iTHEMS数学セミナー
113 イベント
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セミナーQuantum modular form and quantum invariants
2026年3月13日(金) 14:00 - 16:00
村上 友哉 (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 研究員)
Quantum invariants are invariants of knots and 3-manifolds which relate deeply to mathematical physics and representation theory. In recent years, it has become increasingly clear that it is also deeply related to number theory, that is, quantum modularity for quantum invariants. This topic is interesting from a topological viewpoint since this is a refinement of establishing asymptotic expansions of quantum invariants, which is an important problem in quantum topology, and is interesting from a number-theores[tic viewpoint since this gives examples of quantum modular forms, which are mysterious objects in number theory. I obtained two linked results on topology and number theory: Establishing explicit asymptotic expansions of quantum invariants for negative definite plumbed 3-manifolds and establishing quantum modularity of false theta functions in full generality. In this talk, I will outline previous progress on quantum modularity for quantum invariants and my results.
会場: via Zoom / セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
The Rectangular Peg Problem and microlocal sheaf theory
2026年2月17日(火) 14:00 - 15:00
池 祐一 (東京大学 大学院数理科学研究科 准教授)
The Square Peg Problem asks whether every Jordan curve in the plane contains four distinct points that form the vertices of a square. This problem was proposed by Toeplitz in 1911 and remains unsolved in full generality. It can be generalized to the Rectangular Peg Problem, which concerns the existence of inscribed rectangles with a prescribed aspect ratio. Recently, Greene and Lobb successfully applied techniques in symplectic geometry to the problem and obtained new results. In this talk, I will explain how microlocal sheaf theory allows us to further extend their approach and affirmatively solve the Rectangular Peg Problem for a large class of Jordan curves, including all curves of finite length. This is joint work with Tomohiro Asano.
会場: セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
Persistent homology and its applications
2026年2月17日(火) 11:00 - 12:00
池 祐一 (東京大学 大学院数理科学研究科 准教授)
Persistent homology is one of the main tools in topological data analysis (TDA), which encodes the topological features of given data into persistence diagrams. It has been successfully applied to various fields such as material science and computer graphics. In this talk, I will provide an overview of persistent homology and its applications. Furthermore, I will also discuss its integration with machine learning, specifically how persistent-homology-based loss functions can be used to regularize the topological structure of parameters.
会場: セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
Fracture squares and separable algebras
2025年12月12日(金) 16:00 - 17:30
Luca Pol (Postdoctoral Researcher, Max Planck Institute for Mathematics in Bonn, Germany)
In this talk I will present a way to reconstruct a category from its subcategories of complete and local objects while retaining the symmetric monoidal structure. As an application of this machinery I will discuss how to calculate separable algebras in equivariant homotopy theory.
会場: via Zoom / 研究本館 3階 セミナー室(345-347)
イベント公式言語: 英語
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セミナー
From perturbations of operators to noncommutative condensers
2025年12月11日(木) 16:00 - 17:00
Dan Voiculescu (Professor, Department of Mathematics, University of California, Berkeley, USA)
A numerical invariant, the quasicentral modulus underlies the multivariable generalizations of the classical Weyl-von Neumann-Kuroda and Kato-Rosenblum theorems. There are also connections to the Kolmogorov-Sinai dynamical entropy. I will also point out some of the open problems. Recently a noncommutative analogy with condenser capacity in nonlinear potential theory is emerging, that provides a new perspective on the subject.
