## Seminar information archive

Seminar information archive ～08/08｜Today's seminar 08/09 | Future seminars 08/10～

### 2021/06/09

#### Algebraic Geometry Seminar

15:00-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Rational simple connectedness and Fano threefolds (English)

Zoom

**Andrea Fanelli**(Bordeaux)Rational simple connectedness and Fano threefolds (English)

[ Abstract ]

The notion of rational simple connectedness can be seen as an algebro-geometric analogue of simple connectedness in topology. The work of de Jong, He and Starr has already produced several recent studies to understand this notion.

In this talk I will discuss the joint project with Laurent Gruson and Nicolas Perrin to study rational simple connectedness for Fano threefolds via explicit methods from birational geometry.

[ Reference URL ]The notion of rational simple connectedness can be seen as an algebro-geometric analogue of simple connectedness in topology. The work of de Jong, He and Starr has already produced several recent studies to understand this notion.

In this talk I will discuss the joint project with Laurent Gruson and Nicolas Perrin to study rational simple connectedness for Fano threefolds via explicit methods from birational geometry.

Zoom

### 2021/06/08

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Local well-posedness for the Landau-Lifshitz equation with helicity term (Japanese)

https://forms.gle/nc85Mw9Jd6NgJzT98

**SHIMIZU Ikkei**(Osaka University)Local well-posedness for the Landau-Lifshitz equation with helicity term (Japanese)

[ Abstract ]

We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We show that it is locally well-posed in Sobolev spaces $H^s$ when $s>2$. The key idea is to reduce the problem to a system of semi-linear Schr\"odinger equations, called modified Schr\"odinger map equation. The problem here is that the helicity term appears as quadratic derivative nonlinearities, which is known to be difficult to treat as perturbation of the free evolution. To overcome that, we consider them as magnetic terms, then apply the energy method by introducing the differential operator associated with magnetic potentials.

[ Reference URL ]We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We show that it is locally well-posed in Sobolev spaces $H^s$ when $s>2$. The key idea is to reduce the problem to a system of semi-linear Schr\"odinger equations, called modified Schr\"odinger map equation. The problem here is that the helicity term appears as quadratic derivative nonlinearities, which is known to be difficult to treat as perturbation of the free evolution. To overcome that, we consider them as magnetic terms, then apply the energy method by introducing the differential operator associated with magnetic potentials.

https://forms.gle/nc85Mw9Jd6NgJzT98

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Takahiro Matsusita**(University of the Ryukyus)Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)

[ Abstract ]

Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.

In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.

In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.

[ Reference URL ]Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.

In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.

In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.

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

#### Operator Algebra Seminars

16:45-18:15 Online

The generator rank of $C^*$-algebras (English)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Hannes Thiel**(TU Dresden)The generator rank of $C^*$-algebras (English)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Numerical Analysis Seminar

16:30-18:00 Online

Action minimizing random walks and numerical analysis of Hamilton-Jacobi equations (Japanese)

[ Reference URL ]

https://forms.gle/kjhqne4nV6fqEFWB8

**Kohei Soga**(Keio University)Action minimizing random walks and numerical analysis of Hamilton-Jacobi equations (Japanese)

[ Reference URL ]

https://forms.gle/kjhqne4nV6fqEFWB8

#### Lie Groups and Representation Theory

17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)

The multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds (Japanese)

**Kazuki KANNAKA**(RIKEN iTHEMS)The multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds (Japanese)

[ Abstract ]

A \textit{pseudo-Riemannian locally symmetric space} is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$.

Toshiyuki Kobayashi initiated the study of spectral analysis of \textit{intrinsic differential operators} (such as the Laplacian) of a pseudo-Rimannian locally symmetric space. Unlike the classical Riemannian setting,

the Laplacian of a pseudo-Rimannian locally symmetric space is no longer an elliptic differential operator.

In its spectral analysis, new phenomena different from those in the Riemannian setting have been discovered in recent years, following pioneering works by Kassel-Kobayashi.

For instance, they studied the behavior of eigenvalues of intrinsic differential operators of $\Gamma\backslash G/H$ when deforming a discontinuous group $\Gamma$. As a special case, they found infinitely many \textit{stable

eigenvalues} of the (hyperbolic) Laplacian of a compact anti-de Sitter $3$-manifold $\Gamma\backslash

\mathrm{SO}(2,2)/\mathrm{SO}(2,1)$ ([Adv.\ Math.\ 2016]).

