## 過去の記録

### 2021年06月07日(月)

#### 複素解析幾何セミナー

10:30-12:00   オンライン開催

Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane (Japanese)
[ 講演概要 ]
In this talk, I would like to discuss a problem of the geometric quantization for the Cayley projective plane. Our purposes are to show the existence of a Calabi-Yau structure on the punctured cotangent bundle of the Cayley projective plane, and to construct a Bargmann type transformation between a space of holomorphic functions on the bundle and the $L_2$-space on the Cayley projective space. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators. This talk is based on a joint work with Kenro Furutani (Osaka City University Advanced Mathematical Institute): arXiv:2101.07505.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021年06月03日(木)

#### 情報数学セミナー

16:50-18:35   オンライン開催
Zoomでの開催

ＡＩの過去・現在・未来 (Japanese)
[ 講演概要 ]

[ 参考URL ]

### 2021年06月02日(水)

#### 代数幾何学セミナー

15:00-16:00   数理科学研究科棟(駒場) 号室

Quasiexcellence implies strong generation (日本語)
[ 講演概要 ]
BondalとVan den Berghは（小さい）三角圏からの反変関手がいつ表現可能かという問題の考察の中で、対象が三角圏を強生成(strongly generate)することの定義を導入した。強生成する対象が存在するときは良い表現可能性定理が成立する。
どのような有限次元Noetherスキームに対してその連接層の導来圏が強生成であるかについてはBondal–Van den Bergh以降Rouquier, Keller–Van den Bergh, Aihara–Takahashi, Iyengar–Takahashiなどにより多くの結果が得られていたが、最近Neemanは別の手法を用いてそれをalterationが適用できる分離Noetherスキームに対して示した。それを講演者はGabberのweak local uniformizationを用いることでさらに分離的準優秀スキームにまで拡張した。講演ではこの結果およびその証明の手法を紹介する。
[ 参考URL ]
Zoom

#### 東京名古屋代数セミナー

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

An equivariant Hochster's formula for $S_n$-invariant monomial ideals (Japanese)
[ 講演概要 ]

[ 参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2021年06月01日(火)

#### トポロジー火曜セミナー

17:30-18:30   オンライン開催
Lie群論・表現論セミナーと合同。 参加を希望される場合は、セミナーのウェブページをご覧下さい。

On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)
[ 講演概要 ]

[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Lie群論・表現論セミナー

17:30-18:30   数理科学研究科棟(駒場) Online号室
トポロジー火曜セミナーと合同。オンライン開催。

On the discrete decomposability and invariants of representations of real reductive Lie groups (Japanese)
[ 講演概要 ]

また、等質空間の L^2 関数の空間の離散スペクトルを別の等質空間のものから構成するという結果にも用いられている。(T. Kobayashi, J. Funct. Anal. ('98))

#### 作用素環セミナー

16:45-18:15   オンライン開催

KMS states of Toeplitz algebras of graphs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2021年05月31日(月)

#### 複素解析幾何セミナー

10:30-12:00   オンライン開催

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds (Japanese)
[ 講演概要 ]
The CR Paneitz operator, which is a fourth-order CR invariant differential operator, plays a crucial role in three-dimensional CR geometry; it is deeply connected to global embeddability and the CR positive mass theorem. In this talk, I will show that the CR Paneitz operator is nonnegative for embeddable CR manifolds. I will also apply this result to some problems in CR geometry. In particular, I will give an affirmative solution to the CR Yamabe problem for embeddable CR manifolds.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021年05月28日(金)

#### 談話会・数理科学講演会

15:30-16:30   オンライン開催

Physics and algebraic topology (ENGLISH)
[ 講演概要 ]
Although we often talk about the "unreasonable effectiveness of mathematics in the natural sciences", there are great disparities in the relevance of various subbranches of mathematics to individual fields of natural sciences. Algebraic topology was a subject whose influence to physics remained relatively minor for a long time, but in the last several years, theoretical physicists started to appreciate the effectiveness of algebraic topology more seriously. For example, there is now a general consensus that the classification of the symmetry-protected topological phases, which form a class of phases of matter with a certain particularly simple property, is done in terms of generalized cohomology theories.

In this talk, I would like to provide a historical overview of the use of algebraic topology in physics, emphasizing a few highlights along the way. If the time allows, I would also like to report my struggle to understand the anomaly of heterotic strings, using the theory of topological modular forms.

