Mathematical Application Research Team Meeting

Mathematical Application Research Team Meeting #19

September 28 (Mon) 14:00 - 15:15, 2026

Antoine Diez (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

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

Venue: #359, Seminar Room #359 (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #18

August 28 (Fri) 14:00 - 15:15, 2026

Shinichiroh Matsuo (Associate Professor, Graduate School of Mathematics, Nagoya University)

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.

Venue: via Zoom / Okochi Hall

Event Official Language: English

Mathematical Application Research Team Meeting #17

July 17 (Fri) 10:30 - 11:45, 2026

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.

Venue: via Zoom / #359, Seminar Room #359

Event Official Language: English

Mathematical Application Research Team Meeting #16

June 26 (Fri) 10:30 - 12:00, 2026

Yuichi Ike (Associate Professor, Graduate School of Mathematical Sciences, The University of Tokyo)

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.

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #15

May 22 (Fri) 10:30 - 12:00, 2026

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.

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #14

April 24 (Fri) 14:00 - 15:30, 2026

Shin-ichi Ohta (Professor, School of Science, The University of Osaka)

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.

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #13

March 6 (Fri) 14:00 - 15:00, 2026

Chihaya Jibiki (Ph.D. Student, Department of Mathematics, School of Science, Institute of Science Tokyo)

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).

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #12

February 6 (Fri) 14:00 - 15:30, 2026

Riccardo Muolo (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

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].

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #11

December 12 (Fri) 15:00 - 16:30, 2025

So Matsuura (Professor, Department of Physics Hiyoshi, Keio University)

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.

Venue: Seminar Room #359 (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #10

November 14 (Fri) 16:00 - 17:00, 2025

Yoshiko Ogata (Professor, Research Institute for Mathematical Sciences (RIMS), Kyoto University)

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.

Venue: #359, Seminar Room #359 (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #9

October 10 (Fri) 13:30 - 14:30, 2025

Antoine Diez (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

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.

Venue: #359, 3F, Main Research Building (Main Venue) / via Zoom

Event Official Language: English

Mathematical Application Research Team Meeting #8

September 5 (Fri) 10:30 - 11:50, 2025

Sonia Mahmoudi (Assistant Professor, Mathematical Science Group, Advanced Institute for Materials Research (AIMR), Tohoku University)

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

Venue: via Zoom / #359, 3F, RIKEN Wako Campus

Event Official Language: English

Mathematical Application Research Team Meeting #7

July 18 (Fri) 14:00 - 15:30, 2025

Hirosi Ooguri (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

Venue: via Zoom / #359, Seminar Room #359

Event Official Language: English

6th Mathematical Application Research Team Meeting

July 4 (Fri) 11:00 - 12:00, 2025

阪田 直樹 Sakata (Assistant Professor, Mathematical Science Group, Advanced Institute for Materials Research (AIMR), Tohoku University)

Venue: via Zoom / #359, Seminar Room #359

Event Official Language: English

5th Mathematical Application Research Team Meeting

June 20 (Fri) 14:00 - 15:30, 2025

Taketo Sano (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Venue: Seminar Room #359 (Main Venue) / via Zoom

Event Official Language: English

4th Mathematical Application Research Team Meeting

June 6 (Fri) 14:00 - 15:30, 2025

Sinya Aoki (Deputy Director, Fundamental Quantum Science Program, TRIP Headquarters, RIKEN)

An alternative view on AdS/CFT correspondence

Venue: #345-347, Main Research Building, RIKEN Wako Campus (Main Venue) / via Zoom

Event Official Language: English

3rd Mathematical Application Research Team Meeting

May 2 (Fri) 13:30 - 15:00, 2025

Antoine Diez (Research Scientist, Mathematical Application Research Team, Division of Applied Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))

Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359 / via Zoom

Event Official Language: English