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過去の記録
過去の記録 ～10/15｜本日 10/16 | 今後の予定 10/17～
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
高野 暁弘 氏 (東京大学大学院数理科学研究科)
Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
高野 暁弘 氏 (東京大学大学院数理科学研究科)
Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)
[ 講演概要 ]
Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.
More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).
[ 参考URL ]Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.
More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年12月26日(火)
東京名古屋代数セミナー
15:00-16:30 数理科学研究科棟(駒場) ハイブリッド・002号室
ハイブリッドです。Zoomの詳細は参考URLをご覧ください。
Ivan Losev 氏 (Yale University)
t-structures on the equivariant derived category of the Steinberg scheme (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
ハイブリッドです。Zoomの詳細は参考URLをご覧ください。
Ivan Losev 氏 (Yale University)
t-structures on the equivariant derived category of the Steinberg scheme (English)
[ 講演概要 ]
The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.
[ 参考URL ]The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023年12月21日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
山川 高志 氏 (NTT)
量子計算と暗号 (Japanese)
山川 高志 氏 (NTT)
量子計算と暗号 (Japanese)
[ 講演概要 ]
量子計算と暗号理論の関わりについていくつかのトピック、具体的には量子マネーや暗号を用いた量子計算機の検証等について解説する。
量子計算と暗号理論の関わりについていくつかのトピック、具体的には量子マネーや暗号を用いた量子計算機の検証等について解説する。
2023年12月20日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Jinhyun Park 氏 (KAIST)
Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)
Jinhyun Park 氏 (KAIST)
Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)
[ 講演概要 ]
The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.
Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.
The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.
Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.
2023年12月19日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
河東 泰之 氏 (東京大学大学院数理科学研究科)
Topological quantum computing, tensor networks and operator algebras (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
河東 泰之 氏 (東京大学大学院数理科学研究科)
Topological quantum computing, tensor networks and operator algebras (JAPANESE)
[ 講演概要 ]
Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.
[ 参考URL ]Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年12月15日(金)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
石井 志保子 氏 (東京大学)
On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)
石井 志保子 氏 (東京大学)
On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)
[ 講演概要 ]
In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.
In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室(auditorium)号室
数理科学研究科所属以外の方は、[参考URL]から参加登録をお願いいたします。
枡田幹也 氏 (大阪公立大学数学研究所)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
https://forms.gle/42wEF5c2pqsqrHqR7
数理科学研究科所属以外の方は、[参考URL]から参加登録をお願いいたします。
枡田幹也 氏 (大阪公立大学数学研究所)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
[ 講演概要 ]
旗多様体の部分多様体の族であるHessenberg多様体には，幾何学的表現論におけるSpringerファイバー，旗多様体の量子コホモロジーに関連するPeterson多様体，非特異トーリック多様体であるpermutohedral多様体が含まれている．Hessenberg多様体は行列の固有値を求めるQRアルゴリズムや超平面配置とも関連する．最近，Hessenberg多様体がグラフ理論における対称関数に関するStanley-Stembridge予想と関連することが分かり注目されている．本講演では，Hessenberg多様体がこの予想にどのように関連するのかを説明する．
[ 参考URL ]旗多様体の部分多様体の族であるHessenberg多様体には，幾何学的表現論におけるSpringerファイバー，旗多様体の量子コホモロジーに関連するPeterson多様体，非特異トーリック多様体であるpermutohedral多様体が含まれている．Hessenberg多様体は行列の固有値を求めるQRアルゴリズムや超平面配置とも関連する．最近，Hessenberg多様体がグラフ理論における対称関数に関するStanley-Stembridge予想と関連することが分かり注目されている．本講演では，Hessenberg多様体がこの予想にどのように関連するのかを説明する．
https://forms.gle/42wEF5c2pqsqrHqR7
東京無限可積分系セミナー
13:00-14:30 数理科学研究科棟(駒場) 056号室
Laszlo Feher 氏 (University of Szeged, Hungary)
Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)
Laszlo Feher 氏 (University of Szeged, Hungary)
Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)
[ 講演概要 ]
We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models
built on collective spin variables.
Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,
as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,
which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation
from an associated Heisenberg double.
Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the
corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped
with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives
a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.
We also show that
a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context
of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.
Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,
without realizing the bi-Hamiltonian aspect.
Finally, if time permits, the degenerate integrability of some of the reduced systems
will be explained as well.
[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$
to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).
[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).
[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,
Nonlinearity 35, 2971-3003 (2022).
[4] L. Feher and B. Juhasz,
A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,
Lett. Math. Phys. 112:45 (2022).
[5] L. Feher,
Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of
compact Lie groups, arXiv:2309.16245
We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models
built on collective spin variables.
Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,
as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,
which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation
from an associated Heisenberg double.
Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the
corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped
with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives
a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.
We also show that
a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context
of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.
Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,
without realizing the bi-Hamiltonian aspect.
Finally, if time permits, the degenerate integrability of some of the reduced systems
will be explained as well.
[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$
to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).
[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).
[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,
Nonlinearity 35, 2971-3003 (2022).
[4] L. Feher and B. Juhasz,
A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,
Lett. Math. Phys. 112:45 (2022).
[5] L. Feher,
Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of
compact Lie groups, arXiv:2309.16245
2023年12月14日(木)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
枡田 幹也 氏 (大阪公立大学)
Torus orbit closures in the flag variety (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
枡田 幹也 氏 (大阪公立大学)
Torus orbit closures in the flag variety (JAPANESE)
[ 講演概要 ]
The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.
[ 参考URL ]The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
富田 潤一 氏 (NTT)
関数型暗号と属性ベース暗号 (Japanese)
富田 潤一 氏 (NTT)
関数型暗号と属性ベース暗号 (Japanese)
[ 講演概要 ]
関数型暗号は、暗号化されたデータから元データの関数値だけを復号することが可能な暗号である。この講演では関数型暗号とその重要な下位概念の一つである属性ベース暗号について、基本的な内容から最近の研究の進展についてまでを概説する。
関数型暗号は、暗号化されたデータから元データの関数値だけを復号することが可能な暗号である。この講演では関数型暗号とその重要な下位概念の一つである属性ベース暗号について、基本的な内容から最近の研究の進展についてまでを概説する。
東京名古屋代数セミナー
10:30-12:00 オンライン開催
Xiaofa Chen 氏 (University of Science and Technology of China)
On exact dg categories (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Xiaofa Chen 氏 (University of Science and Technology of China)
On exact dg categories (English)
[ 講演概要 ]
In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.
[ 参考URL ]In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2023年12月12日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Stavros Garoufalidis 氏 (南方科技大学)
Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Stavros Garoufalidis 氏 (南方科技大学)
Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)
[ 講演概要 ]
We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.
[ 参考URL ]We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年12月11日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
松田 凌 氏 (京都大学)
On Partial deformations and Bers embedding (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
松田 凌 氏 (京都大学)
On Partial deformations and Bers embedding (Japanese)
[ 講演概要 ]
The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.
[ 参考URL ]The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023年12月07日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
西巻 陵 氏 (NTT)
暗号学的プログラム難読化とその応用 (Japanese)
西巻 陵 氏 (NTT)
暗号学的プログラム難読化とその応用 (Japanese)
[ 講演概要 ]
暗号学的な意味で安全なプログラム難読化とは何かを説明し、その実現方法や応用について解説する。特に実現方法において重要な関数型暗号や暗号学的多重線形写像との関わりについても解説する。
暗号学的な意味で安全なプログラム難読化とは何かを説明し、その実現方法や応用について解説する。特に実現方法において重要な関数型暗号や暗号学的多重線形写像との関わりについても解説する。
2023年12月06日(水)
東京無限可積分系セミナー
13:00-14:30 数理科学研究科棟(駒場) 056号室
Misha Feigin 氏 (University of Glasgow)
本講演はキャンセルとなりました
Flat coordinates of algebraic Frobenius manifolds (ENGLISH)
Misha Feigin 氏 (University of Glasgow)
本講演はキャンセルとなりました
Flat coordinates of algebraic Frobenius manifolds (ENGLISH)
[ 講演概要 ]
本講演はキャンセルとなりました
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.
本講演はキャンセルとなりました
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.
