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.

We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the learning of layerwise propagation is done and optimised independently on each layer. The architecture uses physics-informed renormalisation group flows that provide access to the layerwise propagation step from one layer to the next in terms of a diffusion equation for the respective renormalisation group kernel through a given layer. Thus, it transforms the generative task into that of solving once the set of independent and linear differential equations for the kernels of the transformation. As these equations are analytically known, the kernels can be refined iteratively. This allows us to structurally tackle out-of-domain problems generally encountered in generative models and opens the path to further optimisation. We illustrate the practical feasibility of the architecture within simulations in scalar field theories.

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.

12:00 – 13:30 Participate in Coffee Meeting
13:30 – 14:10 Okuto Morikawa (Special Postdoctoral Researcher, RIKEN iTHEMS) — Research Keywords: Lattice Field Theory, Conformal Field Theory, Quantum Field Theory, Particle Physics
14:10 – 14:30 Break
14:30 – 15:10 Ryosuke Iritani (Senior Research Scientist, RIKEN iTHEMS) — Research Keywords: Mathematical Biology, Evolutionary Ecology

Understanding genetic differences between populations is essential for avoiding confounding in genome-wide association studies and improving polygenic score (PGS) portability. We developed a statistical pipeline to infer fine-scale Ancestry Components and applied it to UK Biobank data. Ancestry Components identify population structure not captured by widely used principal components, improving stratification correction for geographically correlated traits. To estimate the similarity of genetic effect sizes between groups, we developed ANCHOR, which estimates changes in the predictive power of an existing PGS in distinct local ancestry segments. ANCHOR infers highly similar (estimated correlation 0.98 ± 0.07) effect sizes between UK Biobank participants of African and European ancestry for 47 of 53 quantitative phenotypes, suggesting that gene–environment and gene–gene interactions do not play major roles in poor cross-ancestry PGS transferability for these traits in the United Kingdom, and providing optimism that shared causal mutations operate similarly in different populations.

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.

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.

This seminar will be conducted in a hybrid format, both in-person and via Zoom. Since it includes hands-on sessions, we kindly ask you to consider attending in person whenever possible to ensure more effective learning.
The overview of the seminar is as follows:

Program:
9:30 - 10:50 Yuri Kobayashi (IBM Quantum) "Introduction to IBM Quantum and Qiskit"
10:50 - 11:00 Break
11:00 - 12:20 Ori Alberton (QEDMA) "Introduction to QESEM error mitigation software: Theory,  use-case demonstrations and usage tutorial"

Abstract of Yuri Kobayashi's tutorial:
This talk introduces HPC researchers to the IBM Quantum platform and the Qiskit SDK, providing a practical orientation to quantum programming without assuming prior quantum-computing knowledge. Attendees will learn how to construct and execute quantum circuits using Qiskit, explore available simulators, and real quantum backends and submit jobs to IBM’s cloud-based quantum processors. The session will also showcase how to map your problem to quantum circuits through specific use-case applications.

Abstract of Ori Alberton's tutorial:
This talk introduces QESEM, Qedma’s characterization-based software tool for reliable, high-accuracy quasi-probabilistic error mitigation. We will begin by explaining why error mitigation methods are expected to be the first to unlock quantum advantage, and why they will continue to play a central role even as error correction becomes feasible. We will highlight some of the key innovations underlying QESEM’s operation and present recent results on IBM Heron r2 devices demonstrating its capabilities in the largest utility-scale unbiased error mitigation experiment to date. In addition different use-cases and demonstrations ran by QESEM users will be presented. Finally, we will provide guidance on how to start using QESEM to obtain error-mitigated results in experiments on IBM quantum systems.

In this talk, we will introduce a bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the linear Boltzmann equation. Our approach builds upon the previously studied Asymptotic-Preserving Neural Network (APNNs), which employs a micro-macro decomposition to handle the model’s multiscale nature. We specifically address a bottleneck in the original APNNs: the slow convergence of the macroscopic density in the near fluid-dynamic regime. This strategy significantly accelerates the training convergence as well as improves the accuracy of the forward problem solution, particularly in the fluid-dynamic limit. We show several numerical experiments on both linear Boltzmann and the Boltzmann-Poisson system that this new BI-APNN method produces more accurate and robust results for forward and inverse problems compared to the standard APNNs. This is a joint work with Zhenyi Zhu and Xueyu Zhu.

Urbanization is rapidly reshaping landscapes around the world, which poses questions about whether and how quickly animals and plants can adapt. Culex pipiens form molestus, more commonly known as the "London Underground mosquito," has been held up as a benchmark for the potential speed and complexity of urban adaptation. This intraspecific lineage within Cx. pipiens, a major West Nile virus vector, is purported to have evolved human biting and a suite of other human-adaptive behaviors in the subways and cellars of northern Europe within the past 200 years. Form molestus features prominently in textbooks as well as scholarly reviews of urban adaptation. Yet, the hypothesis of in situ urban evolution has never been rigorously tested.

