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Seminar information archive
Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Hidenori Fujiwara (Kindai University)
Polynomial conjectures for nilpotent Lie groups
(Japanese)
Hidenori Fujiwara (Kindai University)
Polynomial conjectures for nilpotent Lie groups
(Japanese)
[ Abstract ]
Let G = exp g be a connected and simply connected nilpotent Lie group with Lie algebra g. Let H = exp h be an analytic subgroup of G with Lie algebra h and χ a unitary character of H. We consider the monomial representation τ = ind^G_H χ of G. It is well known that the multiplicities in the irreducible disintegration of τ are either uniformly bounded or uniformly equal to ∞. In the former case, we say that τ has finite multiplicities.
Now let D_τ (G/H) be the algebra of the G-invariant differential operators on the fiber bundle over G/H associated to the data (H,χ). This algebra is commutative if and only if τ has finite multiplicities. In
1992 Corwin-Greenleaf presented the following polynomial conjecture :
when τ has finite multiplicities, the algebra D_τ (G/H) is isomorphic to the algebra C[Γ_τ]^H of the H-invariant polynomial functions on the affine subspace Γ_τ = {l ∈ g^* ; l |_h = - √ -1 dχ} of g^* .
It is well known in the representation theory of groups that between the two operations of induction and restriction there is a kind of duality. So, we think about a polynomial conjecture for restrictions. Let G be as above a connected and simply connected nilpotent Lie group and π an irreducible unitary representation of G. Let K be an analytic subgroup of G, and we consider the restriction π|_K of π to K. This time also it is known that the multiplicities in the irreducible disintegration of π|_K are either uniformly bounded or uniformly equal to ∞. In the former case, we say that π|_K has finite multiplicities and we assume
this eventuality. Let U(g) be the enveloping algebra of g_C, and we consider the algebra (U(g)/kerπ)_K of invariant differential operators. This means the set of the K-invariant elements. This algebra is commutative if and only if π|_K has finite multiplicities. In this case, is the algebra (U(g)/kerπ)^K isomorphic to the algebra C[Ω(π)]^K of the K-invariant polynomial functions on Ω(π)? Here, Ω(π) denotes the coadjoint orbit of G corresponding to π.
We would like to prove these two polynomial conjectures.
Let G = exp g be a connected and simply connected nilpotent Lie group with Lie algebra g. Let H = exp h be an analytic subgroup of G with Lie algebra h and χ a unitary character of H. We consider the monomial representation τ = ind^G_H χ of G. It is well known that the multiplicities in the irreducible disintegration of τ are either uniformly bounded or uniformly equal to ∞. In the former case, we say that τ has finite multiplicities.
Now let D_τ (G/H) be the algebra of the G-invariant differential operators on the fiber bundle over G/H associated to the data (H,χ). This algebra is commutative if and only if τ has finite multiplicities. In
1992 Corwin-Greenleaf presented the following polynomial conjecture :
when τ has finite multiplicities, the algebra D_τ (G/H) is isomorphic to the algebra C[Γ_τ]^H of the H-invariant polynomial functions on the affine subspace Γ_τ = {l ∈ g^* ; l |_h = - √ -1 dχ} of g^* .
It is well known in the representation theory of groups that between the two operations of induction and restriction there is a kind of duality. So, we think about a polynomial conjecture for restrictions. Let G be as above a connected and simply connected nilpotent Lie group and π an irreducible unitary representation of G. Let K be an analytic subgroup of G, and we consider the restriction π|_K of π to K. This time also it is known that the multiplicities in the irreducible disintegration of π|_K are either uniformly bounded or uniformly equal to ∞. In the former case, we say that π|_K has finite multiplicities and we assume
this eventuality. Let U(g) be the enveloping algebra of g_C, and we consider the algebra (U(g)/kerπ)_K of invariant differential operators. This means the set of the K-invariant elements. This algebra is commutative if and only if π|_K has finite multiplicities. In this case, is the algebra (U(g)/kerπ)^K isomorphic to the algebra C[Ω(π)]^K of the K-invariant polynomial functions on Ω(π)? Here, Ω(π) denotes the coadjoint orbit of G corresponding to π.
