iTHEMS数学セミナー
120 イベント
-
セミナー
Geometry of hyperkahler 4 manifolds
2021年10月22日(金) 13:00 - 15:00
Song Sun (Associate Professor, Department of Mathematics, University of California, Berkeley, USA)
An n dimensional Riemannian metric g defines a holonomy group, which is a subgroup of SO(n) given by parallel transport along all contractible loops (with respect to the Levi-Civita connection). According to the Berger classification we know that if a complete Riemannian metric is not locally symmetric and not locally reducible then its holonomy group is either the entire SO(n) (generic case), or U(n) (Kahler), or is special and belongs to a small list. Riemannian metrics with special holonomy are very interesting geometric objects to study, with many connections to analysis and physics. The simplest model is given by a 4 dimensional hyperkahler metric. We will explain the general background and discuss recent progress on understanding the geometry of hyperkahler 4 manifolds. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
The branched deformations of special Lagrangian submanifolds
2021年10月15日(金) 10:00 - 12:00
Siqi He (Research Assistant Professor, Simons Center for Geometry and Physics, Stony Brook University, USA)
Special Lagrangian submanifolds are a distinguished class of real calibrated submanifolds defined in a Calabi-Yau manifold, which are calibrated by the real part of the holomorphic volume form. Given a compact, smooth special Lagrangian submanifold, Mclean proved that the space of nearby special Lagrangian submanifolds of it could be parametrized by the harmonic 1-forms. In this talk, we will discuss some recent progress on generalizing Mclean’s result to the branched deformations. We will describe how to use multi-valued harmonic functions to construct branched nearby deformations. In the first one hour, we will introduce the background of special Lagrangian submanifold and explain the motivations to study this problem. In this second one hour, we will discuss the technical details and interesting new phenomenon in this branching deformation problem. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Geography of varieties of general type
2021年10月8日(金) 16:00 - 18:10
Chen Jiang (Associate Professor, Shanghai Math Center, Fudan University, China)
We study birational invariants in order to study birational classifications of varieties. Geography is the study of relations among different invariants. We will focus on two fundamental invariants: canonical volume and geometric genus. For surfaces there are classical results such as Miyaoka-Yau inequality and Noether inequality. I will discuss higher dimensional analogue of them, and introduce our recent work on the optimal Noehter inequality for 3-folds joint with Jungkai Chen and Meng Chen. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Donaldson-Thomas invariants, wall-crossing and categorifications
2021年10月1日(金) 16:00 - 18:10
戸田 幸伸 (東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU) 教授)
It is an important subject to study algebraic curves inside algebraic varieties, both in classical algebraic geometry and also enumerative geometry inspired by string theory. The Donaldson-Thomas theory is one of curve counting theories on Calabi-Yau 3-folds, and has developed in these 20 years from several aspects of mathematics and mathematical physics. Among them, the wall-crossing in derived category turned out to be a key phenomena in proving deep structures of generating series of Donaldson-Thomas invariants. In the first one hour, I will review the classical aspect of counting curves inside algebraic varieties, and explain how it leads to modern enumerative geometry such as Gromov-Witten invariants, Donaldson-Thomas invariants. In the second one hour, I will explain wall-crossing phenomena in Donaldson-Thomas theory, and its categorification in the case of the resolved conifold. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
From Yang-Mills theory to enumerative geometry on Calabi-Yau 4-folds
2021年8月6日(金) 16:00 - 18:10
ヤーロン・ツァオ (理化学研究所 数理創造プログラム (iTHEMS) 研究員)
Yang-Mills theory was studied from mathematical perspectives in the 1970s by Atiyah and his collaborators (notably Drinfeld, Hitchin, Singer). Subsequent breakthroughs were made on dimensions 3 and 4 by Floer and Donaldson (based on deep analytic results obtained by Uhlenbeck and Taubes) in the 1980s. In 1996, Donaldson and Thomas proposed to study Yang-Mills theories on dimensions bigger than 4. In higher dimensions, the analytic method is limited and algebro-geometric method is heavily used instead. This powerful tool usually enables us to compute partition functions and lead to amazing links to other invariants in enumerative geometry, e.g. Gromov-Witten and Gopakumar-Vafa invariants. In this talk, I will review some of these inspiring stories and discuss how my works on Calabi-Yau 4-folds fit into them.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
