iTHEMS数学セミナー
122 イベント
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セミナーSome instances where topological illustration induced new mathematics
2026年7月24日(金) 16:30 - 18:00
Sofia Lambropoulou (Professor, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece)
We shall present instances from generalized knot theory, braid theory and their interactions, where illustration promoted understanding and inspired new mathematics. The first instance addresses a question of V.F.R. Jones whether one can make analogous constructions to the (2-variable) Jones polynomial using other braid groups and other types of Hecke algebras. The second instance addresses the question of formulating braid equivalences, analogous to the Markov theorem for classical braids, in settings where we may not even have available algebraic structures for the related braids. The third instance is about the theory of bonded knots and bonded knotoids used for modelling proteins.
会場: via Zoom
イベント公式言語: 英語
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セミナーA first step towards Non-Archimedean Geometric Quantization
2026年7月17日(金) 14:00 - 15:30
後藤 慶太 (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)
Calabi--Yau manifolds have long attracted interest from both mathematics and physics, particularly in the context of mirror symmetry, and form an important class of compact Kähler manifolds. A compact Kähler manifold is Calabi--Yau if and only if it admits a Ricci-flat Kähler metric, which we shall call a CY metric. Such a metric is highly analytic in nature, as it is given as the solution to a second-order PDE on the manifold, namely the complex Monge--Ampère equation. When the Calabi--Yau manifold is a complex projective variety, one algebraic approach to understanding this analytically defined CY metric is to approximate it by algebraically defined metrics called balanced metrics. This framework was initiated by Donaldson and is now known as geometric quantization. In this talk, following the spirit of this theory, we consider a non-Archimedean analogue of this approximation theory. More precisely, for a non-Archimedean analytic space associated with a maximally degenerating family of Calabi--Yau manifolds, we study the approximation of the NACY metric, a non-Archimedean analogue of the CY metric, by algebraically defined metrics. In particular, we introduce NA balanced metrics, which are expected to provide such an approximation, and explain that, for totally degenerating families of abelian varieties, NA balanced metrics indeed approximate the NACY metric.
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
Thom polynomials relative to prescribed maps around the boundary
2026年7月3日(金) 15:00 - 17:30
田邊 真郷 (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)
Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In the first half of this talk, I would like to recall their theory with introduction of algebro-topological materials. In the second half, I would also like to talk about applications of Thom polynomials to topology of non-singular maps. Since this century, various invariants of immersions/embeddings have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, those formulas are obtained in different forms and remain somewhat scattered. As the first step to unify them, I would like to introduce Thom polynomials relative to prescribed maps around the boundary. As a main result, we show a structure theorem of Thom polynomials relative to framable immersions. In fact, most earlier formulas are summarized as the vanishing of "correction terms" appearing in the structure theorem. This is an advanced seminar for mathematical researchers.
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
Primitive Ideals and Hilbert Space Representations of Quantized Coordinate Algebras of Complex Semisimple Lie Groups
2026年6月26日(金) 16:30 - 18:00
Heon Lee (Postdoc Researcher, Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Republic of Korea)
The primitive ideals of the coordinate algebra $ \mathcal{O} ( G ) $ of a complex semisimple Lie group $ G $ are in bijection with the points of $ G $, via the correspondence assigning to each point of $ G $ the kernel of the associated evaluation homomorphism on $ \mathcal{O} ( G ) $. This establishes a direct link between the algebraic structure of $ \mathcal{O} ( G ) $ and the geometry of $ G $. In this talk, we investigate the quantum analogue of this classical relationship for the $ q $-deformation $ G_q $. Specifically, we establish a sharp dichotomy: primitive ideals in homogeneous Joseph strata arise as kernels of irreducible representations of $ \mathcal{O} ( G_q ) $ by bounded operators on Hilbert spaces, which provide a quantum analogue of evaluation homomorphisms at points of $ G $, whereas those in inhomogeneous Joseph strata do not. This clarifies the extent to which the primitive spectrum of $ \mathcal{O} ( G_q ) $ can be accessed through operator-theoretic methods. We also analyze the semiclassical consequences of this result in light of the fact that the primitive ideals of $ \mathcal{O} ( G_q ) $ are parametrized by the symplectic leaves of the natural Poisson structure on $ G $. This talk is based on joint work with Christian Voigt.
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
Classification of certain actions of representation categories
2026年6月5日(金) 15:00 - 17:00
星野 真生 (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)
Last year I showed a classification theorem for certain classes of module categories over the representation category of quantum SU(n). Although its proof is elementary, the classification itself has a natural interpretation based on the concept of quantization.
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
Introduction to categorification and link homology
2026年5月28日(木) 14:00 - 15:30
Mikhail Khovanov (Professor, Department of Mathematics, Johns Hopkins University, USA)
Quantum link invariants relate topology in 3 dimensions to mathematical physics and representation theory. They admit liftings to 4-dimensional structures, known as link homology. We will explain how the skein relations for quantum invariants turn into homological structures at this higher level and how semisimple representation theory turns into non-semisimple representations and homological algebra upon categorification.
会場: 大河内記念ホール (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
Singularities of differentiable maps and Thom polynomials
2026年5月22日(金) 15:00 - 17:30
田邊 真郷 (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)
Singularities are locations where something is exceptional. In particular, singularities of differentiable maps are mathematical concepts corresponding to stationary points of functions and apparent contours of surfaces under projection onto the retina. These are unavoidable in general, but important to study the shape of spaces and behavior of maps. The theory for them was initiated by R. Thom in 1950's, and have been deeply studied by many researchers.
会場: 理化学研究所 和光キャンパス (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
Tropical geometry as a tool in algebraic geometry and beyond
2026年5月13日(水) 15:30 - 17:00
Paul Alexander Helminck (Assistant Professor, Mathematical Institute of the Polish Academy of Sciences, Poland)
Tropical geometry is a field in mathematics that lies at the interface of algebraic geometry and combinatorics. One of the main goals in tropical geometry is to uncover the combinatorial patterns hidden in algebraic geometry. This basic principle can already be found in Bézout’s theorem, which counts the roots of sufficiently generic polynomial equations, and its generalization in the form of the BKK theorem, both of which can be proven tropically. The abstract combinatorial ideas that come out of this study have since also seen applications in economics, machine learning, chemical reaction networks and mathematical physics, among others. In this talk I will give an introduction to tropical geometry and I will discuss some of the main results. I will also discuss some of my latest work on finding the topology of an algebraic variety using tropical methods. In particular, I will discuss how this gives rise to a CW complex structure on a K3 surface. This structure for instance gives us a quick way to see various phenomena from mirror symmetry such as the monodromy of integral affine structures.
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
Six operations in differential topology
2026年5月8日(金) 15:00 - 17:00
前川 拓海 (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)
The formalism of six operations, pioneered by Grothendieck and Verdier, serves as a unifying framework for studying cohomological phenomena. This language realizes Poincaré-type duality and transfer maps as certain adjunctions between stable $\infty$-categories of sheaves. In this talk, we highlight the theory of six operations in topology and apply it to provide an intrinsic version of the Pontryagin-Thom construction. We then discuss the intrinsic construction of invariants coming from Seiberg-Witten theory, which is based on the speaker's previous work.
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
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
122 イベント