We would like to prove these two polynomial conjectures.
2021/06/28
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Yûsuke Okuyama (Kyoto Institute of Technology)
Orevkov's theorem, Bézout's theorem, and the converse of Brolin's theorem (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
Yûsuke Okuyama (Kyoto Institute of Technology)
Orevkov's theorem, Bézout's theorem, and the converse of Brolin's theorem (Japanese)
[ Abstract ]
The converse of Brolin's theorem was a problem on characterizing polynomials among rational functions (on the complex projective line) in terms of the equilibrium measures canonically associated to rational functions. We would talk about a history on the studies of this problem, its optimal solution, and a proof outline. The proof is reduced to Bézout's theorem from algebraic geometry, thanks to Orevkov's irreducibility theorem on polynomial lemniscates. This talk is based on joint works with Małgorzata Stawiska (Mathematical Reviews).
[ Reference URL ]The converse of Brolin's theorem was a problem on characterizing polynomials among rational functions (on the complex projective line) in terms of the equilibrium measures canonically associated to rational functions. We would talk about a history on the studies of this problem, its optimal solution, and a proof outline. The proof is reduced to Bézout's theorem from algebraic geometry, thanks to Orevkov's irreducibility theorem on polynomial lemniscates. This talk is based on joint works with Małgorzata Stawiska (Mathematical Reviews).
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB
2021/06/25
Colloquium
15:30-16:30 Online
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)
Registration is closed (12:00, June 25).
Hisashi Okamoto (Gakushuin University)
The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)
2021/06/24
Tokyo-Nagoya Algebra Seminar
16:00-17:30 Online
Please see the URL below for details on the online seminar.
Kohei Kikuta (Chuo University)
Rank 2 free subgroups in autoequivalence groups of Calabi-Yau categories
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Kohei Kikuta (Chuo University)
Rank 2 free subgroups in autoequivalence groups of Calabi-Yau categories
[ Abstract ]
Via homological mirror symmetry, there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds.
In this talk, as an analogue of mapping class groups of closed oriented surfaces, we study autoequivalence groups of Calabi-Yau triangulated categories. In particular, we consider embeddings of rank 2 (non-commutative) free groups generated by spherical twists. It is interesting that the proof of main results is almost similar to that of corresponding results in the theory of mapping class groups.
[ Reference URL ]Via homological mirror symmetry, there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds.
In this talk, as an analogue of mapping class groups of closed oriented surfaces, we study autoequivalence groups of Calabi-Yau triangulated categories. In particular, we consider embeddings of rank 2 (non-commutative) free groups generated by spherical twists. It is interesting that the proof of main results is almost similar to that of corresponding results in the theory of mapping class groups.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From a neural network to deep learning (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From a neural network to deep learning (Japanese)
[ Abstract ]
Explanation on the neural network and the deep learning
[ Reference URL ]Explanation on the neural network and the deep learning
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
2021/06/23
Number Theory Seminar
17:00-18:00 Online
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
Koto Imai (University of Tokyo)
Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic (Japanese)
[ Abstract ]
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
Galois extensions of local fields is one of the most important subjects in the field of number theory. A ramification filtration is a filtration of a Galois group used to investigate the ramification of the extension. It is particularly useful when the extension is wildly ramified. In this talk, we examine the ramification groups of finite Galois extensions over complete discrete valuation fields of characteristic $p>0$. Brylinski calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
Discrete mathematical modelling seminar
18:00-19:30 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Alexander STOKES (University College London)
Singularity confinement in delay-differential Painlevé equations (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Alexander STOKES (University College London)
Singularity confinement in delay-differential Painlevé equations (English)
[ Abstract ]
Singularity confinement is a phenomenon first proposed as an integrability criterion for discrete systems, and has been used to great effect to obtain discrete analogues of the Painlevé differential equations. Its geometric interpretation has played a role in novel connections between discrete integrable systems and birational algebraic geometry, including Sakai's geometric framework and classification scheme for discrete Painlevé equations.