In this talk, I would like to explain recent results about the \textit{multiplicities} of stable eigenvalues in the anti-de Sitter setting.

A \textit{pseudo-Riemannian locally symmetric space} is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$.

Toshiyuki Kobayashi initiated the study of spectral analysis of \textit{intrinsic differential operators} (such as the Laplacian) of a pseudo-Rimannian locally symmetric space. Unlike the classical Riemannian setting,

the Laplacian of a pseudo-Rimannian locally symmetric space is no longer an elliptic differential operator.

In its spectral analysis, new phenomena different from those in the Riemannian setting have been discovered in recent years, following pioneering works by Kassel-Kobayashi.

For instance, they studied the behavior of eigenvalues of intrinsic differential operators of $\Gamma\backslash G/H$ when deforming a discontinuous group $\Gamma$. As a special case, they found infinitely many \textit{stable

eigenvalues} of the (hyperbolic) Laplacian of a compact anti-de Sitter $3$-manifold $\Gamma\backslash

\mathrm{SO}(2,2)/\mathrm{SO}(2,1)$ ([Adv.\ Math.\ 2016]).

In this talk, I would like to explain recent results about the \textit{multiplicities} of stable eigenvalues in the anti-de Sitter setting.

### 2021/06/07

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Kurando Baba**(Tokyo University of Science)Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane (Japanese)

[ Abstract ]

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.

[ Reference URL ]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.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/06/03

#### Information Mathematics Seminar

16:50-18:35 Online

The past, the present, the future of the AI (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The past, the present, the future of the AI (Japanese)

[ Abstract ]

On the explanation of the past, the present, the future of the AI

[ Reference URL ]On the explanation of the past, the present, the future of the AI

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/06/02

#### Algebraic Geometry Seminar

15:00-16:00 Room # (Graduate School of Math. Sci. Bldg.)

Quasiexcellence implies strong generation (日本語)

Zoom

**Ko Aoki**(Tokyo)Quasiexcellence implies strong generation (日本語)

[ Abstract ]

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。

[ Reference URL ]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。

Zoom

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

Please see the URL below for details on the online seminar.

An equivariant Hochster's formula for $S_n$-invariant monomial ideals (Japanese)

[ Reference URL ]

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

Please see the URL below for details on the online seminar.

**Satoshi Murai**(Waseda University)An equivariant Hochster's formula for $S_n$-invariant monomial ideals (Japanese)

[ Reference URL ]

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

### 2021/06/01

#### Tuesday Seminar on Topology

17:30-18:30 Online

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)

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

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

**Masatoshi Kitagawa**(Waseda University)On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)

[ Abstract ]

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form,

can be obtained as intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J. Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98). The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

[ Reference URL ]A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form,

can be obtained as intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J. Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98). The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

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

#### Lie Groups and Representation Theory

17:30-18:30 Room #Online (Graduate School of Math. Sci. Bldg.)

Joint with Tuesday Seminar on Topology. Online.

On the discrete decomposability and invariants of representations of real reductive Lie groups (Japanese)

Joint with Tuesday Seminar on Topology. Online.

**Masatoshi KITAGAWA**(Waseda University)On the discrete decomposability and invariants of representations of real reductive Lie groups (Japanese)

[ Abstract ]

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form, can be obtained as

intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J.

Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98).

The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form, can be obtained as

intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J.

Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98).

The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

#### Operator Algebra Seminars

16:45-18:15 Online

KMS states of Toeplitz algebras of graphs

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Takuya Takeishi**(Kyoto Institute of Technology)KMS states of Toeplitz algebras of graphs

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2021/05/31

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Yuya Takeuchi**(Tsukuba University)Nonnegativity of the CR Paneitz operator for embeddable CR manifolds (Japanese)

[ Abstract ]

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.

[ Reference URL ]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.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/05/28

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, May 28).

Physics and algebraic topology (ENGLISH)

Registration is closed (12:00, May 28).

**Yuji Tachikawa**(Kavli IPMU)Physics and algebraic topology (ENGLISH)

[ Abstract ]

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.