I will talk our recent efforts to understand the contentious origin and evolutionary history of the urban, human-biting mosquito. Our synthesis and meta-analysis of rich yet confusing literature show that its London Underground origin is unlikely (Haba and McBride 2022 Current Biology). Whole genome resequencing and population genomics of 800+ mosquitoes across ~50 countries again debunk the in situ evolution hypothesis and instead support that molestus first adapted to human environments >1000 years ago in the Mediterranean or Middle East, most likely in ancient Egypt or another early agricultural society (Haba et al. 2025 Science). I will outline implications of our results in urban evolutionary biology as well as in public health.

Speaker Bio
Yuki Haba, Ph.D., is an evolutionary biologist passionate about understanding how and why diverse behaviors evolve in nature. He is currently a Leon Levy Scholar in Neuroscience at Columbia University's Zuckerman Mind Brain Behavior Institute. He aims to take multi-desciplinary approaches, combining genomics, neuroscience, and field-based behavioral ecology to comprehensively understand the evolution of behavior. Yuki completed his PhD at Princeton, MA at Columbia, and undergraduate degree at the University of Tokyo. Personal webpage: https://yukihaba.github.io/

Topological Data Analysis (TDA) applies algebraic topology to the study of data such as point clouds. When applied to image and volumetric data, TDA provides a way to capture the topological features that characterise shapes and spatial structures. In this talk, I will outline the strengths and limitations of TDA for image analysis, and compare its capabilities with those of deep neural networks. I will also present hands-on examples using our open-source software Cubical Ripser. Finally, I will highlight a new direction in the use of TDA for image processing.

I present the systematic construction of gauge theories based on free differential and L-infinity algebras. This provides a consistent algebraic framework for constructing gauge-invariant theories whose field content is extended by higher-degree differential forms as gauge potentials. I derive explicit expressions for the corresponding extended Chern-Simons actions and the generalized anomaly terms that emerge from them. Possible applications to gravity and supergravity will also be discussed.

High-dimensional numerical integration is a ubiquitous challenge across various fields, from mathematical finance to computational physics and Bayesian statistics. While standard Monte Carlo (MC) methods are robust, their probabilistic error convergence rate of $O(N^{-1/2})$ is often insufficient for demanding applications. In this talk, I will introduce Quasi-Monte Carlo (QMC) and Randomized QMC (RQMC) methods, which offer a powerful framework for accelerating integration using low-discrepancy point sets. A key advantage of this deterministic approach is its ability to achieve a convergence rate of $O(N^{-1+\epsilon})$, significantly outperforming the standard MC rate.

The second part of the talk will focus on the construction of point sets, specifically lattice rules and digital nets. I will explain how these methods achieve higher-order convergence rates, faster than $O(N^{-1})$, for sufficiently smooth integrands. I will also discuss their randomized variants and demonstrate how RQMC with mean-based estimators provides practical error estimation while maintaining high-order convergence. Finally, I will discuss recent progress in RQMC involving median-based estimators. I will highlight how these estimators achieve almost optimal convergence rates for various function spaces without requiring prior knowledge of the integrand.

I will describe how to measure the forces that drive cultural change, using inference tools from evolutionary theory. We study time series data from large corpora of parsed English texts to identify what drives language change over the course of centuries. We also measure frequency-dependent effects in time series of baby names and purebred dog preferences. The form of frequency dependence we infer helps to explain the diversity distribution of names, and it replicates across the United States, France, Norway and the Netherlands. We find different growth laws for male versus female names, attributable to different rates of innovation, whereas names from the bible enjoy a genuine advantage at all frequencies. Frequency dependence emerges from a host of underlying social and cultural mechanisms, including a preference for novelty that recapitulates fashion trends in dog owners. Studying culture through the lens of evolutionary theory provides a quantitative account of social pressures to conform or to be different; and it provides inference tools that may be used in biology as genetic and phenotypic time series are increasingly available.

The measurement problem arises in trying to explain how the objective classical world emerges from a quantum one. In this talk I’ll advocate for an alternative approach, in which the existence of a classical system is assumed a priori. By asking that the standard rules of probability theory apply to it when it interacts with a system linearly evolving in Hilbert space, I’ll show that with a few additional assumptions one can recover the unitary dynamics, collapse and Born rule postulates
from quantum theory. This gives an interpretation of quantum mechanics in which classically definite outcomes are always assigned probabilities, rather than superpositions, giving one-world instead of many. The main technical tool used is a change of measure on the space of classical paths, the functional form of which characterises the quantum dynamics and Born rules of a class of quantum-like theories. Time allowing, I will also discuss how these results clarify which additional assumptions must be accepted if one wishes to seriously consider classical alternatives to quantum gravity.

This fifth workshop will bring together researchers exploring the effective field theory (EFT) framework in diverse cosmological contexts. Topics will include EFT formulations of interacting dark matter and dark energy, open EFTs for gravity, and multi-field inflationary dynamics. By highlighting recent progress and open questions, the workshop seeks to bridge insights from the early and late universe through the unifying language of EFT. In addition to the invited talks, the workshop will feature a panel discussion designed to promote interaction between the speakers and participants.

One of the key goals of this event is to foster collaboration among researchers working in neighboring fields, and to encourage participation from young and early-career researchers who are interested in, but may not yet have worked on, these themes. The workshop welcomes a broad audience with an interest in theoretical cosmology, gravitation, and quantum field theory.

The workshops are organised by the Cosmology Study Group at RIKEN 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].