Examples of delay-differential equations, which involve shifts and derivatives with respect to a single independent variable, have been proposed as analogues of the Painlevé equations according to a number of viewpoints. Among these are observations of a kind of singularity confinement and it is natural to ask whether this could lead to the development of a geometric theory of delay-differential Painlevé equations.
In this talk we review previously proposed examples of delay-differential Painlevé equations and what is known about their singularity confinement behaviour, including some recent results establishing the existence of infinite families of confined singularities. We also propose a geometric interpretation of these results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined.
Singularity confinement is a phenomenon first proposed as an integrability criterion for discrete systems, and has been used to great effect to obtain discrete analogues of the Painlevé differential equations. Its geometric interpretation has played a role in novel connections between discrete integrable systems and birational algebraic geometry, including Sakai's geometric framework and classification scheme for discrete Painlevé equations.
Examples of delay-differential equations, which involve shifts and derivatives with respect to a single independent variable, have been proposed as analogues of the Painlevé equations according to a number of viewpoints. Among these are observations of a kind of singularity confinement and it is natural to ask whether this could lead to the development of a geometric theory of delay-differential Painlevé equations.
In this talk we review previously proposed examples of delay-differential Painlevé equations and what is known about their singularity confinement behaviour, including some recent results establishing the existence of infinite families of confined singularities. We also propose a geometric interpretation of these results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined.
2021/06/22
Numerical Analysis Seminar
17:00-18:30 Online
Taiji Suzuki (The University of Tokyo)
On approximation ability and adaptivity of deep neural network (Japanese)
[ Reference URL ]
https://forms.gle/HwetNGXCzbCyMC7B7
Taiji Suzuki (The University of Tokyo)
On approximation ability and adaptivity of deep neural network (Japanese)
[ Reference URL ]
https://forms.gle/HwetNGXCzbCyMC7B7
Operator Algebra Seminars
16:45-18:15 Online
Johannes Christensen (KU Leuven)
KMS spectra for group actions on compact spaces (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Johannes Christensen (KU Leuven)
KMS spectra for group actions on compact spaces (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Online
Pre-registration required. See our seminar webpage.
Ryoma Kobayashi (National Institute of Technology, Ishikawa College)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ryoma Kobayashi (National Institute of Technology, Ishikawa College)
On infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup (JAPANESE)
[ Abstract ]
An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
[ Reference URL ]An infinite presentation for the mapping class group of any compact orientable surface was given by Gervais, and then a simpler one by Luo. Using these results, an infinite presentation for the mapping class group of any compact non orientable surfaces with boundary less than or equal to one was given by Omori (Tokyo University of Science), and then one with boundary more than or equal to two by Omori and the speaker. In this talk, we first introduce an infinite presentation for the twisted subgroup of the mapping class group of any compact non orientable surface. I will also present four simple infinite presentations for the mapping group of any compact non orientable surface, which are an improvement of the one given by Omori and the speaker. This work includes a joint work with Omori.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Yosuke MORITA (Kyoto University)
Cartan projections of some nonreductive subgroups and the existence problem of compact Clifford-Klein forms (Japanese)
Yosuke MORITA (Kyoto University)
Cartan projections of some nonreductive subgroups and the existence problem of compact Clifford-Klein forms (Japanese)
[ Abstract ]
Let G be a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G.
According to the Kobayashi-Benoist criterion, the properness of the Γ-action on G/H is determined by the Cartan projections of H and Γ.
Although the Cartan projections of nonreductive subgroups are usually difficult to compute, there are some exceptions. Using them, we give some examples of homogeneous spaces of reductive type that do not admit compact Clifford-Klein forms.
Let G be a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G.
