3件のイベント / 2026年
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セミナー
Median-based estimators for randomized quasi-Monte Carlo integration
2026年1月9日(金) 15:00 - 17:00
鈴木 航介 (山形大学 准教授)
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.
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
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セミナー
Higher Gauge Structures and Invariant Action Principles
2026年1月6日(火) 15:15 - 16:15
Sebastián Salgado (External Researcher, Instituto de Alta Investigacion, Universidad de Tarapaca, Chile)
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.
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
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セミナー
Invitation to Random Tensor Models: from random geometry, enumeration of tensor invariants, to characteristic polynomials
2026年1月6日(火) 13:30 - 14:30
鳥海 玲子 (沖縄科学技術大学院大学 (OIST) 准教授)
I will introduce random tensor models by first reviewing their motivation coming from random geometric approach to quantum gravity. Then, I will selectively present some of the interesting research results, by highlighting recent results on enumeration of graphs representing tensor invariants, and reporting our recent work on a new notion of characteristic polynomials for tensors via Grassmann integrals and distributions of roots of random tensors. The latter two are based on arXiv:2404.16404[hep-th] and arXiv:2510.04068[math-ph]
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
3件のイベント / 2026年