iTHEMS Math Seminar
70 events
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Seminar
Coherent sheaves, quivers, and quantum groups
February 17 (Fri) at 14:00 - 16:00, 2023
Dr. Gufang Zhao (Senior Lecturer, University of Melbourne, Australia)
This talk aims to illustrate symmetries in geometry. The first half surveys a few examples of parametrizing coherent sheaves on a variety and how quantum groups control the symmetry of parametrization space. The second half aims to illustrate some special cases when the variety is a local toric 3-Calabi-Yau.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Quantum groups and cohomology theories
February 15 (Wed) at 14:00 - 16:00, 2023
Dr. Yaping Yang (Senior Lecturer, University of Melbourne, Australia)
In the first half of my talk, I will review quantum groups at roots of unity and their representation theory. In the second half, I will explain a construction of new quantum groups using cohomology theories from topology. The construction uses the so-called cohomological Hall algebra associated to a quiver and an oriented cohomology theory. In examples, we obtain the Yangian, quantum loop algebra and elliptic quantum group, when the cohomology theories are the cohomology, K-theory, and elliptic cohomology respectively.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Math and Physics of Seiberg-Witten theory
January 20 (Fri) at 16:00 - 18:10, 2023
Dr. Nobuo Iida (JSPS Research Fellow PD, School of Science, Tokyo Institute of Technology)
Math and physics have developed through interactions with each other. For example, classical mechanics and calculous were born together. Einstein's theory of gravitation is written in the language of pseudo-Riemann geometry. Since the late 20th century, physicists centering on Edward Witten have revolutionized modern geometry. Seiberg-Witten theory is one of such breakthroughs, for both mathematicians and physicists. In physics it is regarded as a theory describing strong coupling (i.e. low energy) behavior of some supersymmetric gauge theories. It showes confinement (by a mechanism similar to superconductivity) and electric magnetic duality. Even though this story has not been mathematically justified yet, it is regarded as an important trigger of developments in understanding non perturbative aspects of quantum field theory and string theory, and stimulates broad fields of physics and math. In math, Seiberg-Witten theory is regarded as a fundamental tool to study 3 and 4-dimensional geometry. This is based on a PDE called Seiberg-Witten equation, which originates from the "electric magnetic dual description" of monopoles, but people can use it as a tool to study geometry without knowing such a physical origin. In this talk, developments of Seiberg-Witten theory from both viewpoints will be reviewed and if the time permits, works in math by the speaker and collaborators will be discussed. The speaker thinks it is unusual for a mathematician to talk about something that has not been mathematically justified yet, but hopes this talk will lead to new interactions between math and physics.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
CM minimization and special K-stability
December 16 (Fri) at 14:00 - 16:30, 2022
Mr. Masafumi Hattori (Ph.D. Students, Department of Mathematics, Graduate School of Science, Kyoto University)
Odaka proposed a conjecture predicting that the degrees of CM line bundles for families with fixed general fibers are strictly minimized if the special fibers are K-stable. This conjecture is called CM minimization and a quantitative strengthening of the conjecture of separatedness of moduli spaces of K-stable varieties (K-moduli). This conjecture was already shown for K-ample (Wang-Xu), Calabi-Yau (Odaka) and Fano varieties (Blum-Xu). In this talk, we introduce a new class, special K-stable varieties, and settle CM minimization for them, which is a generalization of the above results. In addition, we would like to explain an important application of this, construction of moduli spaces of uniformly adiabatically K-stable klt trivial fibrations over curves as a separated Deligne-Mumford stack in a joint work with Kenta Hashizume to appear. This is based on arXiv:2211.03108.
