数学応用研究チームミーティング

Mathematical Application Research Team Meeting #19

2026年9月28日(月) 14:00 - 15:15

アントワーヌ・ディエズ (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)

In this meeting, Antoine Diez will give a talk on his work in progress regarding "Scaling limits for active Laguerre tessellations."

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

Mathematical Application Research Team Meeting #18

2026年8月28日(金) 14:00 - 15:15

松尾 信一郎 (名古屋大学 大学院多元数理科学研究科 准教授)

Mathematical Application Research Team is delighted to welcome Prof. Shinichiroh Matsuo from Nagoya University for an upcoming team meeting. We warmly invite everyone to join us to hear his talk. Please note that, exceptionally, this meeting will be held at Okochi Hall. Immediately following Prof. Matsuo’s talk, Prof. Hiraku Nakajima will give a seminar entitled “Coulomb branches in supersymmetric gauge theories.” We encourage participants to join us for both talks. Title: The Index of Wilson--Dirac Operators Revisited: Beyond Regular Lattices on Flat Tori Abstract: This is joint work with Mikio Furuta. Our ultimate goal is to discretise Seiberg--Witten theory. In view of PL = DIFF in dimension four, we would like to construct something like a PL Seiberg--Witten theory. As a first step towards this goal, we have studied the discretisation of the analytic index of Dirac operators. In earlier work, using K-theoretic methods, we showed that the index of the Wilson--Dirac operator associated with a sufficiently fine regular lattice on a flat torus agrees with that of the corresponding continuum Dirac operator. However, this lattice-index construction was confined to regular lattices on flat tori. In this talk, I will introduce “mesoscopic” Wilson--Dirac operators on arbitrary closed Riemannian manifolds. They form a family of bounded integral-difference operators on \(L^2\), parametrised by a mesoscopic length \(a>0\), and they converge, in a suitable sense, to the continuum Dirac operator as \(a \to 0\). The mesoscopic operators are self-adjoint and Fredholm, but not odd, so the usual graded Fredholm index is unavailable. We prove that the “index” of a mesoscopic Wilson--Dirac operator agrees with the index of the corresponding continuum Dirac operator when \(a\) is sufficiently small. Replacing the integrals in our mesoscopic operators by Riemann sums produces finite-dimensional lattice approximations on general closed Riemannian manifolds. The mesoscopic Wilson--Dirac operators thus provide a bridge between the microscopic continuum Dirac operator and the macroscopic lattice Dirac operators.

会場: via Zoom / 大河内記念ホール

イベント公式言語: 英語

Mathematical Application Research Team Meeting #17

2026年7月17日(金) 10:30 - 11:45

Hugo Koubbi (Ph.D. Student, CEREMADE, Université Paris Dauphine, France)

Mathematical Application Research Team is delighted to welcome Hugo Koubbi from CEREMADE, Université Paris Dauphine, for an upcoming team meeting. We warmly invite everyone to join us to hear his talk: Title: Mean-field Transformers Abstract: Since their introduction, Transformers have achieved unprecedented success across a wide range of deep-learning tasks. In this talk, we present a recent line of work that interprets Transformer architectures as interacting particle systems and studies their continuum, or mean-field, limits. By considering idealized attention dynamics on the sphere, we establish connections between Transformers, Wasserstein gradient flows, and synchronization models such as the Kuramoto model. We describe a global clustering phenomenon in which tokens eventually synchronize, following long-lived metastable regimes characterized by the coexistence of several clusters. Finally, we explain how recent work extends these ideas beyond idealized models and reveals analogous phenomena in more realistic Transformer architectures at initialization.

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

Mathematical Application Research Team Meeting #16

2026年6月26日(金) 10:30 - 12:00

池 祐一 (東京大学 大学院数理科学研究科 准教授)

Mathematical Application Research Team is honored to invite Prof. Yuichi Ike from the University of Tokyo to this meeting. Everyone is welcome to join the meeting to listen to his seminar. Title: Persistent Homology: Theory and Applications Abstract: Persistent homology is one of the main tools in topological data analysis (TDA), encoding the topological features of given data into persistence diagrams, which are multisets in two-dimensional space. It has been successfully applied to various fields such as materials science and computer graphics. In this talk, I will provide an overview of persistent homology from both theoretical and practical viewpoints. I would also like to discuss persistent-homology-based loss functions, which can be used to control the topological structure of parameters in machine learning.