According to the Kobayashi-Benoist criterion, the properness of the Γ-action on G/H is determined by the Cartan projections of H and Γ.
Although the Cartan projections of nonreductive subgroups are usually difficult to compute, there are some exceptions. Using them, we give some examples of homogeneous spaces of reductive type that do not admit compact Clifford-Klein forms.
2021/06/17
Applied Analysis
Information Mathematics Seminar
16:50-18:35 Online
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From machine learning to deep learning (Japanese)
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
Hiroshi Fujiwara (BroadBand Tower, Inc.)
From machine learning to deep learning (Japanese)
[ Abstract ]
Explanation on machine learning and deep learning
[ Reference URL ]Explanation on machine learning and deep learning
https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw
2021/06/16
Number Theory Seminar
17:00-18:00 Online
Yasuhiro Terakado (National Center for Theoretical Sciences)
Hecke eigensystems of automorphic forms (mod p) of Hodge type and algebraic modular forms (Japanese)
Yasuhiro Terakado (National Center for Theoretical Sciences)
Hecke eigensystems of automorphic forms (mod p) of Hodge type and algebraic modular forms (Japanese)
[ Abstract ]
In a 1987 letter to Tate, Serre showed that the prime-to-p Hecke eigensystems arising in the space of mod p modular forms are the same as those appearing in the space of automorphic forms on a quaternion algebra. This result is regarded as a mod p analogue of the Jacquet-Langlands correspondence. In this talk, we give a generalization of Serre's result to the Hecke eigensystems of mod p automorphic forms on a Shimura variety of Hodge type with good reduction at p. This is joint work with Chia-Fu Yu.
In a 1987 letter to Tate, Serre showed that the prime-to-p Hecke eigensystems arising in the space of mod p modular forms are the same as those appearing in the space of automorphic forms on a quaternion algebra. This result is regarded as a mod p analogue of the Jacquet-Langlands correspondence. In this talk, we give a generalization of Serre's result to the Hecke eigensystems of mod p automorphic forms on a Shimura variety of Hodge type with good reduction at p. This is joint work with Chia-Fu Yu.
Seminar on Probability and Statistics
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Hiroki Masuda (Kyushu University)
Levy-Ornstein-Uhlenbeck Regression
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
Hiroki Masuda (Kyushu University)
Levy-Ornstein-Uhlenbeck Regression
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the
covariate process. Also discussed will be model-selection issues and some possible model extensions.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the
covariate process. Also discussed will be model-selection issues and some possible model extensions.
https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform
2021/06/15
Operator Algebra Seminars
16:45-18:15 Online
Yuhei Suzuki (Hokkaido Univ.)
$C^*$-simplicity has no local obstruction
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yuhei Suzuki (Hokkaido Univ.)
$C^*$-simplicity has no local obstruction
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Takamichi Sato (Waseda University)
Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takamichi Sato (Waseda University)
Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)
[ Abstract ]
In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.
[ Reference URL ]In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)
Toshiyuki KOBAYASHI (The University of Tokyo)
Limit algebras and tempered representations (Japanese)
Toshiyuki KOBAYASHI (The University of Tokyo)
Limit algebras and tempered representations (Japanese)
[ Abstract ]
I plan to discuss the new connection between the following four (apparently unrelated) topics:
1. (analysis) Tempered unitary representations on homogeneous spaces
2. (combinatorics) Convex polyhedral cones
3. (topology) Limit algebras
4. (symplectic geometry) Quantization of coadjoint orbits
based on a series of joint papers with Y. Benoist "Tempered homogeneous spaces I-IV".
I plan to discuss the new connection between the following four (apparently unrelated) topics:
1. (analysis) Tempered unitary representations on homogeneous spaces
2. (combinatorics) Convex polyhedral cones
3. (topology) Limit algebras
4. (symplectic geometry) Quantization of coadjoint orbits
based on a series of joint papers with Y. Benoist "Tempered homogeneous spaces I-IV".
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
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