuss recent experiments showing light-induced superconductivity through phonon driving in an organic kappa salt [2] and its possible theoretical explanation via dynamical Hubbard U [3]. I will then highlight some recent theoretical and experimental progress in cavity quantum materials [4], where the classical laser as a driving field of light-induced properties is replaced by quantum fluctuations of light in confined geometries. Ideas and open questions for future work will be outlined.

Venue: via Zoom

Event Official Language: English

The 19th MACS Colloquium

April 18 (Mon) at 15:00 - 17:40, 2022

Yasuhiro Inoue (Professor, Department of Micro Engineering, Graduate School of Engineering, Kyoto University)

15:00- The 19th MACS Colloquium: Talk by Prof. Yasuhiro Inoue "Multicellular Dynamics Simulation of Morphogenesis" 16:05- MACS SG information session 17:10- Individual explanation by each study group (Zoom breakout room)

Venue: via Zoom

Event Official Language: Japanese

Introduction to Topological Insulators: From Quantum to Classical Physics 2

April 14 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

Coarse-grained molecular dynamics simulation via Langevin simulation

April 14 (Thu) at 10:00 - 11:00, 2022

Hiroshi Yokota (Postdoctoral Researcher, iTHEMS)

In the cell biology or biophysics, many mechanical properties of proteins or DNA are discussed. In order to consider the dynamics, coarse-grained molecular dynamics simulation (Langevin simulation) is useful. In this seminar, I will give you the introductory and methodology talk about the Langevin simulation.

Venue: via Zoom

Event Official Language: English

Introduction to Topological Insulators: From Quantum to Classical Physics 1

April 7 (Thu) at 15:00 - 17:00, 2022

Tomoki Ozawa (Associate Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)

In this set of lectures, I give an introduction to topological insulators. A goal is to provide an overall understanding of basic concepts of the physics of topological insulators to mathematicians and physicists with no prior knowledge on the subject. Very roughly speaking, topological insulators are materials whose wavefunctions show nontrivial topological structure in momentum space. Materials with topologically nontrivial wavefunction in momentum space have been found to host modes which are localized at the surface (edge) of the material: a property known as the bulk-edge correspondence. The bulk-edge correspondence results in experimentally observable signature of somewhat abstract notion of topology of the wavefunction in momentum space. Originally, topological insulators were found and studied for electrons in solid-state materials, which are quantum mechanical. However, certain properties of topological insulators, including the bulk-edge correspondence, have been found to hold also for purely classical materials, such as electromagnetic waves obeying Maxwell’s equations, or waves described by Newtonian mechanics. I will try to introduce topological insulators in a way general enough to be applied to quantum as well as classical materials. In the final part of the lectures, I take this opportunity to discuss some of my own works, where I studied some relations between the two-dimensional topological insulators and Kähler geometry.

Venue: via Zoom

Event Official Language: English

iTHEMS - Kyoto University Joint Seminar: Single-trajectory map equation

April 1 (Fri) at 8:30 - 10:00, 2022

Tatsuro Kawamoto (Researcher, Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology (AIST))

This seminar is a joint seminar of Blockchain research group in Kyoto University and EcoP WG in iTHEMS.

Venue: via Zoom

Event Official Language: English