iTHEMS Math Seminar
61 events

Seminar
Product Replacement Algorithm, Semidefinite Programming, and Operator Algebras
August 2 (Tue) at 16:00  17:00, 2022
Prof. 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 infinitedimensional topologicalalgebraic 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.
Venue: Hybrid Format (Common Room 246248 and Zoom)
Event Official Language: English

Seminar
Introduction to instanton knot homology
July 25 (Mon) at 16:00  18:00, 2022
Mr. Hayato Imori (Ph.D. Student, Division of Mathematics and Mathematical Sciences, Graduate School of Science, Kyoto University)
Floer theory is an infinitedimensional version of Morse theory and has provided powerful invariants in the study of lowdimensional topology. In the context of YangMills 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.
Venue: Hybrid Format (Common Room 246248 and Zoom)
Event Official Language: English

SeibergWitten Floer homotopy
July 15 (Fri) at 14:00  16:30, 2022
Dr. Hokuto Konno (Assistant Professor, Graduate School of Mathematical Sciences, The University of Tokyo)
I will survey a mathematical object called the SeibergWitten Floer homotopy type introduced by Manolescu. This is a machinery that extracts interesting aspects of 3 and 4dimensional manifolds through the SeibergWitten equations. This framework assigns a 3manifold 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 3manifold, 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 SeibergWitten Floer homotopy theory. If you are not familiar with the mathematical formulation of TQFT and categorification, I recommended you to watch Dr. Sano's recent talk in advance (see related links).
Venue: Hybrid Format (Common Room 246248 and Zoom)
Event Official Language: English

Algebraic geometry in mixed characteristic
June 10 (Fri) at 14:00  16:30, 2022
Dr. 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.
Venue: Hybrid Format (Common Room 246248 and Zoom)
Event Official Language: English

A mathematical formulation of twodimensional conformal field theory
May 23 (Mon) at 14:00  16:30, 2022
Dr. Yuto Moriwaki (Special Postdoctoral Researcher, iTHEMS)
The mathematical construction of nontrivial quantum field theory in four dimensions, known as the "YangMills 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, twodimensional 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.
Venue: Hybrid Format (Common Room 246248 and Zoom)
Event Official Language: English

Khovanov homology theory  an introduction to categorification
May 13 (Fri) at 14:00  16:30, 2022
Dr. 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 lowdimensional 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 246248 and Zoom)
Event Official Language: English

Seminar
Recurrence theorems for topological Markov chains
April 22 (Fri) at 17:00  19:00, 2022
Dr. 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 246248 and Zoom) (Main Venue)
Event Official Language: English

Seminar
Explore the possibility to control hurricanes
March 18 (Fri) at 16:00  18:00, 2022
Dr. 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 10^{14} Watt, while the most powerful manmade engines have the power of only 10^{8} Watt. This sixordermagnitude 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 hurricaneriskfree future come earlier.
Venue: via Zoom
Event Official Language: English

Seminar
Extracting rules from trained machine learning models with applications in Bioinformatics
March 11 (Fri) at 16:00  18:00, 2022
Dr. Pengyu Liu (Postdoctoral Researcher, Medical Data Mathematical Reasoning Team, RIKEN Information R&D and Strategy Headquarters (RIH))
Recently, Machine learning methods have achieved great success in various areas. However, some machine learningbased 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 premiRNAs 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 premiRNA are more important for the prediction.
Venue: via Zoom
Event Official Language: English

Seminar
Introduction to stability conditions 2
March 9 (Wed) at 16:00  17:30, 2022
Dr. Naoki Koseki (Postdoctoral Research Associate, School of Mathematics, University of Edinburgh, UK)
In 2002, Bridgeland defined the notion of stability conditions on a triangulated category, motivated by string theory and mirror symmetry. Since then, Bridgeland stability conditions have been found very useful not only in Mathematical Physics, but also in various areas of Pure Mathematics. In the first part, I will review basic background and open problems in the theory of Bridgeland stability conditions. In the second part, I will explain recent developments of the theory, especially its applications to algebraic geometry.
Venue: via Zoom
Event Official Language: English

Seminar
Introduction to stability conditions 1
March 2 (Wed) at 16:00  17:30, 2022
Dr. Naoki Koseki (Postdoctoral Research Associate, School of Mathematics, University of Edinburgh, UK)
In 2002, Bridgeland defined the notion of stability conditions on a triangulated category, motivated by string theory and mirror symmetry. Since then, Bridgeland stability conditions have been found very useful not only in Mathematical Physics, but also in various areas of Pure Mathematics. In the first part, I will review basic background and open problems in the theory of Bridgeland stability conditions. In the second part, I will explain recent developments of the theory, especially its applications to algebraic geometry.
Venue: via Zoom
Event Official Language: English

Seminar
How to understand Earth science system using data science
February 25 (Fri) at 16:00  18:00, 2022
Dr. Kaman Kong (Postdoctoral Researcher, Computational Climate Science Research Team, RIKEN Center for Computational Science (RCCS))
Hi everyone, my name is Kaman Kong. After I graduated from Nagoya University last April, I joined the computational climate science research team, RCCS 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 10minute 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).
Venue: via Zoom
Event Official Language: English