### 2021年05月27日(木)

#### 数理人口学・数理生物学セミナー

15:00-16:00   オンライン開催
ZOOMによる遠隔講演となります。参加希望の方は稲葉までご連絡ください。

(Japanese)
[ 講演概要 ]

#### 情報数学セミナー

16:50-18:35   オンライン開催
Zoomでの開催

[ 講演概要 ]
今日のデータ量増大、処理の高度化への要求に伴い、各種の古典コンピューティングによる高速化手法が考案されている。また、根本的なコンピューティングの原理の革新としての量子コンピューティングの世界が拓かれようとしている。そこで、本講では、前回に続き、コンピューティングの歴史として、1980年代から現代への系譜について述べる。また、古典コンピューティングの高速化として、「演算数」「演算の重さ」「メモリジャンプ」手法について述べる。さらに、量子コンピューティングの基礎として、「量子計算の本質」について触れる。
[ 参考URL ]

### 2021年05月26日(水)

#### 代数幾何学セミナー

15:00-16:00   数理科学研究科棟(駒場) zoom号室

Multiplier ideals via ultraproducts (日本語)
[ 講演概要 ]

#### 代数学コロキウム

17:00-18:00   オンライン開催

Geometric Structure of Affine Deligne-Lusztig Varieties for $\mathrm{GL}_3$ (Japanese)
[ 講演概要 ]
The Langlands correspondence, which contains class field theory as a special case, is one of the most important topics in number theory. Shimura varieties have been used, with great success, towards applications in the realm of the Langlands program. In this context, geometric and homological properties of affine Deligne-Lusztig varieties have been used to examine Shimura varieties and the local Langlands correspondence.
In this talk we study the geometric structure of affine Deligne-Lusztig varieties $X_{\lambda}(b)$ for $\mathrm{GL}_3$ and $b$ basic.
We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.

### 2021年05月25日(火)

#### 解析学火曜セミナー

16:00-17:30   オンライン開催

Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer (Japanese)
[ 講演概要 ]
In this talk, we consider the initial value problem for the Navier-Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation, and show that the global solution converges to that of 2D incompressible Navier-Stokes equations in some global in time space-time norms. This talk is based on the joint work with Hiroki Ohyama (Kyushu University).
[ 参考URL ]
https://forms.gle/wHpi7BSpppsiiguD6

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

On a characteristic class associated with deformations of foliations (JAPANESE)
[ 講演概要 ]
A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### 作用素環セミナー

16:45-18:15   オンライン開催
Rajarama Bhat 氏 (Indian Statistical Institute)
Lattices of logmodular algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2021年05月24日(月)

#### 複素解析幾何セミナー

10:30-12:00   オンライン開催

Cartan-Hartogs領域の固有正則写像 (Japanese)
[ 講演概要 ]
2つの球の間の固有正則写像は自己同型写像である。球を別の領域にしたらどうなるかを調べたい。球の一般化として複素擬楕円体や有界対称領域が考えられる。これら2つの領域を合わせた領域としてHua領域がある。これは有界対称領域の上に複素擬楕円体が乗っているような領域である。Hua領域の一番簡単な場合としてCartan-Hartogs領域があり、これらの間の固有正則写像の分類問題を考える。分類すると本質的には１種類の写像しかないことが分かる。ここでは2つの多項式写像が自己同型写像の差を省いて一致すれば、Isotoropy写像の差を省いて一致することを使う。
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021年05月20日(木)

#### 情報数学セミナー

16:50-18:35   オンライン開催
Zoomでの開催

[ 講演概要 ]

そこで、本講では、古典コンピューティングにおける高速化原理と量子コンピューティングに革新をもたらした因果律の考え方について数理科学的視点から概観する。
[ 参考URL ]

#### 東京名古屋代数セミナー

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

This talk is based on joint work with Tsutomu Nakamura. For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable flat cotorsion right modules and the isoclasses of indecomposable injective left modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality between Ziegler spectra.
[ 参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2021年05月19日(水)

#### 統計数学セミナー

14:30-16:00   オンライン開催

Federico Camia 氏 (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics (ENGLISH)
[ 講演概要 ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
[ 参考URL ]

#### 統計数学セミナー

14:30-16:00   数理科学研究科棟(駒場) 号室
Federico Camia 氏 (NYU Abu Dhabi)
Limit Theorems and Random Fractal Curves in Statistical Mechanics
[ 講演概要 ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.
[ 参考URL ]

### 2021年05月18日(火)

#### 作用素環セミナー

16:45-18:15   オンライン開催

Simplicity of $C^*$-algebras associated to some self-similar groups
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

Geoffrey Powell 氏 (CNRS and University of Angers)
On derivations of free algebras over an operad and the generalized divergence (ENGLISH)
[ 講演概要 ]
This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.

One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.

The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Lie群論・表現論セミナー

17:00-17:30   数理科学研究科棟(駒場) Online号室

アファインヤンギアンと長方形W代数 (Japanese)
[ 講演概要 ]
Motivated by the generalized AGT conjecture, in this talk I will construct surjective homomorphisms from Guay's affine Yangians to the universal enveloping algebras of rectangular W-algebras of type A.
This result is a super affine analogue of a result of Ragoucy and Sorba, which gave surjective homomorphisms from finite Yangians of type A to rectangular finite W-algebras of type A.

### 2021年05月17日(月)

#### 代数幾何学セミナー

17:00-18:00   数理科学研究科棟(駒場) zoom号室
いつもと日時が異なります。京大と共催
Ivan Cheltsov 氏 (エジンバラ)
Calabi problem for smooth Fano threefolds (English)
[ 講演概要 ]
In this talk I will explain which three-dimensional complex Fano manifolds admit Kahler-Einstein metrics.