2023年12月05日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
北野 晃朗 氏 (創価大学)
On the Euler class for flat S1-bundles, C∞ vs Cω (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
北野 晃朗 氏 (創価大学)
On the Euler class for flat S1-bundles, C∞ vs Cω (JAPANESE)
[ 講演概要 ]
We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
[ 参考URL ]We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023年12月04日(月)
日仏数学拠点FJ-LMIセミナー
14:00- 数理科学研究科棟(駒場) 056号室
Philippe G. LEFLOCH 氏 (Sorbonne University & CNRS)
An introduction to Einstein constraints and the seed-to-solution method
https://fj-lmi.cnrs.fr/seminars/
Philippe G. LEFLOCH 氏 (Sorbonne University & CNRS)
An introduction to Einstein constraints and the seed-to-solution method
[ 講演概要 ]
I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).
[ 参考URL ]I will present an introduction to the constraint equations associated with Einstein’s field equations of general relativity, and to recent developments based on the seed-to-solution method developed in collaboration with The-Cang Nguyen (Montpellier) and Bruno Le Floch (LPTHE, Sorbonne).
https://fj-lmi.cnrs.fr/seminars/
2023年11月30日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催
Philippe G. LeFloch 氏 (Sorbonne University and CNRS)
Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)
https://forms.gle/HPsYinKweUW3AQGv9
対面・オンラインハイブリッド開催
Philippe G. LeFloch 氏 (Sorbonne University and CNRS)
Einstein spacetimes: dispersion, localization, collapse, and bouncing (English)
[ 講演概要 ]
I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).
Blog: philippelefloch.org
[ 参考URL ]I will overview recent developments on Einstein's field equations of general relativity, especially the global evolution problem from initial data sets. A variety of phenomena may arise in this evolution: gravitational waves, dispersion, collapse, formation of singularities, and bouncing. While many problems remain widely open and very challenging, in the past decades major mathematical advances were made for several classes of spacetimes. I will review recent results on the (1) nonlinear stability of Minkowski spacetime, (2) localization problem at infinity, (3) collapse of spherically symmetric fields, and (4) scattering through quiescent singularity. This talk is based on joint work with Y. Ma (Xi'an), T.-C. Nguyen (Montpellier), F. Mena (Lisbon), B. Le Floch (Paris), and G. Veneziano (Geneva).
Blog: philippelefloch.org
https://forms.gle/HPsYinKweUW3AQGv9
2023年11月28日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Gwénaël Massuyeau 氏 (Université de Bourgogne)
An analogue of the Johnson-Morita theory for the handlebody group (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Gwénaël Massuyeau 氏 (Université de Bourgogne)
An analogue of the Johnson-Morita theory for the handlebody group (ENGLISH)
[ 講演概要 ]
The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.
[ 参考URL ]The Johnson-Morita theory provides an approach for the mapping class group of a surface by considering its actions on the successive nilpotent quotients of the fundamental group of the surface. In this talk, after an outline of the original theory, we will present an analogue of the Johnson-Morita theory for the handlebody group, i.e. the mapping class group of a handlebody. This is joint work with Kazuo Habiro; as we shall explain if time allows, our motivation is to recover the "tree reduction" of a certain functor on the category of bottom tangles in handlebodies that we introduced (a few years ago) using the Kontsevich integral.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
日仏数学拠点FJ-LMIセミナー
16:00- 数理科学研究科棟(駒場) 117号室
Maud DELATTRE 氏 (Université Paris-Saclay, INRAE)
Some contributions on variable selection in nonlinear mixed-effects models
https://fj-lmi.cnrs.fr/seminars/
Maud DELATTRE 氏 (Université Paris-Saclay, INRAE)
Some contributions on variable selection in nonlinear mixed-effects models
[ 講演概要 ]
In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.
References
[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.
[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.
[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.
[ 参考URL ]In the first part of this presentation, we will introduce the general formalism of nonlinear mixed effects models (NLMEM) that are specifically designed models to describe dynamic phenomena from repeated data on several subjects. In the second part, we will focus on specific variable selection technics for NLMEM through two contributions. In the first one, we will discuss the proper definition and use of the Bayesian information criterion (BIC) for variable selection in a low dimensional setting. High dimensional variable selection is the subject of the second contribution.
References
[1] Delattre, M., Lavielle, M. and Poursat, M.A. (2014) A note on BIC in mixed effects models, Electronic Journal of Statistics 8(1) p. 456-475.