会場: via Zoom / 研究本館 3階 359号室
イベント公式言語: 英語
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セミナー
Graph polynomials and quantum field theory
2025年12月9日(火) 15:00 - 17:00
Michael McBreen (Assistant Professor, Department of Mathematics, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong)
The Tutte polynomial was introduced in the 1940s as a two-variable generalisation of the chromatic polynomial of a graph. It is the universal matroid invariant satisfying a deletion-contraction relation, and is the subject of much recent work. I will describe a geometric realisation of the Tutte polynomial via the cohomology of a symplectic dual pair of hypertoric varieties. The same construction associates an interesting two-variable polynomial to any pair of symplectically dual spaces, whose one-variable specialisations recover the respective Poincare polynomials. Joint work with Ben Davison.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
Full exceptional collections on Fano threefolds and the braid group action
2025年12月5日(金) 16:00 - 17:30
Anya Nordskova (カブリ数物連携宇宙研究機構 (Kavli IPMU) Postdoctoral researcher)
The bounded derived category D^b(X) of coherent sheaves on an algebraic variety X is a powerful tool that encodes a wealth of information about X. In some cases D^b(X) admits a particularly nice description via so-called full exceptional collections, which allow one to view D^b(X) as being glued from the simplest building blocks, each equivalent to the derived category D^b(pt) of a point. In this situation the set of all full exceptional collections admits an action of the braid group. In 1993, Bondal and Polishchuk conjectured that this braid group action is always transitive. After a short historical overview I will sketch the idea behind the proof of Bondal-Polishchuk's conjecture in the case when X is a Fano threefold of Picard rank 1 (e.g. the projective space P^3). This is the first 3-dimensional case where the transitivity of the braid group action has been verified. The talk is based on joint work with Michel Van den Bergh.
会場: 研究本館 3階 セミナー室(345-347) (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
Compact Association Schemes and Fourier Analysis
2025年10月17日(金) 15:00 - 17:00
中田 彬文 (広島大学 大学院先進理工系科学研究科 博士課程／日本学術振興会 特別研究員 DC)
Error-correcting codes are a fundamental tool in information and communication technologies. They can be viewed as collections of points in a space that are sufficiently far apart to allow error detection and correction. More broadly, coding theory studies good arrangements of points in spaces. This theory has been particularly developed in the frameworks of association schemes and compact homogeneous spaces, where harmonic analysis plays a central role. In this talk, we will begin with an introduction to error-correcting codes and then present compact association schemes, which we define as a generalization of these spaces in which harmonic analysis can be developed.
会場: 研究本館 3階 359号室とZoomのハイブリッド開催
イベント公式言語: 英語
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セミナー
Bonded Knotted Structures and Applications
2025年10月16日(木) 16:00 - 18:00
Sofia Lambropoulou (Professor, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece)
We present the theory of bonded knots and bonded knotoids, as well as their algebraic counterparts, the theory of bonded braids and bonded braidoids. We also discuss some applications to the topological study of proteins.
会場: via Zoom / セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
Separability criteria for loops via the Goldman bracket
2025年9月12日(金) 15:00 - 17:00
和久田 葵 (東京大学 大学院数理科学研究科 博士課程)
In this talk, we give algebraic criteria using the Goldman bracket to determine whether two free homotopy classes of loops on an oriented surface have disjoint representatives. As an application, we determine the center of the Goldman Lie algebra of a pair of pants. We extend Kabiraj's method, which was originally limited to oriented surfaces filled by simple closed geodesics, and show that in this case, the center is generated by the class of loops homotopic to a point, and the classes of loops winding multiple times around a single puncture or boundary component.
会場: via Zoom / セミナー室 (359号室) 3階 359号室
イベント公式言語: 英語
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セミナー
Geometry of 2d topological field theories and integrable hierarchies
2025年9月4日(木) 15:00 - 17:00
テツ・オウ (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 研究員)
In this talk, I will explain a mathematical formulation of 2d topological field theories making use of integrable hierarchies, which is a framework initiated by B. Dubrovin and developed by many other mathematicians. The talk is divided into two parts. The first 45 minutes is a gentle introduction on how the mathematical structure called Frobenius manifolds naturally appears from topological field theories. The remaining part of the talk is devoted to explaining relationships between Frobenius manifolds and integrable hierarchies via the example of the KdV hierarchy.