Venue: via Zoom
Event Official Language: English
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Seminar
Tropical methods in Enumerative Geometry and Mirror Symmetry
November 25 (Fri) at 14:00 - 16:00, 2022
Dr. Michel Van Garrel (Assistant Professor, School of Mathematics, University of Birmingham, UK)
Abstract for the 1st hour: Enumerative Geometry has been a feature of mathematics from its beginnings, just think about the number of lines in the plane passing through 2 points. I will take you on a history of the subject and its relationship to other areas of mathematics and physics. Abstract for the 2nd hour: Many problems in mathematics are solved by taking a limit and solving the limiting problem. Tropical geometry is a key technique that allows us to do this systematically. I will talk about the following problem. Take the complex projective plane S and an elliptic curve E in S. Count algebraic maps from the affine line into the complement S \ E. This counting problem is solved via tropical geometry as I will describe in this talk.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Mathematics of Post-Quantum Cryptography
November 18 (Fri) at 14:00 - 16:30, 2022
Dr. Yusuke Aikawa (Researcher, Information Technology R&D Center, Mitsubishi Electric Corporation)
Cryptography keeps our everyday information communications secure. Cryptography based on key sharing have been used mainly for military purposes since ancient times in human history, but with the advent of the Internet, cryptography that does not require key sharing has become necessary. In 1976, Diffie and Hellman proposed the concept of public key cryptography, which does not require key sharing among communicators. Since then, research on public key cryptography has progressed, involving not only computer science but also mathematics, and has become an essential technology for the society we live in. The security of public key cryptography is supported by computational hardness of problems derived from mathematics. For example, the integer factoring problem is a basis for the security of RSA cryptography, and the discrete logarithm problem is for elliptic curve cryptography. However, in 1994, Shor proposed an efficient quantum algorithm that solves these problems. This means that emergence of large-scale quantum computers will break RSA and elliptic curve cryptography we use today. For this reason, research on next-generation cryptography, so-called Post-Quantum Cryptography (PQC for short), is currently underway to prepare for a future in which quantum computers will emerge. In this talk, without assuming any knowledge of cryptography, I will give a brief overview of cryptography and the progress of PQC. The first half of the talk will mainly outline the relationship between mathematics and cryptography, while the second half will discuss isogeny-based cryptography, one of the promising PQC, with our recent results.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Arithmetic dynamics on algebraic varieties
November 11 (Fri) at 14:00 - 16:30, 2022
Dr. Yosuke Matsuzawa (Associate Professor, Department of Mathematics, Graduate School of Science, Osaka Metropolitan University)
The study of self-maps of algebraic varieties is a relatively new and active area in mathematics. Such a self-map can be considered as a discrete dynamical system, and we can study the asymptotic properties of such systems from various points of views, including number theoretic viewpoint. I will introduce several problems in arithmetic dynamics and some of my results in this area.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Measuring diversity: species similarity
October 28 (Fri) at 16:00 - 17:00, 2022
Prof. Tom Leinster (Professor, University of Edinburgh, UK)
Traditional measures of the diversity of an ecological community depend only on how abundant the species are, not the similarities or differences between them. To better reflect biological reality, species similarity should be incorporated. Mathematically, this corresponds to moving from probability distributions on sets to probability distributions on metric spaces. I will explain how to do this and how it can change ecological judgements. Finally, I will describe a surprising theorem on maximum diversity (joint with Meckes and Roff), which reveals close connections between maximum diversity and invariants of geometric measure.
Venue: via Zoom
Event Official Language: English
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Seminar
Measuring diversity: the axiomatic approach
October 21 (Fri) at 16:00 - 17:00, 2022
Prof. Tom Leinster (Professor, University of Edinburgh, UK)
Ecologists have been debating the best way to measure diversity for more than 50 years. The concept of diversity is relevant not only in ecology, but also in other fields such as genetics and economics, as well as being closely related to entropy. The question of how best to quantify diversity has surprising mathematical depth. I will argue that the best approach is axiomatic: to enable us to reason logically about diversity, the measures we use must satisfy certain mathematical conditions, and those conditions dramatically limit the choice of measures. This point will be illustrated with a theorem: using a simple model of ecosystems, the only diversity measures that behave logically are the Hill numbers, which are very closely related to the Rényi entropies of information theory.
Venue: via Zoom
Event Official Language: English
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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 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.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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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 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.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
Seiberg-Witten 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 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. 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 246-248 and Zoom)
Event Official Language: English
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Seminar
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 246-248 and Zoom)
Event Official Language: English
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Seminar
A mathematical formulation of two-dimensional conformal field theory
May 23 (Mon) at 14:00 - 16:30, 2022
Dr. 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.
Venue: Hybrid Format (Common Room 246-248 and Zoom)
Event Official Language: English
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Seminar
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 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
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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 246-248 and Zoom) (Main Venue)
Event Official Language: English
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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 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.
Venue: via Zoom
Event Official Language: English
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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 (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.
Venue: via Zoom
Event Official Language: English
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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
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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
70 events