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Seminar information archive
Seminar information archive ～04/24｜Today's seminar 04/25 | Future seminars 04/26～
2021/06/14
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Takayuki Koike (Osaka City University)
Projective K3 surfaces containing Levi-flat hypersurfaces (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Takayuki Koike (Osaka City University)
Projective K3 surfaces containing Levi-flat hypersurfaces (Japanese)
[ Abstract ]
In May 2017, I reported on the gluing construction of a K3 surface at Seminar on Geometric Complex Analysis.
Here, by the gluing construction of a K3 surface, I mean the construction of a K3 surface by holomorphically gluing two open complex surfaces which are the complements of tubular neighborhoods of elliptic curves included in the blow-ups of the projective planes by nine points.
As of 2017, it was an open problem whether a projective K3 surface can be obtained by the gluing construction. Recently, I and Takato Uehara found a very concrete way to construct a projective K3 surface by the gluing method. As a corollary, we obtained the existence of non-Kummer projective K3 surface with compact Levi-flat hypersurfaces.
In this talk, I will explain the detail of the concrete gluing construction of such a K3 surface.
[ Reference URL ]In May 2017, I reported on the gluing construction of a K3 surface at Seminar on Geometric Complex Analysis.
Here, by the gluing construction of a K3 surface, I mean the construction of a K3 surface by holomorphically gluing two open complex surfaces which are the complements of tubular neighborhoods of elliptic curves included in the blow-ups of the projective planes by nine points.
As of 2017, it was an open problem whether a projective K3 surface can be obtained by the gluing construction. Recently, I and Takato Uehara found a very concrete way to construct a projective K3 surface by the gluing method. As a corollary, we obtained the existence of non-Kummer projective K3 surface with compact Levi-flat hypersurfaces.
In this talk, I will explain the detail of the concrete gluing construction of such a K3 surface.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Algebraic Geometry Seminar
17:00-18:00 Room # (Graduate School of Math. Sci. Bldg.)
Wahei Hara (University of Glasgow)
Rank two weak Fano bundles on del Pezzo threefolds of degree 5 (日本語)
Zoom
Wahei Hara (University of Glasgow)
Rank two weak Fano bundles on del Pezzo threefolds of degree 5 (日本語)
[ Abstract ]
None
[ Reference URL ]None
Zoom
2021/06/10
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
A technical base of the AI and machine learning as the basis (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
A technical base of the AI and machine learning as the basis (Japanese)
[ Abstract ]
Explanation on a technical base of the AI and machine learning as the basis
[ Reference URL ]Explanation on a technical base of the AI and machine learning as the basis
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
2021/06/09
Algebraic Geometry Seminar
15:00-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Andrea Fanelli (Bordeaux)
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
SHIMIZU Ikkei (Osaka University)
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.
Takahiro Matsusita (University of the Ryukyus)
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
Hannes Thiel (TU Dresden)
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
Kohei Soga (Keio University)
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.)
Kazuki KANNAKA (RIKEN iTHEMS)
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
Kurando Baba (Tokyo University of Science)
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
Hiroshi Fujiwara (BroadBand Tower, Inc.)
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.)
Ko Aoki (Tokyo)
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.
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
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.
Masatoshi Kitagawa (Waseda University)
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.
Masatoshi KITAGAWA (Waseda University)
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
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
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
Yuya Takeuchi (Tsukuba University)
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).
Yuji Tachikawa (Kavli IPMU)
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
Nariyuki Minami (Keio University School of Medicine)
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
Hiroshi Fujiwara (BroadBand Tower, Inc.)
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.)
Itsuki Yamaguchi (Tokyo)
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
Ryosuke Shimada (University of Tokyo)
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
TAKADA Ryo (Kyushu University)
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.
Taro Asuke (The University of Tokyo)
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
Rajarama Bhat (Indian Statistical Institute)
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
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