会場: セミナー室 (359号室) 3階 359号室 (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
Tamely Ramified Geometric Langlands Correspondence
2025年8月22日(金) 15:00 - 19:00
Yuki Matsubara (Ph.D. Student, Centre for Quantum Mathematics, University of Southern Denmark, Denmark)
The geometric Langlands correspondence (GLC) is a geometric analogue of the Langlands conjecture in number theory, relating algebraic geometry, representation theory, and many other areas. Since A. Kapustin and E. Witten pointed out the relation between GLC and mirror symmetry, there have been various studies on GLC from a physics perspective as well as a mathematical perspective. First talk: An introduction to Langlands conjecture for everyone This is an entirely accessible overview of the Langlands conjecture. Starting from famous topics, such as the Pythagorean theorem and Fermat’s Last Theorem, I will introduce the statement and motivations behind the Langlands conjecture. No prior background will be assumed, and technical details will often be sketched rather than fully developed, so that anyone with a general mathematical curiosity can follow along. Second talk: On a certain tamely ramified geometric Langlands correspondence In this talk, I will present my research. Arinkin’s 2001 result established the geometric Langlands correspondence for the case G = SL2 on the complex projective line P1 with four fixed regular singularities. When one attempts to extend this to five or more singularities, it turns out to be more natural to decompose the correspondence into a Radon transform-type correspondence and a “GLC‑like” correspondence. I will report on the calculations of cohomology that support the proof of this GLC‑like correspondence in the P1 with five fixed regular singularities case.
会場: via Zoom / セミナー室 (359号室) 3階 359号室
イベント公式言語: 英語
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セミナー
Birational Geometry, Iitaka Program, and Positivity of Canonical and Anticanonical Divisor
2025年7月11日(金) 14:00 - 16:00
張 繼剛 (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 基礎科学特別研究員)
In birational geometry, one of the very interesting question is the Iitaka Program, that is, we want to "factorize" a given variety into "basic type" varieties. "Basic type" varieties are varieties of general type (canonincal divisor is ample), varieties of Calabi-Yau type (canonical divisor is "trivial"), and Fano type (anti-canonical divisor is ample). The (anti)canonical divisor is one of the most important ingredients of (projective) algebraic varieties. Even if the canonical divisor or anticanonical divisor of a given variety is not ample, if it is "positive" in some sense, then the positivity of the (anti)canonical divisor will provide us with important information about the geometry structure of the variety. On the other hand, given a morphism, it is also interesting to study the relation between the (anti)canonical divisor of the source space and the target space. In this talk, we will introduce some conjectures and known results around the positivity about varieties with positive (anti)canonical divisor in the few decades.
会場: via Zoom / セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms
2025年6月26日(木) 15:00 - 17:00
佐野 岳人 (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 数学応用研究チーム 研究員)
Rasmussen’s s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of 3-strand pretzel knots can be computed by hand.
会場: 理化学研究所 和光キャンパス 研究本館3階 345-347 (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
Spectral flow and applications
2025年6月23日(月) 14:00 - 16:00
クリストファー・ボーン (名古屋大学 教養教育院 准教授)
Given a family of symmetric matrices indexed by a parameter (e.g. time, external field), changing this parameter will cause the eigenvalues to move along the real axis. The spectral flow tracks these eigenvalues and counts how many cross the point 0. This idea turns out to be very useful for both pure mathematics as well as applications to physics and elsewhere. In this talk, I will introduce the spectral flow and how it can be generalised to a variety of settings that are also relevant for applications in quantum physics.
会場: 研究本館 3階 359号室とZoomのハイブリッド開催 (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
Categorification and K-theory
2025年6月20日(金) 15:30 - 17:30
ウアジーミャ・ソスニロ (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 研究員)
In this talk, I will explain and motivate the concept of categorification and present various examples. The Euler characteristic is an invariant of a topological space, that serves as a shadow of a more refined category theoretic invariant—homology—which retains significantly more information. The existence of such a categorical construction underlying a numerical one is a common phenomenon in topology and algebra. I will also discuss Khovanov's question on the existence of categorification of arbitrary rings.
