Seminar
1057 events
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SeminarAI and Scientific Discovery
October 19 (Mon) 14:00 - 15:30, 2026
Joseph Ledsam (Google Health Lead, Japan, Google Japan)
Artificial intelligence is having a transformative impact on health and scientific discovery. This presentation will trace the evolution from foundational breakthroughs to the sophisticated capabilities of today's large-scale AI models. It will explore how these advanced systems are creating new possibilities across the healthcare landscape, from accelerating therapeutic development to enhancing diagnostic processes and interpreting complex medical data. The session will also take a deeper look at the future possibilities for AI in health and explore the emerging role of agentic AI in scientific discovery. The core theme is the responsible development of AI to create tools that assist scientists, support healthcare professionals, and empower users. Bio: Dr Joseph Ledsam leads Google Health in Japan, where he works across AI research, digital health and health in Google products. He has led research in medical AI, genomics and drug discovery published in journals including Nature, Nature Medicine and Nature Methods. Before moving to Japan he worked as a medical doctor in the UK, and founded the Health Research and Genomics teams in Google DeepMind. He obtained his medical degree from The University of Leeds, UK, and was a research fellow at University College London during his clinical residency.
Venue: #435-437, Main Research Building (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Center-vortex condensation and monopole condensation in 4d gapped phases
July 27 (Mon) 14:00 - 15:30, 2026
Yui Hayashi (JSPS Postdoctoral Research Fellow, Yukawa Institute for Theoretical Physics, Kyoto University)
Two well-known scenarios for quark confinement are center-vortex proliferation and monopole condensation. We consider gauge-invariant criteria for center-vortex condensation and monopole condensation in terms of Z(N) 1-form symmetry. The condensation of a soliton can be characterized by the non-suppression of the partition function with a proper twisted boundary condition, and we utilize this idea for these criteria. With these definitions, we show that gapped phases with the center-vortex condensation necessarily exhibit the monopole condensation.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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SeminarSome instances where topological illustration induced new mathematics
July 24 (Fri) 16:30 - 18:00, 2026
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.
Venue: via Zoom
Event Official Language: English
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Seminar
Unraveling the very early universe with black holes, boson stars, and cannibal stars
July 24 (Fri) 14:00 - 16:00, 2026
Takeshi Kobayashi (Associate Professor, International School for Advanced Studies (SISSA), Italy)
According to the standard picture of cosmology, the rich structure of our universe began to form roughly 50,000 years after the big bang. In this talk I will explore the possibility that cosmic structures could also have formed in the extremely early universe, within a fraction of a second after inflation. I will show how this early structure formation can give rise to compact objects, including exotic stars and primordial black holes. These relics provide powerful probes of the first instants of cosmic history, especially the reheating epoch, and may even act as seeds for cosmological phase transitions. Note: This seminar is jointly organized by the iTHEMS-phys Study Group and the iTHEMS-ABBL Joint Astro Study Group.
Venue: Seminar Room #359 / via Zoom
Event Official Language: English
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SeminarThe decision intelligence of humans and machines
July 24 (Fri) 10:30 - 11:30, 2026
Petter Holme (Professor, Department of Computer Science, Aalto University, Finland)
The event has been rescheduled from July 22 to July 24. To understand our near-future of artificial intelligence firmly integrated into many levels of social life, a challenge is to understand the differences and similarities between human and AI decision-making. In controlled laboratory settings assessing risk and uncertainty, LLMs demonstrate superhuman efficiency but fundamentally diverge from human behavior through a rigid hyper-rationality and an inability to disengage from obsolete strategies. However, when applied to messy, real-world dilemmas "in the wild," these models pivot to function as highly effective "satisficers". Human subjects consistently prefer this artificial counsel over human peer advice, noting its ability to carefully balance emotional context with logical constraints while actively reducing anxiety and regret. Ultimately, this synthesis shows that while AI can offer near-optimal laboratory performance and therapeutic impact in daily life, they also have a distinct lack of behavioral plasticity that we need to account for in models of the future.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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SeminarA first step towards Non-Archimedean Geometric Quantization
July 17 (Fri) 14:00 - 15:30, 2026
Keita Goto (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
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.
