Narutaka Ozawa (Professor, Research Institute for Mathematical Sciences (RIMS), Kyoto University)
Suppose you are given a large finite set G and want to estimate the size |G| or see how a typical element x in G looks like. In this talk, G will be a finite group generated by g_1,...,g_d. The "Product" Replacement Algorithm" is a popular algorithm for random sampling in the group G. The PRA shows outstanding performance in practice, but the theoretical explanation has remained mysterious. I will talk how an infinite-dimensional topological-algebraic analysis (operator algebra theory) connects this problem to a convex (semidefinite) optimization problem that can be rigorously solved by computer.
This talk is intended for a general audience.
Aug. 2, 16:00-17:00, on Zoom + Common Room
Hayato Imori (Ph.D. Student, Division of Mathematics and Mathematical Sciences, Graduate School of Science, Kyoto University)
Floer theory is an infinite-dimensional version of Morse theory and has provided powerful invariants in the study of low-dimensional topology. In the context of Yang-Mills gauge theory, some versions of Floer homology groups for knots have been developed. These knot invariants are called instanton knot homology groups and are strongly related to representations of the fundamental group of the knot complement.
In this talk, the speaker introduces basic constructions of instanton knot homology groups and recent developments related to the equivariant version of instanton knot homology theory.
Jul. 25, 16:00-18:00, on Zoom + Common Room
Hokuto Konno (Assistant Professor, Graduate School of Mathematical Sciences, The University of Tokyo)
I will survey a mathematical object called the Seiberg-Witten Floer homotopy type introduced by Manolescu. This is a machinery that extracts interesting aspects of 3- and 4-dimensional manifolds through the Seiberg-Witten equations. This framework assigns a 3-manifold to a "space" (more precisely, the stable homotopy type of a space), and this space contains rich information that is strong enough to recover the monopole Floer homology of the 3-manifold, which is known already as a strong invariant.
I shall sketch how this theory is constructed along Manolescu's original work, and introduce major applications. If time permits, I will also explain recent developments of Seiberg-Witten Floer homotopy theory.
Jul. 15, 14:00-16:30, on Zoom + Common Room
Shou Yoshikawa (Special Postdoctoral Researcher, iTHEMS)
In algebraic geometry, we study the geometry of algebraic varieties, which are sets defined by algebraic equations.
There are two types of algebraic varieties, they are varieties over characteristic zero and varieties over positive characteristic.
Algebraic geometry in characteristic zero is similar to analytic geometry, so it is related to many other subjects.
In this talk, I will introduce the notion of algebraic geometry in positive characteristic and relationships between positive characteristic and characteristic zero.
In order to study it, we consider families consisting of varieties over characteristic zero and varieties over positive characteristic, called mixed characteristic.
Jun. 10, 14:00-16:30, on Zoom + Common Room
Yuto Moriwaki (Special Postdoctoral Researcher, iTHEMS)
The mathematical construction of non-trivial quantum field theory in four dimensions, known as the "Yang-Mills existence and mass gap problem", is a very important issue in mathematical sciences. There are many examples of rigorous quantum field theories in two dimensions, although the four dimensions have not yet been solved. In particular, two-dimensional conformal field theory, which is a quantum field theory with conformal symmetry, has good properties and can be formulated mathematically using algebraic structures formed by "products of a field and a field" (operator product expansion).
In this talk, this algebraic formulation (full vertex algebra) will be explained. Various construction methods and concrete examples (construction using codes, construction from quantum groups, and construction by deformation) will then be discussed.
All the talk here is mathematical, but I will try to speak in a way that is motivated by physics as much as possible throughout the talk. I hope to receive various comments from the viewpoints of other fields.
May. 23, 14:00-16:30, on Zoom + Common Room
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.
May. 13, 14:00-16:30, on Zoom + Common Room
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.
Apr. 22, 17:00-19:00, on Zoom + Common Room
Lin Li (Postdoctoral Researcher, Prediction Science Laboratory, RIKEN Cluster for Pioneering Research (CPR))
Hurricanes, also known as tropical cyclones and typhoons, are the biggest and the most devastating storms on Earth. In this seminar, I will talk about the possibility to control hurricanes with existing human capability. Energetically speaking, controlling hurricanes is a very challenging task due to a large gap: hurricanes are gigantic heat engines with a power of around 1014 Watt, while the most powerful manmade engines have the power of only 108 Watt. This six-order-magnitude gap is the major obstacle toward using existing engines to control hurricanes. To fill in this gap, we propose to utilize the chaotic nature of hurricanes, namely, the sensitivity of a chaotic system to its initial condition, to control hurricanes. In this presentation, I will first review the basics of hurricanes and existing chaos control methods, and then present my thoughts on hurricane control and preliminary results I acquired since joining Prediction Science Laboratory. Future directions on using reinforcement learning to control hurricanes will also be discussed. Since it is a very challenging task, I welcome any discussions, questions, and comments. I hope we can make the hurricane-risk-free future come earlier.
