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)

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.

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.

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.

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.

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.

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.

The widely acclaimed 1995/1996 papers by Ho, Perelson and others [1,2] demonstrated the important insights that come from mathematical modelling of virus infection kinetics within a person. But there are key dynamical differences between chronic and acute infections, namely whether the infection reaches or maintains some equilibrium or not. In this talk, I will introduce the equations used to describe a virus infection within a person. I will show some of the tricks used by mathematical modellers to extract important rate estimates from measurements in patients infected with chronic diseases, like HIV or Hepatitis C virus. I will explain why it is difficult to extract meaningful information from measurements in patients with an acute infection, like influenza or possibly COVID-19 [3]. I hope to hear from the audience if they have any thoughts about overcoming the issue to extract better rate information from limited data in patients with acute infections.

(This seminar is a joint seminar between Nonequilibrium working group and Biology study group)