Venue: Seminar Room #359, Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
What determines accuracy in matrix projection models?
July 10 (Fri) 14:30 - 15:30, 2026
Richard Shefferson (Professor, Graduate School of Arts and Sciences, The University of Tokyo)
Matrix projection models (MPMs) have grown in complexity as ecologists have sought to include more factors that may influence population size and structure. However, some studies suggest that MPMs may lead to predictions inaccurate enough as to question their overall utility. I used long-term (21-36 year) demographic datasets on 6 herbaceous perennial species to examine and compare the ability of MPMs with different structural characteristics to predict future population size and structure. In absolute terms, almost all models performed poorly. In relative terms, density-dependent, ahistorical stage-based models with simple life histories and fewer stages were most successful in predicting population size. My results indicate that MPMs and IPMs are typically poor predictors of absolute population size and structure, but, when constructed properly, can still be used as useful qualitative predictors of population change.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Multi-field Inflation with spectator Axions
July 9 (Thu) 14:00 - 16:00, 2026
Diederik Roest (Professor, Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Netherlands)
We will review the inflationary paradigm, with a focus on multi-field inflation. We then propose a generic mechanism in which a light axion spectator reshapes inflationary observables through purely gravitational multi‑field dynamics. In this scenario, the axion is frozen during inflation and starts rolling towards the end, inducing a turn in field space and transient tachyonic phases of the isocurvature mode. This generates a nearly scale‑invariant enhancement of the curvature power spectrum, suppressing the tensor‑to‑scalar ratio and shifting the scalar tilt to a weighted combination of adiabatic and entropic tilts at horizon crossing. We show that these effects can reconcile otherwise disfavored inflaton potentials with current CMB constraints, and predict order-one non-Gaussianities.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Sampling Lattice Gauge Theories with Gauge-Equivariant Neural Networks and Diffusion Models
July 8 (Wed) 14:00 - 15:30, 2026
Andreas Ipp (Senior Scientist, Institute for Theoretical Physics, Technische Universität Wien, Austria)
Thomas Ranner (Project Assistant (FWF), Institute for Theoretical Physics, Technische Universität Wien, Austria)Simulating non-Abelian lattice gauge theories using classical Markov chain Monte Carlo (MCMC) methods is often bottlenecked by critical slowing down and topological freezing. Incorporating physical symmetries into machine learning architectures offers a powerful way towards overcoming these computational limitations. In this talk, we present an overview of how gauge-equivariant neural networks can enhance lattice simulations. In the first part, we introduce Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs), which build local gauge symmetry directly into the network structure. We discuss their ability to learn Wilson loops and highlight their versatility across different applications, such as approximating effective actions. In the second part, we focus on their application in generative modeling: gauge-equivariant diffusion models. Using a Metropolis-adjusted annealed Langevin scheme, these models are designed to generate uncorrelated field configurations. We demonstrate accurate sampling of 2D U(2) and SU(2) theories, showcase recent advancements in scaling up to 4D SU(3) pure gauge theory, and show that these models extrapolate remarkably well to larger lattices and inverse couplings beyond their training regime.
Venue: #445--447, 4F, Main Research Building (Main Venue) / via Zoom
Event Official Language: English
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Seminar
iTHEMS-FQSP joint seminar “Aspects of Tripartite Haar Random States”
July 8 (Wed) 10:30 - 12:00, 2026
Beni Yoshida (Research Faculty Senior Faculty, Perimeter Institute for Theoretical Physics, Canada / Senior Visiting Scientist, Fundamental Quantum Science Program, RIKEN)
Randomness plays central roles in understanding strongly entangled quantum systems. The foundational result is Page’s theorem: a bipartite Haar random state is nearly maximally entangled. In this talk, I will ask what happens when the system is divided into three parts. We show that tripartite Haar random states have a very different structure: when each subsystem contains fewer than half of the total qubits, no EPR-like bipartite entanglement can be distilled between any pair by local unitaries or local operations. I will discuss several consequences of this observation, including its implications for quantum error correction, complementary recovery, connected entanglement wedges in AdS/CFT, and possible baby-universe degrees of freedom.