Seminar
Recent progress on dualities in Wsuperalgebras
January 28 (Fri) at 16:00  18:00, 2022
Dr. 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 Wsuperalgebras obtained from them by cohomology parametrized by nilpotent orbits. Historically, the Walgebras associated with simple Lie algebras and principal nilpotent orbit have been studied intensively and are wellknown to play an essential role in the quantum geometric Langlands program. In particular, they enjoy a duality, called the FeiginFrenkel 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 Wsuperalgebras since then in terms of several aspects: algebras, modules, and fusion rules.
Venue: via Zoom
Event Official Language: English

Seminar
The OhsawaTakegoshi $L^2$ extension theorem and variations of Bergman kernels
January 14 (Fri) at 16:00  18:00, 2022
Dr. Genki Hosono (Mathematical Institute, Graduate School of Science, Tohoku University)
In complex analysis and geometry, $L^2$ methods are very important and widely used. Recent studies show that the $L^2$ theory and the variational theory are closely related. In particular, the (optimal) $L^2$ 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. *Please contact Keita Mikami mailing address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English

Generalized Bernoulli process and computation of proportional areas for Venn diagram
December 8 (Wed) at 16:00  18:00, 2021
Dr. Ryosuke Iritani (Research Scientist, iTHEMS)
*For detailed information about the seminar, please refer to the email.
Venue: via Zoom
Event Official Language: English

Seminar
The Conley index of topological dynamical systems
December 3 (Fri) at 16:00  18:00, 2021
Prof. Yosuke Morita (Assistant Professor, Department of Mathematics, Kyoto University)
The study of topological dynamical systems, i.e. continuous selfhomeomorphisms (or continuous flows) on topological spaces, is important in both pure mathematics and applications. To each isolated invariant subset of a topological dynamical system, we can assign an invariant called the Conley index, which is (roughly speaking) a based space that describes the dynamics around the isolated invariant subset. It is used not only in the study of topological dynamical systems themselves but also in Manolescu’s construction of the SeibergWittenFloer homotopy type (a spectrumvalued (3+1)dimensional TQFT). In this talk, I am planning to explain a new construction of Conley indices, which is entirely nonhomotopical and uses only basic general topology. *Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English

Seminar
Selfadjointness from quantumclassical correspondence
November 26 (Fri) at 16:00  18:00, 2021
Prof. Koichi Taira (Assistant Professor, College of Science and Engineering Department of Mathematical Sciences, Ritsumeikan University)
Selfadjointness is a fundamental property of a linear operator in quantum mechanics. In physics, a selfadjoint operator is usually defined to be an operator which is own adjoint. However, this definition is in fact not satisfactory since a selfadjoint operator in this definition does not always have nice properties such as the spectral decomposition. Hence, in mathematics, a kind of completeness is also assumed in the definition of a selfadjoint operator. Here a natural question is how to judge whether an operator is selfadjoint. It has been believed that selfadjointness is closely related to completeness of the classical dynamics for a long time although a complete description of such relations has not been given so far. I am planning to talk about how selfadjointness is important in mathematical physics. Moreover, I will explain relations between selfadjointness and classical dynamics by introducing some examples. *Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English

Seminar
The graph removal lemma
November 19 (Fri) at 16:00  18:00, 2021
Dr. Shinichiro Seki (Assistant Professor, Aoyama Gakuin University)
We have recently proved an extension of the GreenTao theorem on arithmetic progressions to number fields, in collaboration with Kai, Mimura, Munemasa and Yoshino. (Kai gave a talk on this result in March.) There are several promising approaches in this area, including ergodic theory and Fourier analysis, but we used a combinatorial tool, the relative hypergraph removal lemma proved by Conlon, Fox and Zhao. In the first half of this talk, I will give a survey of Szemerédi's regularity lemma and the graph removal lemma, and explain how to extend the removal lemma to the case of (weighted) hypergraphs. In the second half of this talk, I will present Fox's result on a quantitative version of the graph removal, and discuss the prospects for future research. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English

Seminar
Confluence for the Ktheoretic Jfunction
November 12 (Fri) at 16:00  18:00, 2021
Prof. Todor Milanov (Associate Professor, Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo)
I am planning to talk about my recent paper (1) written in collaboration with Alexis Roquefeuil. In the first part of the talk I would like to explain the background of our project: quantum differential equations and Ktheoretic quantum qdifference equations in genus0 GromovWitten theory. In the second part of the talk, I would like to explain our main result with an interesting application. Namely, under the assumption that the first Chern class of the tangent bundle is positive, we proved that the small Jfunction in quantum cohomology can be obtained as a limit q >1 of the small Jfunction in quantum Ktheory. In the case of a Fano toric manifold of Picard rank 2, we proved the Ktheoretic version of an identity due to Iritani that relates the Ifunction of the toric manifold and the oscillatory integral of the toric mirror. In particular, our confluence result yields a new proof of Iritani's identity in the case of a Fano toric manifold of Picard rank 2. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English

Seminar
Geometry and Physics of Mirror Symmetry
November 5 (Fri) at 16:00  18:00, 2021
Prof. Naichung Conan Leung (Professor of Mathematics, Department of Mathematics, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong)
In the first half of this talk, I will describe the geometry and physics behind mirror symmetry in layman's terms. In the second half of this talk, I will provide a more mathematical explanation of the concepts involved in this mysterious conjecture. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English
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