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

Starobinsky Inflation and Primordial Black Holes Production in Light of ACT, Planck and Swampland

2025年7月8日(火) 16:00 - 17:30

Sergei Ketov (東京都立大学 大学院理学研究科 物理学専攻 准教授 / 東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU) 客員研究員)

After a review of Starobinsky inflation, it is demonstrated how it fits both Planck and ACT observations, even in the presence of production of primordial black holes (as dark matter) at smaller scales. The Swampland Program constraints on the Starobinsky inflation are resolved also. Further constraints to inflation in the supergravity framework, arising via renormalization of precision LHC physics on electroweak scales are briefly outlined.

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

On the Entanglement and Energy Dynamics of Continuous Floquet-driven CFTs

2025年7月8日(火) 13:00 - 14:00

Yu-Xuan Zhang (Postdoctoral Fellow, Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, China)

A key approach to studying non-equilibrium quantum many-body systems is to suddenly alter their Hamiltonian and observe the resulting dynamical evolution. A single change is called a "quench", while periodic changes are termed "Floquet driving". Recently, Floquet driving protocols in two-dimensional conformal field theories (CFTs) have attracted widespread attention due to their exact solvability and rich phase structure. However, most studies are limited to discrete-type driving (e.g., as a square wave) and the associated stroboscopic dynamics (i.e., evolution at integer multiples of the driving period). A key obstacle is that a generic continuous driving is rarely analytically tractable. In this talk, I will introduce a class of exactly solvable continuous Floquet driving protocols. I will discuss the energy and entanglement dynamics under these protocols in 2D CFTs, as well as their holographic duals. Crucially, the results show that stroboscopic dynamics, if overinterpreted, can qualitatively misrepresent the system’s true continuous-time evolution.

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

Computational Problems in Post-Quantum Cryptography

2025年7月7日(月) 15:30 - 17:00

高木 剛 (東京大学 情報理工学系研究科 数理情報学専攻 教授)

The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these computational problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography (PQC) using alternative mathematical problems that are secure in the era of quantum computers. In this talk, we give an overview of recent developments in the research on PQC. We explain a standardization project of PQC conducted by the National Institute of Standards and Technology (NIST). We then introduce an efficient digital signature, QR-UOV, based on the hardness of solving a system of multivariate quadratic polynomial equations over a finite field (the MQ problem). We also introduce a computational challenge problem, Fukuoka MQ Challenge, which aims at evaluating the hardness of the MQ problem with practical parameters.

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

Boundary Scattering and Non-invertible Symmetries in 1+1 Dimensions

2025年7月4日(金) 14:00 - 15:00

嶋守 聡一郎 (大阪大学 大学院理学研究科 博士課程)

Recent studies by Copetti, Córdova and Komatsu have revealed that when non-invertible symmetries are spontaneously broken, the conventional crossing relation of the S-matrix is modified by the effects of the corresponding topological quantum field theory (TQFT). We extend these considerations to (1+1)-dimensional quantum field theories (QFTs) with boundaries. In the presence of a boundary, one can define not only the bulk S-matrix but also the boundary S-matrix, which is subject to a consistency condition known as the boundary crossing relation. We show that when the boundary is weakly-symmetric under the non-invertible symmetry, the conventional boundary crossing relation also receives a modification due to the TQFT effects. As a concrete example of the boundary scattering, we analyze kink scattering in the gapped theory obtained from the Φ(1,3)-deformation of a minimal model. We explicitly construct the boundary S-matrix that satisfies the Ward-Takahashi identities associated with non-invertible symmetries. This talk is based on the collaboration with Satoshi Yamaguchi.

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

iTHEMS Biology welcomes a new member!

2025年7月3日(木) 16:00 - 17:00

アイナ・コロメ ビラパナ (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 数理遺伝学理研ECL研究ユニット 特別研究員)

This meeting will be used to welcome a new members to the iTHEMS Biology Study Group: Postdoc Aina Colomer, who is joining Unit Leader Leo Speidel's Mathematical Genomics RIKEN ECL Research Unit. She will give us a 15-20 min talk to introduce her research. If time permits, let's also use this time to catch up on each other's current research. I hope that many people will join us to welcome this new member and come meet her and hear about her research.