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.

### 2021/05/27

#### Mathematical Biology Seminar

15:00-16:00 Online

Modeling infective contact by point process (Japanese)

**Nariyuki Minami**(Keio University School of Medicine)Modeling infective contact by point process (Japanese)

#### Information Mathematics Seminar

16:50-18:35 Online

The practice of the speedup technique of the classic computing and quantum computing basics=superposition principle (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The practice of the speedup technique of the classic computing and quantum computing basics=superposition principle (Japanese)

[ Abstract ]

Explanation on the practice of the speedup technique of the classic computing and on quantum computing basics=superposition principle.

[ Reference URL ]Explanation on the practice of the speedup technique of the classic computing and on quantum computing basics=superposition principle.

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/05/26

#### Algebraic Geometry Seminar

15:00-16:00 Room #zoom (Graduate School of Math. Sci. Bldg.)

Multiplier ideals via ultraproducts (日本語)

**Itsuki Yamaguchi**(Tokyo)Multiplier ideals via ultraproducts (日本語)

[ Abstract ]

正標数の可換環と複素数体上の可換環の性質を比較する方法の一つにultraproductを用いた手法がある. このultraproductは超準解析において超実数の構成などに用いられているものである. これを可換環論へ応用する研究としてSchoutensによるnon-standard hullがある. この手法は等標数0の局所環に対するbig Cohen-Macaulay 代数の構成などにも応用がある. 彼の研究の一つに川又対数端末特異点のultraproductを用いた特徴付けがある. 本講演では, この結果の一般化として乗数イデアルがultraproductを用いて記述できることを説明する.

正標数の可換環と複素数体上の可換環の性質を比較する方法の一つにultraproductを用いた手法がある. このultraproductは超準解析において超実数の構成などに用いられているものである. これを可換環論へ応用する研究としてSchoutensによるnon-standard hullがある. この手法は等標数0の局所環に対するbig Cohen-Macaulay 代数の構成などにも応用がある. 彼の研究の一つに川又対数端末特異点のultraproductを用いた特徴付けがある. 本講演では, この結果の一般化として乗数イデアルがultraproductを用いて記述できることを説明する.

#### Number Theory Seminar

17:00-18:00 Online

Geometric Structure of Affine Deligne-Lusztig Varieties for $\mathrm{GL}_3$ (Japanese)

**Ryosuke Shimada**(University of Tokyo)Geometric Structure of Affine Deligne-Lusztig Varieties for $\mathrm{GL}_3$ (Japanese)

[ Abstract ]

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.

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.

### 2021/05/25

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer (Japanese)

https://forms.gle/wHpi7BSpppsiiguD6

**TAKADA Ryo**(Kyushu University)Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer (Japanese)

[ Abstract ]

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).

[ Reference URL ]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).

https://forms.gle/wHpi7BSpppsiiguD6

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

On a characteristic class associated with deformations of foliations (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Taro Asuke**(The University of Tokyo)On a characteristic class associated with deformations of foliations (JAPANESE)

[ Abstract ]

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.

[ Reference URL ]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.

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

#### Operator Algebra Seminars

16:45-18:15 Online

Lattices of logmodular algebras

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Rajarama Bhat**(Indian Statistical Institute)Lattices of logmodular algebras

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2021/05/24

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Cartan-Hartogs領域の固有正則写像 (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Atsushi Hayashimoto**(Nagano National College of Technology)Cartan-Hartogs領域の固有正則写像 (Japanese)

[ Abstract ]

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。

[ Reference URL ]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。

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/05/20

#### Information Mathematics Seminar

16:50-18:35 Online

Speedup principle of the classic computing and Innovation of the law of causation in the quantum computing (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Speedup principle of the classic computing and Innovation of the law of causation in the quantum computing (Japanese)

[ Abstract ]

Explanation on the speedup principle of the classic computing and innovation of the law of causation in the quantum computing.

[ Reference URL ]Explanation on the speedup principle of the classic computing and innovation of the law of causation in the quantum computing.

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

Please see the URL below for details on the online seminar.

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.

[ Reference URL ]

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

Please see the URL below for details on the online seminar.

**Ryo Kanda**(Osaka city University)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.

[ Reference URL ]

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

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188 Next >