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #15

2026年5月22日(金) 10:30 - 12:00

Pietro De Lellis (Associate Professor, Department of Electrical Engineering and Information Technology, University of Naples Federico II, Italy)

Mathematical Application Research Team is delighted to welcome Dr. Pietro De Lellis from University of Naples Federico II, for an upcoming team meeting. We warmly invite everyone to join us for this opportunity to hear about his latest research. Title: Synchronization and Control in Higher-Order Network Dynamics Abstract Understanding how network structure shapes coordinated behavior in coupled dynamical systems is a central question in network science. Although pairwise interactions among identical nodes are well understood, much less is known about the effects of directed higher-order interactions, especially in systems with heterogeneous nodes. In this seminar, I will discuss recent results on the emergence and control of collective behavior in such systems. I will first present an extension of the standard pairwise framework to higher-order directed interactions and derive conditions for synchronization in the identical-node setting. I will then introduce a mathematically grounded heuristic for steering the system toward a prescribed trajectory. Moving to heterogeneous dynamics, I will present a new notion of network synchronizability that quantifies how hypergraph topology can promote trajectory alignment even when node parameters differ. The resulting metric is analytically derived, agrees closely with numerical observations, and scales efficiently to large networks. This makes it possible to compare higher-order and pairwise interactions systematically, and to identify when multi-body interactions favor or obstruct synchronization. I will conclude with an application to opinion dynamics, where the framework highlights which hyperedges are most conducive to consensus formation.

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #14

2026年4月24日(金) 14:00 - 15:30

太田 慎一 (大阪大学 理学研究科 教授)

Mathematical Application Research Team is honored to invite Prof. Shin-ichi Ohta from the University of Osaka to this meeting. Everyone is welcome to join the meeting to listen to his seminar. Title: Synthetic and comparison Lorentzian geometry Abstract: In this talk we review recent developments of synthetic geometric approaches to Lorentzian geometry, motivated by the theory of less regular spacetimes in general relativity as well as comparison geometry in the Riemannian setting. Among others, optimal transport theory plays a vital role.

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #13

2026年3月6日(金) 14:00 - 15:00

地引 知栄 (東京科学大学 理学院 数学科 博士課程)

The Mathematical Application Research Team is pleased to welcome Chiyaha Jibiki, who will join the team as an SPDR in April. He will give a talk at this meeting prior to his official start date. Everyone is welcome to join the meeting. Title: Left-Orders and Dynamics: Applications to Hyperbolic Geometry and Low-Dimensional Topology Abstract: A left-order on a group is a total order that is invariant under left-multiplication. The concept dates back to the early 20th century, when Dedekind and Hölder characterized the natural order on the real line purely in terms of group actions. In the 21st century, this theory has evolved significantly through connections with discrete dynamical systems. Currently, there is active research linking geometric structures to left-orders on geometrically significant groups, such as fundamental groups and mapping class groups. In this talk, I will introduce the framework of left-order theory, starting from the simple perspective of binary operations on infinite sets. I will then provide an overview of the field by presenting, as much as possible, the diverse applications arising from its high versatility. In particular, I will discuss the speaker's recent results concerning the structure of the space of left-orders (comparisons between left-orders) and methods for constructing specific left-orders. This talk includes joint work with Shuhei Maruyama (Kanazawa University).

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #12

2026年2月6日(金) 14:00 - 15:30

リッカルド・ムオロ (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)

Mathematical Application Research Team invites Riccardo Muolo fom Division of Fundamental Mathematical Science to this meeting. You are welcome to join the meeting. Title: Dynamics beyond nodes: a topological framework for oscillatory dynamics on higher-order networks Abstract: In recent years, increasing attention has been given to dynamical processes taking place on higher-order networks, where interactions are not limited to links, but may involve also higher-dimensional simplices [1]. While classical network models assume that state variables live on nodes and interact through links, many real systems — including brain, climate, and transportation systems — cannot be fully described within this node-centric perspective [2]. In this seminar, I will introduce the framework of higher-order networks and the concept of topological signals, namely, dynamical variables defined on simplices of higher dimensions. I will briefly present the basic tools required for this setting, including elementary notions of discrete calculus, discrete topology and geometric algebra, which serve as the mathematical foundation for modeling dynamical processes beyond the node-based paradigm. Next, I will discuss models of oscillatory dynamics extended to this framework. First, I will present the topological Kuramoto model [3], in which phases are not restricted to nodes but may also be associated with links, and where the coupling arises from the combinatorial structure of the simplicial complex. Then, I will introduce the discrete Hodge Laplacian and the Dirac-Bianconi operator [4], the former generalizing diffusive interactions to the higher-order setting, while the latter provides cross-talk between signals defined on simplices of different dimensions. Finally, I will introduce the notion of Dirac-Bianconi driven oscillators, where the dynamics of node- and link-signals coexist, interact and may give rise to collective oscillatory behaviors [5].