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

Quantum Computing Algorithms and Institute of Mathematics-for-Industry

2025年7月3日(木) 15:30 - 17:00

落合 啓之 (九州大学 マス・フォア・インダストリ研究所 教授)

This is the kickoff talk of the Kyushu University Collaboration Team, which aims to foster communication between iTHEMS and IMI. I will introduce some of IMI's activities and organization, as well as my own work, including research on quantum algorithms that began with the launch of the Quantum Computing System Center in 2022.

会場: 研究本館 3階 345-347室

イベント公式言語: 英語

Exact WKB as unified analytic structure for resonance physics

2025年6月27日(金) 15:00 - 17:00

森川 億人 (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)

We develop a unified framework for analyzing quantum mechanical resonances using the exact WKB method. The non-perturbative formulation based on the exact WKB method works for incorporating well-established phenomenological regularizations, the ABC theorem (proof of the completeness of Hilbert space), and the rigged Hilbert space in resonant phenomena. By examining the inverted Rosen-Morse potential, we illustrate how the exact WKB analysis captures resonant phenomena rigorously. Also, we clarify the corresponding linear spaces defined in each step of the exact WKB manipulations. The complementarity between the essential analyticity for resonance and the ABC theorem leads us to construct a modified Hilbert space called the rigged Hilbert space within the exact WKB framework. This offers a deeper understanding of resonant states and their analytic structures. Our results provide a concrete demonstration of the non-perturbative accuracy of exact WKB methods in unstable quantum systems.

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

Universal Pseudo-Goldstone Damping from the Real-Time Functional Renormalization Group

2025年6月26日(木) 15:00 - 16:00

Yang-Yang Tan (Ph.D. Candidate, Dalian University of Technology, China)

Strongly correlated systems, from QCD matter to condensed matter, exhibit universal dynamics near phase transitions. However, despite the successes of various theoretical approaches, systematic treatments of fluctuations are scarce. This talk unveils a novel universal damping mechanism for pseudo-Goldstone modes in systems with spontaneously broken approximate symmetries. I will introduce the real-time functional renormalization group (fRG) method, a powerful non-perturbative framework for studying real-time dynamics near critical points. Using this approach within a critical O(N) model, we uncover a new universal scaling for pseudo-Goldstone damping. Different from the conventional damping found in holography and hydrodynamics, the new one is controlled by critical fluctuations, hence is invisible in mean-field systems or strongly correlated systems with classical gravity duals. Since the critical damping depends solely on the universalities of the critical point, irrespective of the microscopic details, our conclusion should be applicable to a wide class of interacting systems.

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

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

Simulating the spread of infection in networks with quantum computers

2025年6月26日(木) 13:00 - 14:00

王 啸洋 (理化学研究所 数理創造研究センター (iTHEMS) 数理展開部門 量子数理科学チーム 特別研究員)

Many classical stochastic processes can be modeled as Markovian processes, including the spreading of infection in networks. Simulating the Markovian processes using classical computers is generally unscalable for large networks. In this seminar, I will introduce the Hamiltonian evolution on quantum computers and how the Markovian spreading of infection can be efficiently simulated using the Hamiltonian evolution. In particular, we analytically and numerically analyze the evolution of a specifically designed Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. As an example, we simulate the infection spreading process of the SARS-CoV-2 variant Omicron in a small-world network. The simulation results are qualitative consistent with the infection spreading in the west coast of USA.

会場: via Zoom / セミナー室 (359号室)

イベント公式言語: 英語

Generative Models for Statistical Field Theories

2025年6月25日(水) 15:00 - 16:00

王 凌霄 (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 the final talk of the DEEP-IN series, we will explore the role of generative models in learning phase transitions and sampling in lattice systems. First, we demonstrate how generative models can serve as global samplers by learning the underlying probability distributions. This enables the sampling of configurations more efficiently for lattice field theories. We will also demonstrate how the ferromagnetic phase transition, the Kosterlitz-Thouless transition, and quantum phase transitions can be identified from generative models. I will briefly introduce generative diffusion models, which can be interpreted as a stochastic quantization scheme. This opens a new path for understanding deep generative models. This is an informal seminar, we will start with the methodology and some practical examples, and finally reserve time for everyone interested to discuss it together.