An introduction to modular functions, conformal field theories, and moonshine phenomena
2021年7月2日(金) 16:00 - 18:10
及川 瑞稀 (理化学研究所 数理創造プログラム (iTHEMS) 大学院生リサーチ・アソシエイト / 理化学研究所 数理創造プログラム (iTHEMS) 研修生 / 東京大学 大学院数理科学研究科 博士課程)
Moonshine phenomena are certain mysterious connections between modular functions and finite groups. The first example is the celebrated monstrous moonshine, which connects the J-invariant and the Monster group. Surprisingly, this relationship can be well understood in terms of chiral conformal field theory. In this talk, I would like to explain what is chiral conformal field theory and how it gives moonshine phenomena. In the first part of the talk, the notion of modular function will be introduced and the precise statement of the monstrous moonshine will be given. Then the monstrous moonshine will be explained in terms of vertex operator algebra, a mathematical model of chiral conformal field theory. In the second part of the talk, we focus on the question: what is chiral conformal field theory mathematically? In addition to vertex operator algebras, other mathematical models of chiral conformal field theory, namely conformal nets and Segal conformal field theories, will be introduced. Recent progress on the relationship among these three models, including the Carpi--Kawahigashi--Longo--Weiner correspondence and the geometric realization of conformal nets will also be reviewed.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Stable eigenvalues of compact anti-de Sitter 3-manifolds
2021年6月18日(金) 16:00 - 18:10
甘中 一輝 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)
Geometric objects that have been investigated in detail so far, such as closed Riemann surfaces, are sometimes locally homogeneous. Loosely speaking, their infinitesimal behavior is the same at each point. In this talk, I would like to explain the idea of investigating such objects using the Lie group theory.In the first part of the talk, I will recall the notions of Lie group actions and their quotient spaces with examples, and then explain the definitions of locally homogeneous spaces and their deformations (Teichmüller spaces). In the second part of the talk, I will consider anti-de Sitter manifolds as a special case, i.e., Lorentzian manifolds of negative constant curvature. As in the Riemannian case, a differential operator called the Laplacian (or the Klein-Gordon operator) is defined on Lorentzian manifolds. Unlike the Riemannian case, it is no longer an elliptic differential operator but a hyperbolic differential operator. In its spectral analysis, new phenomena different from those in the Riemannian case have been discovered in recent years, following pioneering works by Toshiyuki Kobayashi and Fanny Kassel. I would like to explain stable eigenvalues of the hyperbolic Laplacian of anti-de Sitter 3-manifolds with recent progress.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Loewner's theorem for maps on operator domains / The structure of maps on the space of all quantum pure states that preserve a fixed quantum angle
2021年5月24日(月) 16:00 - 18:10
森 迪也 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)
This talk is divided into two independent topics. In the first part of my talk we consider the order structure of hermitian matrices. Given two matrix domains (open connected sets of n-by-n hermitian matrices), what is the general form of order isomorphisms between them? I will explain that there is a complete correspondence between the class of order isomorphisms and that of biholomorphic mappings. In the second part we consider the metric structure of the space P(H) of all quantum pure states (= the projective space of a complex Hilbert space H). Wigner's theorem asserts that every surjective isometry of P(H) onto itself is implemented by a unitary or an antiunitary operator. Uhlhorn generalized Wigner's theorem by showing that every bijective transformation of P(H) that preserves orthogonality is implemented by a unitary or an antiunitary operator. We consider some variants of Uhlhorn's result. The first part is joint work with P. Semrl (Univ. of Ljubljana), and the second part with G.P. Geher (Univ. of Reading). Only basic linear algebra is assumed in both parts.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Geometry of canonical metrics on Kähler manifolds
2021年5月14日(金) 16:00 - 18:10
井上 瑛二 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)