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #11

2025年12月12日(金) 15:00 - 16:30

松浦 壮 (慶応義塾大学 日吉物理学教室 教授)

Mathematical Application Research Team invites Prof. So Matsuura from Keio University for this meeting. You are welcome to join the meeting. Title: Phases and Duality in Fundamental Kazakov-Migdal Model on the Graph Abstract: In this talk, we will explore the fundamental Kazakov-Migdal (FKM) model on a generic graph, where the partition function is represented by the Ihara zeta function weighted by unitary matrices. The effective action of the FKM model is described by a summation of all Wilson loops on the graph, which can be regarded as an extension of the usual Wilson action in lattice gauge theory. We show that the FKM model on regular graphs exhibits an exact strong/weak coupling duality, reflecting the functional equation of the Ihara zeta function. We also discuss the relation between the stability of the FKM model and the pole distribution of the Ihara zeta function. Interestingly, the FKM model universally exhibits the so-called Gross-Witten-Wadia (GWW) phase transitions. We estimate the phase structure of the FKM model in both small and large coupling regions, which is validated through numerical simulations. If time permits, we will examine the phase transition of the FKM model from the Young diagram perspective and discuss its relation with the GWW phase transition indicated by the eigenvalue distribution.

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

Mathematical Application Research Team Meeting #10

2025年11月14日(金) 16:00 - 17:00

緒方 芳子 (京都大学 数理解析研究所 (RIMS) 教授)

Mathematical Application Research Team invites Prof. Yoshiko Ogata from RIMS for this meeting. Her talk title will be announced later. You are welcome to join the meeting. The title and the abstract of her talk are: Title: Mixed state topological order: operator algebraic approach Abstract: We consider anyons in mixed states of two-dimensional quantum spin systems within the operator-algebraic framework of quantum statistical mechanics. To each state satisfying a mixed-state version of approximate Haag duality, we associate a braided C*-tensor category, which we interpret as describing the anyonic excitations of the state. We then investigate how these anyonic structures behave under interactions with the environment.

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

Mathematical Application Research Team Meeting #9

2025年10月10日(金) 13:30 - 14:30

アントワーヌ・ディエズ (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)

In this meeting, Antoine Diez will give a talk entitled "Mean-field limits a la Tanaka and large deviations for particle systems with network interactions." Feel free to join if you are interested.

会場: 研究本館 3階 359号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Mathematical Application Research Team Meeting #8

2025年9月5日(金) 10:30 - 11:50

ソニア・マムーディ (東北大学 材料科学高等研究所 (AIMR) 数学連携グループ 助教)

The 8th meeting of the Mathematical Application Research Team invites Sonia Mahmoudi for a talk.

会場: via Zoom / 理化学研究所 和光キャンパス 3階 359号室

イベント公式言語: 英語

Mathematical Application Research Team Meeting #7

2025年7月18日(金) 14:00 - 15:30

大栗 博司 (Fred Kavli Professor and Director, Walter Burke Institute for Theoretical Physics, California Institute of Technology, USA)

As the 7th meeting of the Mathematical Application Research Team, we invite Prof. Hirosi Ooguri to give a lecture. Title: Gravity is Different - Counterexamples to the Wilsonian Paradigm of Low Effective Theory

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

6th Mathematical Application Research Team Meeting

2025年7月4日(金) 11:00 - 12:00

阪田 直樹 (東北大学 材料科学高等研究所 (AIMR) 数学連携グループ 助教)

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

5th Mathematical Application Research Team Meeting

2025年6月20日(金) 14:00 - 15:30

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)

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

4th Mathematical Application Research Team Meeting

2025年6月6日(金) 14:00 - 15:30

青木 愼也 (理化学研究所 最先端研究プラットフォーム連携 (TRIP) 事業本部 基礎量子科学研究プログラム 副プログラムディレクター)

An alternative view on AdS/CFT correspondence

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

3rd Mathematical Application Research Team Meeting

2025年5月2日(金) 13:30 - 15:00

アントワーヌ・ディエズ (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)

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 / via Zoom

イベント公式言語: 英語