[2] Delattre, M. and Poursat, M.A. (2020) An iterative algorithm for joint covariate and random effect selection in mixed effects models., The International Journal of Biostatistics 16(2), 20190082.
[3] Naveau, M., Kon Kam King, G., Rincent, R., Sansonnet, L. and Delattre, M. Bayesian high dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm. hal-03685060.
https://fj-lmi.cnrs.fr/seminars/
2023年11月27日(月)
複素解析幾何セミナー
11:00-12:30 数理科学研究科棟(駒場) 128号室
小川 智史 氏 (大阪公立大学)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
小川 智史 氏 (大阪公立大学)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
[ 講演概要 ]
Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
[ 参考URL ]Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
東京確率論セミナー
17:00-18:30 数理科学研究科棟(駒場) 126号室
Stefan Junk 氏 (学習院大学)
Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)
Stefan Junk 氏 (学習院大学)
Local limit theorem for directed polymer in (almost) the whole weak disorder regime (English)
[ 講演概要 ]
We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time
polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show
that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.
We consider the directed polymer model in the weak disorder (high temperature) phase in spatial dimension d>2. In the case where the (normalized) partition function is L^2-bounded it is known for that time
polymer measure satisfies a local limit theorem, i.e., that the point-to-point partition function can be approximated by two point-to-plane partition functions at the start- and endpoint. We show
that this result continues to hold true if the partition function is L^p-bounded for some p>1+2/d. We furthermore show that for environments with finite support the required L^p -boundedness holds in the whole weak disorder phase, except possibly for the critical value itself.
2023年11月24日(金)
代数幾何学セミナー
14:00-15:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
Haidong Liu 氏 (Sun Yat-sen University)
On Kawamata-Miyaoka type inequality
Haidong Liu 氏 (Sun Yat-sen University)
On Kawamata-Miyaoka type inequality
[ 講演概要 ]
For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.
For klt projective varieties with nef and big canonical divisors, there exists a Miyaoka-Yau type inequality concerning the first and the second Chern classes. In this talk, I will present a Kawamata-Miyaoka type inequality for terminal Q-Fano varieties, which is a mirror version of the Miyaoka-Yau type inequality. This is a joint work with Jie Liu.
日仏数学拠点FJ-LMIセミナー
14:00-14:40 数理科学研究科棟(駒場) 117号室
Gwénaël MASSUYEAU 氏 (Université de Bourgogne & CNRS)
Surgery equivalence relations on 3-manifolds (English)
https://fj-lmi.cnrs.fr/seminars/
Gwénaël MASSUYEAU 氏 (Université de Bourgogne & CNRS)
Surgery equivalence relations on 3-manifolds (English)
[ 講演概要 ]
By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.
[ 参考URL ]By some classical results in low-dimensional topology, any two 3-manifolds (with the “same” boundaries) are related one to the other by surgery operations. In this survey talk, we shall review this basic fact and, next, by restricting the type of surgeries, we shall consider several families of non-trivial equivalence relations on the set of (homeomorphism classes of) 3-manifolds. Those “surgery equivalence relations” are defined in terms of filtrations of the mapping class groups of surfaces, and their characterization / classification involves the notion of “finite-type invariant” which arises in quantum topology.
https://fj-lmi.cnrs.fr/seminars/
2023年11月22日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
山崎隆雄 氏 (中央大学)
曲面のねじれ双有理モチーフ不変量と不分岐コホモロジー (Japanese)
山崎隆雄 氏 (中央大学)
曲面のねじれ双有理モチーフ不変量と不分岐コホモロジー (Japanese)
[ 講演概要 ]
対角線の分解を許容する曲面の捻じれ双有理モチーフについて，不分岐コホモロジーが普遍的な不変量を与えるという結果について講演する．整係数Hodge予想への新たな反例についても触れる．また，正標数では単純な類似が成立し得ないことを論じる．（佐藤周友氏との共同研究）
対角線の分解を許容する曲面の捻じれ双有理モチーフについて，不分岐コホモロジーが普遍的な不変量を与えるという結果について講演する．整係数Hodge予想への新たな反例についても触れる．また，正標数では単純な類似が成立し得ないことを論じる．（佐藤周友氏との共同研究）
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