The aim of this talk is to report recent trends in Kähler geometry. Kähler geometry consists of two aspects: the one is algebraic geometry and the other is metric geometry.The first one hour is an introduction for non-mathematicians. I begin with a simple example of algebraic variety from ancient Greek, which I believe is the simplest example illustrating motivation for compact complex manifolds. On the other hand, I explain the first motivation for canonical metrics in Kähler geometry via Riemann’s uniformization theorem.The last one hour is an introduction to recent trends in Kähler geometry, especially Kähler-Einstein metrics. The existence of Kähler-Einstein metrics turns out to be related to geometry of degenerations of space, which is so called Yau-Tian-Donaldson conjecture. I explain various aspects of this topic. We encounter deep studies in metric geometry, birational geometry and non-archimedean geometry. I finally explain recent breakthrough on Kähler-Ricci flow.The goal of this talk is the starting point of my study. I briefly explain my study if time permits.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Alternative tsunami observing and forecasting systems
2021年4月22日(木) 16:00 - 18:10
イヤン・ムリア (理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 研究員)
Dedicated tsunami observing systems are mostly expensive and are often not sustainable. Therefore, alternative approaches should be implemented to overcome the issues. We introduced innovative ways to observe tsunamis using existing instrumentation available on unconventional platforms such as commercial vessels and airplanes. Our study demonstrated that the accuracy of the proposed observing systems is adequate for detecting large tsunamis offshore. The use of such systems is expected to provide more cost-effective and sustainable observations for the future. Additionally, we also developed a tsunami forecasting system based on machine learning to improve or complement the conventional methods that typically require considerable computational resources. On the contrary, the main appealing feature of the machine learning is the computational speed that would be suitable for a real-time prediction of tsunami inundation or flooding. We found that the application of machine learning can significantly improve the computing time without sacrificing the accuracy compared to the conventional methods.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Long-time behavior of moving solids in a fluid and the kinetic theory of gases
2021年4月7日(水) 16:00 - 18:10
小池 開 (京都大学 工学研究科 特別研究員)
Understanding dynamics of solids in a fluid is a fundamental problem in fluid dynamics. Due to the growing interest in engineering in out-of-equilibrium situations, moving boundary problems for kinetic equations such as the Boltzmann equation have become an active area of research. In the first part of the talk, I shall explain recent, especially mathematical, developments in this field. Then in the second part, I'd like to explain my results concerning the long-time behavior of a point particle moving in a 1D viscous compressible fluid. These results aim to give some explanation of related numerical simulations for a BGK model of the Boltzmann equation.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
The Green-Tao theorem for number fields
2021年3月22日(月) 16:00 - 18:10
甲斐 亘 (東北大学 理学部数学科 助教)
5, 11, 17, 23, 29 are prime numbers which form an arithmetic progression of length 5. A famous theorem of Ben Green and Terence Tao in 2008 says there are arbitrarily long arithmetic progressions of prime numbers. Algebraic number theorists are also interested in more general numbers like square roots of integers. Recently, Mimura, Munemasa, Seki, Yoshino and I have established a generalization of the Green-Tao theorem in such a direction. In the first 50 minutes of my talk, I would like to explain some background and technology behind the Green-Tao theorem. In the second half after a break, I explain the concept of number fields to formulate our generalization of their result. I will also discuss how one of the new difficulties, which I call the norm vs length conflict, is handled by a technique called Geometry of Numbers. *Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Scattering theory for half-line Schrödinger operators: analytic and topological results
2020年12月7日(月) 16:00 - 18:10
井上 秀樹 (名古屋大学)