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

中性子星の物性物理II

2025年6月25日(水) 14:00 - 16:30

猪谷 大輔 (慶応義塾大学 自然科学研究教育センター 訪問研究員)

宇宙で最もコンパクトな天体である中性子星は様々な物質で構成されていますが、低温高密度な環境故、物質中で強い相互作用、ないし凝縮状態を示します。そうした量子物質の記述に物性物理の知見は欠かせません。本講演では、参加者との活発的な議論のもと、中性子星物質を記述する物性物理の理論的側面の解説が行われます。

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

イベント公式言語: 日本語

中性子星の物性物理I

2025年6月25日(水) 10:00 - 12:30

田島 裕之 (東京大学 大学院理学系研究科 助教)

宇宙で最もコンパクトな天体である中性子星は様々な物質で構成されていますが、低温高密度な環境故、物質中で強い相互作用、ないし凝縮状態を示します。そうした量子物質の記述に物性物理の知見は欠かせません。本講演では、参加者との活発的な議論のもと、中性子星物質を記述する物性物理の理論的側面の解説が行われます。

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: 日本語

ComSHeL introductions meeting

2025年6月24日(火) 14:00 - 15:30

Following our Launch Meeting on May 1st, in this second meeting of our study group we plan for each member of the ComSHeL Study Group and anyone who joins us that day to introduce their research briefly to get to know one another's focus and expertise. If you are interested in possibly collaborating with ComSHeL members and/or you would like to get to know some of the researchers who joined us as part of iTHEMS new Division of Applied Mathematical Science, please join us. I extended the duration to 90 min (from our usual 60 min) to make sure we have enough time to hear from everyone. Each attendee will have approximately 4 minutes to explain their past, current, or upcoming research and time will be kept strictly. Time might be adjusted on the day of the meeting based on the number of applicants. If you would like to show some slides (max 3 slides), please prepare them in advance and send them to cbeau@riken.jp in PDF format no later than June 20. But no one should feel they must prepare slides: it is fine to speak freely and informally about your work.

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

LLM-based physics analysis assistant at BESIII

2025年6月23日(月) 15:00 - 16:00

廖 一朴 (Ph.D. Student, Institute of High Energy Physics, Chinese Academy of Sciences, China)

The data processing and analyzing is one of the main challenges at HEP experiments. To accelerate the physics analysis and drive new physics discovery, the rapidly developing Large Language Model (LLM) is the most promising approach, it have demonstrated astonishing capabilities in recognition and generation of text while most parts of physics analysis can be benefitted. In this talk we will discuss the construction of a dedicated intelligent agent, an AI assistant names Dr.Sai at BESIII based on LLM, the potential usage to boost the data analysis. I will also provide a brief overview of the construction of the AI platform at the Institute of High Energy Physics (ai.ihep.ac.cn) and outline the roadmap for AI4HEP. Yipu Liao (廖一朴) is a Ph.D. student at the Institute of High Energy Physics, Chinese Academy of Sciences. His research is centered on particle physics data analysis, with a special emphasis on Charmonium(-like) and tau physics within the BESIII and Belle II experiments. He is actively engaged in the development of the AI assistant project (DrSai) for the BESIII experiment, and leads the design and evaluation of automated processes.

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

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

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

Programmed chromosome eliminations in flies

2025年6月19日(木) 13:00 - 14:00

ロバート・バイアード (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 訪問研究員)

Species that break the traditional rules of genetics and inheritance offer perhaps some of the best opportunities to study fundamental biological questions. Sciarids (fungus gnats) are a species-rich family of flies with highly unorthodox chromosome inheritance. Asymmetric male meiotic divisions result in elimination of the paternal genome every generation, and maternally-controlled eliminations of chromosomes in the developing embryo determine offspring sex. I use a combination of genomics, population genetics, and cytogenetics to understand both the mechanisms and the evolution of this system. I will discuss how these approaches have allowed us to uncover some fascinating biology as well as tackle broader biological questions.

会場: via Zoom / 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

Gauge-equivariant multigrid neural networks

2025年6月19日(木) 10:30 - 12:00

Tilo Wettig (Professor, Universität Regensburg, Germany)

In lattice QCD simulations, the most time-consuming element is typically the solution of the Dirac equation in the presence of a given gauge field. The current state of the art is to use a multigrid preconditioner to reduce the condition number of the Dirac operator matrix. We show how such preconditioners can be constructed using gauge-equivariant neural networks. For the multigrid solve we employ parallel-transport convolution layers. For the multigrid setup we consider two versions: the standard construction based on the near-null space of the operator, and a gauge-equivariant construction using pooling and subsampling layers. We show that both versions eliminate critical slowing down.

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