会場: セミナー室 (359号室)
イベント公式言語: 英語
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セミナー
Ubiquity of geometric Brascamp--Lieb data
2025年2月21日(金) 15:00 - 17:00
辻 寛 (埼玉大学 大学院理工学研究科 日本学術振興会 特別研究員 PD)
This talk is based on a joint work with Neal Bez (Nagoya university) and Anthony Gauvan (Saitama university). The Brascamp--Lieb inequality is a futher general inequality involving some data (we call it the Brascamp--Lieb datum), which has been studied in harmonic analysis and convex geometry. For instance, the Hölder inequality and the Young convolution inequality are particular cases. In this talk, we have an interest in geometric Brascamp--Lieb data, which are specific data satisfying nice properties, for which the best constant of the Brascamp--Lieb inequality is well-understood. Our goal in this talk is to show that geomtric Brascamp--Lieb data are dense in general Brascamp--Lieb data in certain sence. Our result substantially follows from the work by Garg, Gurvits, Oliveira and Wigderson.
会場: セミナー室 (359号室) 3階 359号室とZoomのハイブリッド開催
イベント公式言語: 英語
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セミナー
The Topology, Geometry and Physics of non-Hausdorff manifolds
2025年2月19日(水) 15:00 - 17:00
O'Connell David (沖縄科学技術大学院大学 (OIST) 博士課程)
Non-Hausdorff manifolds are manifolds containing "doubled points" that cannot be separated by disjoint open sets. In this talk we will survey some mathematical and physical results surrounding these unusual spaces. As a theme, we will start with their fundamental description as a topological space, and slowly add in more and more structure of interest until we can meaningfully phrase questions of physics. On the mathematical side, we will see descriptions of non- Hausdorff manifolds as colimits of ordinary manifolds, which allows us to describe their geometric features without appealing to arbitrarily- existent partitions of unity. On the physical side, we will consider the inclusion of non-Hausdorff manifolds in a naïve 2d Lorentzian path integral for gravity, and (time permitting) explain how construct quantum fields on a non-Hausdorff background. Ultimately, we will see that these latter two arguments suggest that non-Hausdorff manifolds may be more appropriate than the standard "Trousers space" for the modelling of topology change in Lorentzian signature.
会場: セミナー室 (359号室) 3階 359号室とZoomのハイブリッド開催
イベント公式言語: 英語
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セミナー
Operator-algebraic approach to point processes
2025年2月14日(金) 15:00 - 17:00
佐藤 僚亮 (中央大学 理工学部 学振特別研究員PD)
A point process is a mathematical description of a particle system with random interactions, and it naturally appears in various areas of mathematical physics and mathematics, including statistical mechanics, random matrix theory, combinatorics, and representation theory. In particular, a random particle system with repulsive interactions is associated with a determinantal point process, in which the correlation of any number of particles is expressed in terms of the two-particle correlation via a determinant. Furthermore, this determinantal structure enables an algebraic analysis using CAR algebras, which are operator algebras determined by canonical anti-commutation relations. In the first half of the talk, we will review the relationship between determinantal point processes and operator algebras, with a focus on why operator algebras naturally lend themselves to analyses in probability theory and statistical mechanics. In the second half, based on recent work, we will examine the dynamic relationship between point processes and operator algebras, discussing how dynamics on CAR algebras give rise to stochastic processes on determinantal point processes.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
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セミナー
D-modules and the Riemann-Hilbert correspondence as a foundation for mixed Hodge modules
2025年1月31日(金) 14:00 - 16:00
齋藤 隆大 (中央大学 理工学部 助教)
Algebraic analysis is a field which began with the study of differential equations in an algebraic framework, known as D-modules. The Riemann-Hilbert correspondence lies at the heart of this field, which bridges the worlds of analysis and geometry. Thanks to this, some geometric problems can be studied by using D-module theory, and vice versa. Based on D-module theory, Morihiko Saito introduced the concept of mixed Hodge modules, realizing Hodge theory on constructible sheaves, which brings us a functorial treatment of Hodge theory and various applications. In this talk, we will begin with the linear differential equations on the complex plane and introduce monodromy, regularity and Deligne's Riemann-Hilbert correspondence. Then, as a generalization of it, I will explain the basics of the theory of D-modules and the Riemann-Hilbert correspondence. Finally, I will describe the role they play in the theory of Hodge modules and recent progress in this area. For the audience's background knowledge, I will assume basic complex function theory. I will start with a simple example, so people outside the field are welcome.
会場: セミナー室 (359号室) (メイン会場) / via Zoom
イベント公式言語: 英語
113 イベント