Levinson’s theorem is a surprising result in quantum scattering theory, which relates the number of bound states and the scattering part of the underlying quantum system. For the last about ten years, it has been proved for several models that once recast in an operator algebraic framework this relation can be understood as an index theorem for the Møller wave operators. Resulting index theorems are called topological version of Levinson’s theorem or shortly topological Levinson’s theorem. In this talk, we first review the background and the framework of our investigation. New analytical and topological results are provided for Schrödinger operators on the half-line. This talk is based on my Ph.D thesis.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Flat and spherical surface approximations
2020年11月30日(月) 16:00 - 17:30
スクロツキ マーティン (理化学研究所 数理創造プログラム (iTHEMS) 客員研究員 / Fellow, German Academic Scholarship Foundation, Germany)
State-of-the-art acquisition devices produce surface representations of increasingly high resolution. While these detailed representations are important for production, they are problematic e.g. when exchanging drafts via the internet or when a quick rendering for comparison is necessary. In the first part of the talk, I will present results and further research questions from a paper I recently co-authored on 'Variational Shape Approximation'. This approach aims at linearizing the input surface and representing it via a set of localized planar segments. In the second part of the talk, I will present some ongoing research on surface representations via balls. This work started with constructions from spherical neodym magnets and provided a set of mathematical questions. These investigations are joint work with FU Berlin and OIST.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Representations of fundamental groups and 3-manifold topology
2020年11月16日(月) 16:00 - 18:10
北山 貴裕 (東京大学 大学院数理科学研究科 准教授)
In 3-dimensional topology the great progress during the last two decades revealed that various properties of 3-manifolds are well understood from their fundamental groups. I will give an introduction to the study of splittings of 3-manifolds along surfaces, with an emphasis on an application of group representations. A fundamental and difficult problem in general is to find surfaces essentially embedded in a given 3-manifold. I will explain how such surfaces are detected by deformations of representations of the fundamental group, and what information of detected surfaces is described in terms of topological invariants derived from representations.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Efficient probabilistic assessment of building performance: sequential Monte Carlo and decomposition methods
2020年11月13日(金) 16:00 - 18:10
ティエンフォン・ホウ (理化学研究所 数理創造プログラム (iTHEMS) 特別研究員 / 理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 特別研究員 / 理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム 特別研究員)
The use of numerical simulations for complex systems is common. However, significant uncertainties may exist for many of the involved variables, and in order to ensure the reliability of our simulation results and the safety of such complex systems, a stochastic approach providing statistics of the probability distribution of the results is of crucial importance. However, when a highly accurate result is required, the conventional Monte Carlo based probabilistic methodology inherently requires many repetitions of the deterministic analysis and in cases where that deterministic simulation is (relatively) time consuming, such probabilistic assessment can easily become computationally intractable. Hence, to reduce the computational expense of such probabilistic assessments as much as possible, the targets of this seminar are twofold: (1), to exploit an efficient sampling strategy to minimize the number of needed simulations of Monte Carlo based probabilistic analysis; (2), to investigate a surrogate model to reduce the computational expense of single deterministic simulation. This seminar contains two parts and will be accompanied by a set of illustrative building physical case studies (analysis of the heat and moisture transfer through building components). The first part of this seminar focusses on the use of quasi-Monte Carlo based probabilistic assessment for building performance, since it has the potential to outperform the standard Monte Carlo method. More specifically, the quasi-Monte Carlo sampling strategies and related error estimation techniques will be introduced in detail. In addition, questions on under which conditions the quasi-Monte Carlo can outperform the standard Monte Carlo method will be answered by a set of analyses. The second part of this seminar targets the investigation of using model order reduction methods for optimizing the deterministic simulation, given that it generally allows a (large) reduction of the simulation time without losing the dynamic behavior of the conventional models (such as the transient finite element analysis). Particularly, the fundamental concepts of one common model order reduction method – proper orthogonal decomposition (POD) will be provided, and its potential use for simulating (building physical) problems with different levels of non-linearity and complexity will be illustrated.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Mathematical aspects of quasi-Monte Carlo integration