Mar. 18, 16:00-18:10, on Zoom
Pengyu Liu (Postdoctoral Researcher, Medical Data Mathematical Reasoning Team, RIKEN Information R&D and Strategy Headquarters (R-IH))
Recently, Machine learning methods have achieved great success in various areas. However, some machine learning-based models are not explainable (e.g., Artificial Neural Networks), which may affect the massive applications in medical fields.
In this talk, we first introduce two approaches that extract rules from trained neural networks. The first one leads to an algorithm that extracts rules in the form of Boolean functions. The second one extracts probabilistic rules representing relations between inputs and the output. We demonstrate the effectiveness of these two approaches by computational experiments.
Then we consider applying an explainable machine learning model to predict human Dicer cleavage sites. Human Dicer is an enzyme that cleaves pre-miRNAs into miRNAs. We develop an accurate and explainable predictor for the human Dicer cleavage site -- ReCGBM. Computational experiments show that ReCGBM achieves the best performance compared with several existing methods. Further, we find that features close to the center of pre-miRNA are more important for the prediction.
Mar. 11, 16:00-18:10, on Zoom
Kaman Kong (Postdoctoral Researcher, Computational Climate Science Research Team, RIKEN Center for Computational Science (R-CCS))
Hi everyone, my name is Kaman Kong. After I graduated from Nagoya University last April, I joined the computational climate science research team, R-CCS at Kobe. Although I have still not yet had the important results now, I would like to share my idea and future plan here.
In this talk, different from the previous seminar, I would like to highlight how to use data science approaches to understand our Earth system science. In the first 60 minutes, I would like to share my research experiences in ecosystems, dust outbreaks, and atmospheric sciences and try to discuss their limitation in my study. After a 10-minute break, the 30 minutes will be spent discussing the potential methodology to overcome these limitations and new opportunities and challenges in Earth system science.
(Part 1)
In the first 60 minutes, I would like to talk about the relationships among ecosystems, dust outbreaks, and atmospheric conditions. I used the models of dust and ecosystem to explore seasonal variations of threshold wind speed, an index of soil susceptibility to dust outbreak, and its relations with land surface conditions, such as plant growth and soil moisture and temperature changes, in the Mongolian grasslands. On the other side, I am improving the weather forecast model to accurately predict dust emission and discuss its effects on the Earth system. Meanwhile, I am integrating the dust model into the ecosystem model. During this period, I realized there are many uncertainties of simulation.
(Part 2)
In the second 30 minutes, I will explain these limitations as I mentioned before and try to discuss how to solve these problems. For example, using deep learning to identify the green and brown plants separately for discussing their different effect on the dust model. And, used data assimilation (e.g., EnKF and Bayesian calibration) to improve the simulated performance of land surface parameters (e.g., soil moisture and vegetation).
Feb. 25, 16:00-18:10, on Zoom
Shigenori Nakatsuka (JSPS Fellow, Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo)
Vertex superalgebras are algebras which describe the chiral part of two dimensional superconformal field theory. A rich and fundamental class is provided by the affine vertex superalgebras associated with simple Lie superalgebras and the W-superalgebras obtained from them by cohomology parametrized by nilpotent orbits. Historically, the W-algebras associated with simple Lie algebras and principal nilpotent orbit have been studied intensively and are well-known to play an essential role in the quantum geometric Langlands program. In particular, they enjoy a duality, called the Feigin-Frenkel duality, which is a chiral analogue of the isomorphism between centers of the enveloping algebras of simple Lie algebras in Langlands duality.
Recently, physicists found a suitable generalization for other types of nilpotent orbits from study on four dimensional supersymmetric gauge theory. In this talk, I will report the recent progress on our understanding of dualities in W-superalgebras since then in terms of several aspects: algebras, modules, and fusion rules.
Jan. 28, 16:00-18:10, on Zoom
Genki Hosono (Mathematical Institute, Graduate School of Science, Tohoku University)
In complex analysis and geometry, L2 methods are very important and widely used. Recent studies show that the L2 theory and the variational theory are closely related. In particular, the (optimal) L2 extension theorem can be proved by subharmonicity of variations of Bergman kernels and vice versa. In this talk, I will explain the background, results, and key ideas of the proof.
Jan. 14, 16:00-18:10, on Zoom