Venue: Okochi Hall (Main Venue) / via Zoom
Event Official Language: English
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Seminar Tomorrow
Overview of quantum error correcting codes
July 7 (Tue) 15:00 - 16:30, 2026
Takaya Matsuura (Postdoctoral Researcher, Quantum Computing Theory Research Team, RIKEN Center for Quantum Computing (RQC))
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar In Session
Toward an understanding of microbial circulation in the Mongolian nomadic ecosystem
July 6 (Mon) 13:00 - 14:00, 2026
Akari Shinoda (Assistant Professor, Faculty of Environmental, Life, Natural Science and Technology, Okayama University)
I have been studying microorganisms in the Mongolian nomadic ecosystem from several perspectives. First, I seek to characterize the microbial communities in traditional fermented dairy products—most notably airag (fermented mare's milk)—and their features. Second, I am analyzing the relationship between the traditional Mongolian diet and the gut microbiome. Third, focusing on environmental microorganisms (bioaerosols) in regions undergoing desertification, I aim to trace their origins and atmospheric transport. In the course of these studies, I have come to suspect that microorganisms may circulate among humans, livestock, fermented foods, and the environment. In this research, I aim to understand such microbial circulation by combining approaches from each of these perspectives and by investigating the relationships among these elements. In this talk, I will provide an overview of each topic and discuss the potential of an interdisciplinary approach that connects them.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Thom polynomials relative to prescribed maps around the boundary
July 3 (Fri) 15:00 - 17:30, 2026
Masato Tanabe (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
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.
Venue: Seminar Room #359, Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Cosmic-ray bath in a past supernova gives birth to Earth-like planets
July 3 (Fri) 14:00 - 15:15, 2026
Ryo Sawada (Special Postdoctoral Researcher, Division of Fundamental Mathematical Science, RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS))
A key question in astronomy is how ubiquitous Earth-like rocky planets are. The formation of terrestrial planets in our Solar System was strongly influenced by the radioactive decay heat of short-lived radionuclides (SLRs), particularly 26 Al (aluminum-26), likely delivered from nearby supernovae. However, current models struggle to reproduce the abundance of SLRs inferred from meteorite analysis without destroying the protosolar disk. We propose the "immersion" mechanism, where cosmic-ray nucleosynthesis in a supernova shockwave reproduces estimated SLR abundances at a supernova distance (~1 parsec), preserving the disk. We estimate that solar mass stars in star clusters typically experience at least one such supernova within 1 parsec, supporting the feasibility of this scenario. This suggests that Solar System─like SLR abundances and terrestrial planet formation are more common than previously thought.
Venue: #424-426, Main Research Building
Event Official Language: English
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Seminar
Gauge and Homological Structures in Quantum Error Correction
July 2 (Thu) 16:00 - 17:00, 2026
Junichi Haruna (Program-Specific Researcher, Graduate School of Informatics, Kyoto University)
Gauge theory, quantum error correction, and homology theory share a common mathematical backbone that, when made explicit, becomes a practical toolkit for fault-tolerant quantum computation. A CSS code is naturally a length-2 chain complex in which the X-stabilizers act as Gauss-law generators and the code space is the gauge-invariant subspace, the toric code being the prototypical realization of a Z_2 lattice gauge theory. Building on this correspondence, I present two results. First, I introduce a gauge-field formalism in which logical gates are written as exponentials of polynomials of operator-valued cochains—the lattice gauge fields—on the underlying chain complex. Requiring no special structure on the code, the construction applies to general CSS codes and yields explicit physical-gate decompositions of logical S, H, CZ, and T gates whose action depends only on the cohomology class of the logical qubits. Second, I show that the transversal implementability of logical Pauli-Z rotations has a purely homological origin: their logical action is classified by a Z_{2^m}-module extending logical Pauli operators to higher levels of the Clifford hierarchy, and transversality is governed by compatibility and lifting obstructions on homology classes beyond the usual Z_2 coefficient. From a high-energy-physics viewpoint, a level-m transversal gate is a gauge-invariant "2^{m-1}-th root of a Wilson loop." Together these results offer a unifying language for designing logical gates and point toward fault-tolerance from lattice gauge theory and algebraic topology. This talk is based on arXiv:2511.15224 and arXiv:2602.14499.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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Seminar