2020年11月5日(木) 16:00 - 18:10
鈴木 航介 (広島大学 大学院先進理工系科学研究科 助教)
In this talk, I will introduce mathematical aspects of quasi-Monte Carlo (QMC) integration. We aim to approximate the integral of a function on the d-dimensional hypercube [0,1]^d. A useful approach is Monte-Carlo (MC) integration, which uses randomly chosen samples. A drawback of MC is the rate of convergence; the standard deviation of the estimator converges as 1/sqrt(n) asymptotically in n. To have a better rate of convergence as O(log^d N/N) or more, QMC uses deterministic, uniformly distributed points. In the first part, I will give an overview of QMC, such as star-discrepancy, Koksma-Hlawka inequality, and some explicit constructions as lattices and digital nets. In the second part, I will show that QMC using lattices and digital nets can achieve a higher rate of convergence for smooth integrands.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Math Seminars by Dr. Genki Ouchi and Dr. Kenta Sato
2020年9月24日(木) 16:00 - 18:10
大内 元気 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)
佐藤 謙太 (理化学研究所 数理創造プログラム (iTHEMS) 基礎科学特別研究員)[Talk 1] (16:00 - 17:00) Dr. Genki Ouchi Automorphism groups of cubic fourfolds and K3 categories In this talk, I would like to talk about symmetries of algebraic varieties, especially cubic fourfolds and K3 surfaces. It is known that symmetries of cubic fourfolds and K3 surfaces are related to sporadic finite groups as Mathieu groups and Conway groups in both algebraic geometry and string theory. Relations between cubic fourfolds and K3 surfaces are studied in the context of derived categories, Hodge theory and so on. I would like to explain the direct relation among symmetries of cubic fourfolds and K3 surfaces via their derived categories. [Talk 2] (17:10 - 18:10) Dr. Kenta Sato An algebraic approach to the four color theorem The four color theorem states that, given any separation of a plane into contiguous regions, no more than four colors are required to color the regions. Although this theorem was already proved about 40 years ago, another proof without using a computer is not found still now. In this talk, I will introduce an algebraic approach to this theorem, which states that a conjecture about singularities of algebraic varieties implies the four color theorem. In particular, I would like to focus on the connection of three different fields in mathematics: graph theory, convex geometry and algebraic geometry. *Detailed information about the seminar refer to the email.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Maximal Regularity and Partial Differential Equations
2020年9月8日(火) 16:00 - 18:10
古川 賢 (理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 特別研究員)
The theory of maximal regularity is a powerful tool to get solutions having the best regularity to linear partial differential equations (PDEs) of parabolic type. The theory is also applicable to show well-posedness of various non-linear PDEs. In the first part, We introduce the history of the development of the theory of maximal regularity and the way to apply non-linear PDEs. In the second part, We give some applications to PDEs, e. g. the primitive equations, the Navier-Stokes equations, and elliptic equations with dynamic boundary conditions. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
会場: via Zoom
イベント公式言語: 英語
-
セミナー
Stability of ferromagnetism in many-electron systems
2020年7月31日(金) 16:00 - 18:10
宮尾 忠宏 (北海道大学 理学部数学科 准教授)
First part Title: Stability of ferromagnetism in many-electron systems Abstract: I construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems. Within the new framework, I reinterpret the Marshall-Lieb-Mattis theorem and Lieb’s theorem; in addition, from the new perspective, I prove that Lieb’s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. I also examine the NagaokaThouless theorem and its stability. These examples verify the effectiveness of the new viewpoint. Second part Title: Order preserving operator inequalities in many-electron systems Abstract: In this talk, I will introduce order preserving operator inequalities and explain how these inequalities are applied to the mathematical study of ferromagnetism. As examples of applications, Lieb's theorem of the Hubbard model and its stabilities will be discussed in terms of the inequalities.
会場: via Zoom
イベント公式言語: 英語
120 イベント