過去の記録

過去の記録 ~03/18本日 03/19 | 今後の予定 03/20~

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)
[ 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



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)
[ 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 ]
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)
[ 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。

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)
[ 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 ]
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)
[ 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 ]
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)
[ 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 ]
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)
[ 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。

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)
[ 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.

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)
[ 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 ]
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
[ 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 ]
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)
[ 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 ]
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)
[ 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 ]
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
[ 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 ]
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)
[ 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 ]
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)
[ 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.

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
[ 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.

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)
[ 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 ]
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)
[ 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)

2023年11月21日(火)

トポロジー火曜セミナー

17:30-18:30   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。
古宇田 悠哉 氏 (慶應義塾大学)
Shadows, divides and hyperbolic volumes (JAPANESE)
[ 講演概要 ]
In 2008, Costantino and D.Thurston revealed that the combinatorial structure of the Stein factorizations of stable maps from 3-manifolds into the real plane can be used to describe the hyperbolic structures of the complement of the set of definite fold points, which is a link. The key was that the Stein factorizations can naturally be embedded into 4-manifolds, and nice ideal polyhedral decompositions become visible on their boundaries. In this talk, we consider divides, which are the images of a proper and generic immersions of compact 1-manifolds into the 2-disk. Due to A'Campo's theory, each divide is associated with a link in the 3-sphere. By embedding a polyhedron induced from a given divide into the 4-ball as was done to Stein factorization, we can read off the ideal polyhedral decompositions on the boundary. We then show that the complement of the link of the divide can be obtained by Dehn filling a hyperbolic 3-manifold that admits a decomposition into several ideal regular hyperbolic polyhedra, where the number of each polyhedron is determined by types of the double points of the divide. This immediately gives an upper bound of the hyperbolic volume of the links of divides, which is shown to be asymptotically sharp. As in the case of Stein factorizations, an idea from the theory of Turaev's shadows plays an important role here. This talk is based on joint work with Ryoga Furutani (Hiroshima University).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室
星野真生 氏 (東大数理)
Finite index quantum subgroups of DQGs
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2023年11月20日(月)

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
木上淳 氏 (京都大学)
Yet another construction of “Sobolev” spaces on metric spaces (日本語)
[ 講演概要 ]
距離空間上への”ソボレフ空間”の構成については、「Lipschitz連続な関数の局所Lipschitz定数を微分の代替物としてもちいる。」という発想のもと、Hajlasz, Cheeger, Shanmugalingam らによる Newtonian 空間などの理論が研究の主流となっている。ところが、最近のKajino-Muruganの研究により、Sierpinski Carpet などの多くの自己相似集合では、この方法が通用しないことがわかってきた。本講演では、Sierpinski carpet 等を含むコンパクトな自己相似集合上に””ソボレフ””空間を構成するための新しい方法について述べる。

2023年11月16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
山内 卓也 氏 (東北大理)
超特殊アーベル多様体上の同種グラフ: 固有値, Bruhat-Tits ビルディングおよびProperty (T)  (Japanese)
[ 講演概要 ]
正整数$g$, 素数$p$, $\ell$に対して, 標数$p$の有限体上の次元$g$をもつsuperspecial abelian varietiesであって$\ell$-marking が指定されたもの全体の成す類から有限向き付き正則グラフを構成することができる. 講演ではこのグラフに対するランダムウォーク行列の性質を対応するBruhat-Tits buildingsを解析することで調べることができることを説明する. また, $g=2$のとき, 保型形式, 保型表現論の観点からランダムウォーク行列の固有値に関して何が期待されるかも説明する. 本研究は東京大学の相川 勇輔 氏、京都大学の田中 亮吉 氏との共同研究である. 

2023年11月14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。
横山 知郎 氏 (埼玉大学)
曲面上の流れの正方向と負方向の極限の振る舞いの依存性 (JAPANESE)
[ 講演概要 ]
We discuss the dependence of a flow's positive and negative limit behaviors on a surface. In particular, I introduce the list of possible pairs of positive and negative limit behaviors that can and cannot occur. The idea of the dependence mechanism is illustrated using the dependence of the limit behavior of a toy model, a circle homeomorphism. We overview with as few prior knowledge assumptions as possible.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
古川賢 氏 (理化学研究所)
いくつかの力学系とそのデータ同化による予測について (Japanese)
[ 講演概要 ]
データ同化による力学系の予測について得られた2つの結果を紹介する.前半では,2次元3種のオートマトンのカオス的な離散力学系を導入し,その離散力学系の時間発展を粒子フィルターによるデータ同化によって予測する方法とその結果について紹介する.後半では,プリミティブ方程式のナッジングによるデータ同化にまつわる問題について紹介する.特に,データ自身の持つ情報量とデータ同化によって得られる近似解(予測)のもつ情報量の関係性を正則性の観点から特徴づける.
[ 参考URL ]
ハイブリッド開催です。参加の詳細は参考URLをご覧ください。

解析学火曜セミナー

16:15-17:15   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,日時・場所にご注意ください
Arne Jensen 氏 (Aalborg University)
Resolvent expansions for magnetic Schrödinger operators (English)
[ 講演概要 ]
I will present some new results resolvent expansions around threshold zero for magnetic Schrödinger operators in dimension three. The magnetic field and the electric potential are assumed to decay sufficiently fast. Analogous results for Pauli operators will also be presented.
Joint work with H. Kovarik, Brescia, Italy.
[ 参考URL ]
https://forms.gle/qyEUeo4kVuPL1s289

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