Cosmology with Galaxy Shapes: Intrinsic Alignments as a Probe of Fundamental Physics
July 2 (Thu) 14:00 - 16:00, 2026
Teppei Okumura (Research Fellow, ASIAA, Academia Sinica, Taiwan)
Galaxies in the Universe are not oriented randomly. Their shapes exhibit coherent alignments across cosmological scales due to the surrounding tidal gravitational field. For many years, these intrinsic alignments were regarded mainly as a contaminating effect in weak gravitational lensing observations. In recent years, however, they have emerged as a new cosmological probe, complementary to conventional galaxy-clustering analyses. In this talk, I will review recent theoretical and observational developments that establish galaxy shapes as a tool for studying the growth of cosmic structure and testing gravity on cosmological scales. I will present the first measurements demonstrating that intrinsic galaxy alignments can constrain cosmological parameters directly from observational data. The results are consistent with general relativity and provide information complementary to traditional galaxy-clustering analyses. I will also discuss future prospects for using galaxy alignments to probe dark energy, modified gravity, gravitational waves, and the physics of the early Universe with next-generation galaxy surveys.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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Seminar
120th Data Assimilation and Prediction Science Seminar
July 2 (Thu) 14:00 - 16:00, 2026
Upmanu Lall (Professor, Columbia University, USA)
Mengqian Lu (Professor, Hong Kong University of Science and Technology, Hong Kong)
Hyun-Han Kwon (Professor, University of Seoul, Republic of Korea)Speaker: Professor Lall (Columbia University) Title: "Taming the Storm: Can We Predict, Engineer, and Reduce Losses from Climate and Weather Extremes?" Abstract: Climate and weather extremes — storms, heat waves, floods, droughts, and compound events — have become the defining natural hazard challenge of the 21st century. Their growing frequency and intensity are overwhelming engineered infrastructure, disrupting global supply chains, and propagating risks across societies through teleconnections that no single country can insulate itself against. While climate change mitigation through decarbonization remains an urgent priority, even optimistic emissions trajectories leave us facing decades of increasing exposure. Climate adaptation efforts — improved infrastructure design, financial instruments, early warning systems — are essential but are constrained by limited data, deep uncertainty in future projections, and the diffuse question of who bears responsibility for action. This talk argues that a third pillar is emerging and demands serious scientific and institutional attention: Climate Stabilization, or the deliberate modification of developing weather and climate extremes to reduce their societal impact. Rather than waiting for disasters to unfold and recovering afterward, this paradigm asks whether the physical dynamics of the atmosphere offer leverage points — windows in time and space — where strategically placed, small perturbations could redirect the trajectory of an extreme event. This is the core idea of Weather Jiu-Jitsu: exploiting the inherent instabilities and nonlinear sensitivities of atmospheric circulation to achieve large-scale redirection of an extreme using energy borrowed from the circulation itself, not brute-force external forcing. J The talk will address the foundational questions this agenda raises for a forecasting and Earth science community: What physical mechanisms enable or constrain atmospheric steering? How can ensemble prediction systems, adjoint methods, and emerging AI tools be harnessed to identify intervention points and compute impact outcomes with spatial specificity? What are the data and modeling gaps? How do we frame the ethical and governance dimensions as this moves from laboratory curiosity to potential operational deployment and commercial application? I will sketch a research roadmap integrating chaos-informed perturbation theory to AI-enabled adaptive control optimization that builds on AI-accelerated impact forecasting to provide the foundation for Climate Stabilization as a rigorous scientific enterprise and, within a decade, a viable business with measurable returns to investors and societies alike. We hope that this will stimulate discussion with RIken's Moonshot Goal 8 program, which is exploring similar scientific and technological frontiers. Speaker: Professor Mengqian Lu (Hong Kong University of Science and Technology) Title: Bridging Climate Data to Actionable Decision-Making Across Industries Abstract: Extreme weather is escalating—impacting infrastructure, supply chains, and profitability across the world. At the same time, sustainability targets demand that businesses go green without sacrificing growth. The question is no longer if climate risk matters, but how to act on it—quickly and smartly. This talk presents climate solutions that combine advanced climate modeling with AI to deliver industry-specific, actionable insights. Developed at HKUST through the Center for