iTHEMS数学セミナー
85 イベント
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セミナー
Introduction to Schroedinger Operators
2019年7月12日(金) 16:00 - 18:10
三上 渓太 (数理創造プログラム 研究員)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: In this seminar, I will talk about mathematical study of Schroedinger operators (or Schroedinger equation). Part 1: I will talk about what mathematicians do to find a solution to Schroedinger equation. The goal of the first part is to be able to check the existence of solutions of Schroedinger equations in terms of decay/growth rate of potentials. Part 2: I will talk about what can we say about solutions to Schroedinger equation constructed in the first part. Especially, the relationship to the corresponding classical mechanic is introduced.
会場: セミナー室 (160号室)
イベント公式言語: 英語
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セミナー
Asymmetric metric and coarse geometry
2019年6月20日(木) 16:00 - 18:10
児玉 大樹 (数理創造プログラム 客員研究員 / 東北大学 材料科学高等研究所 (AIMR) 助教)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: For most of mathematicians, metric is symmetric. However, we can define asymmetric metric without any difficulty. "Coarse" is a notion to describe some large scale viewpoint. For example, the set of real numbers is coarse equivalent to the set of integers (with respect to standard metric). I will discuss asymmetric metric space in "coarse" sense. Part 1: I will define metric space and asymmetric metric space. I will also explain a notion of coarse equivalence. Part 2: I will discuss what kind of asymmetric metric space is not coarse equivalent to (symmetric) metric space. I also would like to give other generalizations of metric.
会場: セミナー室 (160号室)
イベント公式言語: 英語
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セミナー
Certain invariants as dimension
2019年5月24日(金) 16:00 - 18:10
大内 元気 (数理創造プログラム 基礎科学特別研究員)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Abstract: In this talk, I would like to talk about certain invariants that look like dimension. This talk has independent two parts. In part 1, I will talk about finite metric spaces. In 2013, Leinster introduced the notion of magnitude of finite metric spaces. It measures effective number of points in finite metric spaces. Considering magnitude and scale transformation, Leinster and Willerton defined dimension of finite metric space with scale. I will explain the definition of magnitude of finite metric spaces and see examples. In part 2, I will talk about derived categories of smooth projective varieties or finite dimensional algebras. In 2014, Dimitrov, Heiden, Katzarkov and Kontsevich introduced the notion of entropy of endofunctors of derived categories. It measures complexity of endofunctors under iteration. Serre functor is an autoequivalence of derived category, that describes Serre duality. Entropy of Serre functor looks like dimension of derived categories. I will talk about known results for entropy of Serre functors and some related topics.
会場: セミナー室 (160号室)
イベント公式言語: 英語
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セミナー
Introduction to Singularity Theory in Algebraic Geometry
2019年5月16日(木) 16:00 - 18:10
佐藤 謙太 (数理創造プログラム 基礎科学特別研究員)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. In this talk, I will explain for all scientists how singularities are studied in algebraic geometry. In algebraic geometry, we study algebraic varieties, which are figures defined as the zero sets of polynomial equations. To study an algebraic variety, we often expect that the variety is smooth, that is, the variety locally resembles Euclidian spaces. However, even if we start from smooth varieties, we sometimes encounter non-smooth varieties. This is one of the reasons why we need to study singularities. Part I: In the first one hour, I will explain how singularities are studied. I will introduce two invariants of singularities by which we can compare singularities numerically. One invariant is defined in terms of resolution of singularities and the other is defined in terms of positive characteristic methods. I also explain a surprising relation of these invariants. Part II: In the second one hour, I will explain how singularity theory is used to study smooth projective varieties. I will introduce Minimal Model Program and explain the relation with singularity theory.
会場: セミナー室 (160号室)
イベント公式言語: 英語
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セミナー
Gauge theory and symmetries of 4-dimensional spaces
2019年4月26日(金) 16:00 - 18:10
今野 北斗 (数理創造プログラム 基礎科学特別研究員)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Although the term "gauge theory" is usually used in physical contexts, in the early 1980's, mathematicians found that gauge theory has many striking applications to purely mathematical problems. Most of typical applications are related to topology of 4-dimensional spaces. As a recent development in this direction, I used gauge theory to study "the shape of the space of all symmetris of a 4-dimensional space". In the first one hour, I will explain a notion of mathematical spaces, called manifolds, and try to describe the idea: how mathematicians make use of gauge theory to study the topology of a 4-dimensional manifold. In the second one hour, I will explain what the space of symmetries of a manifold means, and which type of theorems about the space of symmetries can be obtained using gauge theory.
会場: セミナー室 (160号室)
イベント公式言語: 英語
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セミナー
Introduction to Galois Theory and Class Field Theory
2019年4月18日(木) 16:00 - 18:00
宮﨑 弘安 (数理創造プログラム 基礎科学特別研究員)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Part I: Galois theory is one of the most important theories in mathematics. Speaking in one phrase, it explains the correspondence between “extensions of numbers” and “subgroups of Galois group”. Basically, finding subgroups of a finite group is much easier than finding extensions of numbers. As a result, Galois theory has incredibly strong applications. For example, we can prove polynomial equations of degree greater than 4 are not always solvable by radicals, which is a celebrated result by Abel and Galois. In the first part of the talk, I will introduce Galois theory in an accessible way for all scientists. Part II: Class Field Theory (CFT) is a monumental work in number theory. Given Galois theory, which is explained in Part I, classifying “extension of numbers” is reduced to classifying “subgroups of Galois group”. So, the next thing to do would be to analyze the structure of Galois groups. CFT enables us to describe the Galois group of a number field K by using only the language of K, i.e., not by using its extensions. In the second part of the talk, I will explain CFT in an as accessible way as possible for all scientists (in particular, also for mathematicians). If time permits, I would like to explain a geometric interpretation of Galois theory, and higher dimensional CFT.
会場: セミナー室 (160号室)
イベント公式言語: 英語
85 イベント