Climate Resilience and Sustainability (CCRS) and the World Sustainable Development Institute (WSDI), this AI–dynamical hybrid system is already being applied across key sectors, including renewable energy, Arctic logistics, and disaster risk management. These tools enable organizations to make faster, more informed decisions under uncertainty. Backed by UNESCO and the WMO, this Research-to-Operation (R2O) framework turns complex climate data into operational tools that drive resilience, reduce losses, and uncover new opportunities. Real-world case studies will be shared to spark cross-sector collaboration between science, business, and policy. Speaker: Professor Hyun-Han Kwon (University of Seoul) Title: Bayesian Mixture Extreme-Value Modeling of Nonstationary Extreme Precipitation Across U.S. Regions Abstract Extreme precipitation is a major driver of flood risk, infrastructure stress, and climate-related disaster losses. However, annual maximum rainfall often reflects multiple physical mechanisms, including frontal or convective systems, tropical-cyclone-related rainfall, and transitional atmospheric regimes. Treating these extremes as samples from a single homogeneous process can obscure how regional rainfall risks are changing. This talk presents an ongoing study of nonstationary extreme precipitation using a Bayesian mixture extreme-value model. The model represents annual maximum daily precipitation as a combination of latent low- and high-intensity rainfall regimes, with time-varying component behavior and regime probabilities. This allows changes in return levels to be separated into contributions from baseline rainfall intensity, high-intensity event magnitude, and the probability of entering an extreme-producing regime. The framework is applied to long-term U.S. station records across the Southeast/Gulf, Mid-Atlantic, Northeast, and inland-control regions. Tropical-cyclone proximity and ERA5-based atmospheric diagnostics are used as external physical evidence, rather than as imposed predictors in the likelihood, to interpret the latent high-intensity regime and its regional variability. The broader goal is to move extreme-value analysis beyond stationary design estimation toward mechanism-aware and decision-relevant understanding of climate risk. By linking Bayesian uncertainty quantification, hydrometeorological interpretation, and regional comparison, this work provides a basis for improved infrastructure planning, impact-based forecasting, and future AI-enabled climate risk services.
Venue: Hybrid Format (RIKEN R-CCS room C107 and Zoom)
Event Official Language: English
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Seminar
Genome Structural Variation and the Evolutionary Potential of Sex in the Unicellular Green Alga Closterium
July 2 (Thu) 13:00 - 14:00, 2026
Yawako W. Kawaguchi (Postdoctoral Researcher, Molecular Life History Laboratory, National Institute of Genetics)
Genome size varies widely among eukaryotes, even between closely related species and within species. However, we still know relatively little about where such variation originates, how organisms tolerate its potential negative effects, and whether it can contribute to adaptation. In this seminar, I will present our studies on the unicellular green alga Closterium peracerosum–strigosum–littorale complex. I will first show that genome size variation in this alga is largely explained by extensive genome-wide copy number variation, and that gene expression can be buffered against changes in gene copy number. I will then show that a single episode of sexual reproduction can generate substantial variation in population growth rates under dual environmental stressors, with some F1 populations growing even when both parental strains decline. Finally, I will discuss how sexual reproduction may drive rapid evolutionary change not only by reshuffling alleles, but also by rearranging genome structure.
Venue: Seminar Room #359 (Main Venue) / via Zoom
Event Official Language: English
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Seminar
Phase Transitions as the Breakdown of Statistical Indistinguishability
June 29 (Mon) 15:00 - 16:00, 2026
Hideyuki Miyahara (Associate Professor, Faculty of Information Science and Technology, Hokkaido University)
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This perspective provides a general, order-parameter-free framework that does not rely on model-specific insights or learning procedures. We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework. As a concrete realization, we employ a distribution-free two-sample run test and demonstrate that the critical point of the two-dimensional Ising model is accurately identified without prior knowledge of the order parameter.
Venue: Hybrid Format (3F #359 and Zoom), Seminar Room #359
Event Official Language: English
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Seminar
Primitive Ideals and Hilbert Space Representations of Quantized Coordinate Algebras of Complex Semisimple Lie Groups
June 26 (Fri) 16:30 - 18:00, 2026
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.
Venue: via Zoom / Seminar Room #359
Event Official Language: English
1057 events