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過去の記録
過去の記録 ～09/23｜本日 09/24 | 今後の予定 09/25～
2026年09月10日(木)
東京確率論セミナー
14:00-17:30 数理科学研究科棟(駒場) 126号室
講演の開始が早くなっています。
Sung-Soo Byun 氏 (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
講演の開始が早くなっています。
Sung-Soo Byun 氏 (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
[ 講演概要 ]
Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
Jacek Wesolowski 氏 (Warsaw University of Technology) 16:00-17:30Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
[ 講演概要 ]
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
東京無限可積分系セミナー
14:00-16:00 数理科学研究科棟(駒場) 123号室
村瀬元彦 氏 (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
村瀬元彦 氏 (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
[ 講演概要 ]
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
2026年09月09日(水)
日仏数学拠点FJ-LMIセミナー
11:15-12:00 数理科学研究科棟(駒場) 056号室
Léo BÉNARD 氏 (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
https://fj-lmi.cnrs.fr/seminars
Léo BÉNARD 氏 (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
[ 講演概要 ]
I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
[ 参考URL ]I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
https://fj-lmi.cnrs.fr/seminars
日仏数学拠点FJ-LMIセミナー
15:00-16:00 数理科学研究科棟(駒場) 126号室
Herbert GANGL 氏 (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Herbert GANGL 氏 (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
[ 講演概要 ]
In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
[ 参考URL ]In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
日仏数学拠点FJ-LMIセミナー
16:15-17:15 数理科学研究科棟(駒場) 126号室
Luc PIRIO 氏 (CNRS FJ-LMI)
Polylogarithms and Webs
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Luc PIRIO 氏 (CNRS FJ-LMI)
Polylogarithms and Webs
[ 講演概要 ]
In this rather informal talk, I will discuss how web geometry provides a geometric approach
to functional identities that are formally similar to those satisfied by polylogarithms.
[ 参考URL ]In this rather informal talk, I will discuss how web geometry provides a geometric approach
to functional identities that are formally similar to those satisfied by polylogarithms.
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
2026年08月21日(金)
代数幾何学セミナー
13:15-14:45 数理科学研究科棟(駒場) 128号室
（8/17更新）講演者の都合で中止となりました。
Heath Pearson 氏 (the University of Nottingham)
TBA
（8/17更新）講演者の都合で中止となりました。
Heath Pearson 氏 (the University of Nottingham)
TBA
[ 講演概要 ]
TBA
TBA
2026年08月04日(火)
博士論文発表会
16:15-17:30 数理科学研究科棟(駒場) 122号室
朝永 龍 氏 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
朝永 龍 氏 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
2026年07月31日(金)
代数幾何学セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
[ 講演概要 ]
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
2026年07月27日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
坪谷 玲緒 氏 (京都大学)
Weak solution theory for the stochastic compressible Navier-Stokes equations with slip boundary conditions
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
坪谷 玲緒 氏 (京都大学)
Weak solution theory for the stochastic compressible Navier-Stokes equations with slip boundary conditions
[ 講演概要 ]
Navier-Stokes方程式は、粘性のある流体の運動を記述する方程式であり、流体力学だけでなく非線形偏微分方程式論においても中心的な研究対象である。確率論の文脈では、外部からの不確実な影響や微視的な揺らぎを記述するため、ノイズを含む確率Navier-Stokes方程式が研究されている。非圧縮性流体の解析は古くから盛んに行われてきた一方で、気体のように密度変化を伴う圧縮性流体の解析は、特に確率論において比較的新しく、現在も多くの課題が残されている。さらに、流体の解析において境界条件の選択は重要な意味をもつ。近年では、流体が境界面に沿って滑ることを許す滑り境界条件が、物理的に自然な境界条件の一つとして注目を集めている。以上の背景を踏まえ、本講演では、まず確率圧縮性Navier-Stokes方程式の構造について概説し、その後、滑り境界条件のもとでの弱解理論について、講演者の結果を紹介する。
Navier-Stokes方程式は、粘性のある流体の運動を記述する方程式であり、流体力学だけでなく非線形偏微分方程式論においても中心的な研究対象である。確率論の文脈では、外部からの不確実な影響や微視的な揺らぎを記述するため、ノイズを含む確率Navier-Stokes方程式が研究されている。非圧縮性流体の解析は古くから盛んに行われてきた一方で、気体のように密度変化を伴う圧縮性流体の解析は、特に確率論において比較的新しく、現在も多くの課題が残されている。さらに、流体の解析において境界条件の選択は重要な意味をもつ。近年では、流体が境界面に沿って滑ることを許す滑り境界条件が、物理的に自然な境界条件の一つとして注目を集めている。以上の背景を踏まえ、本講演では、まず確率圧縮性Navier-Stokes方程式の構造について概説し、その後、滑り境界条件のもとでの弱解理論について、講演者の結果を紹介する。
2026年07月23日(木)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 122号室
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
2026年07月21日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年07月17日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) NISSAY Lecture Hall号室
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
[ 講演概要 ]
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
2026年07月15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
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
[ 講演概要 ]
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
2026年07月14日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
[ 講演概要 ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
トポロジー火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) hybrid/056号室
Lie群論・表現論セミナーと合同開催。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie群論・表現論セミナーと合同開催。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
[ 講演概要 ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
[ 参考URL ]A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
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
榊原航也 氏 (金沢大学理工研究域)
制約付き平面閉曲線流に対する安定化 dual-SAV パラメトリック有限要素法 (Japanese)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
榊原航也 氏 (金沢大学理工研究域)
制約付き平面閉曲線流に対する安定化 dual-SAV パラメトリック有限要素法 (Japanese)
[ 講演概要 ]
曲率に駆動される平面閉曲線の時間発展をパラメトリック有限要素法で計算する際には，高階の幾何学的剛性に加え，節点の集中・疎化によるメッシュの劣化，さらに面積や酋長などの大域的制約に由来する非線型性を同時に扱う必要がある．本講演では，物理的な幾何エネルギーと人工的なメッシュ正則化エネルギーに対して，独立な2つの scalar auxiliary variable (SAV) を導入する安定化 dual-SAV パラメトリック有限要素法を紹介する．メッシュ正則化に対応する力を接線方向にのみ作用させることで，曲線の法線方向の幾何学的運動を変えることなく，節点の再配置を実現する．また，既知時刻の計量を凍結した半陰的離散化と，速度そのものに作用する零次安定化を組み合わせることにより，各時間ステップに現れる空間方向の問題を正定値対称な線型応答問題へと帰着させ，幾何 SAV エネルギーおよびメッシュ修正 SAV エネルギーに対する離散散逸則を導く．さらに，K 個の大域的制約を課す場合，ブロック消去によって残る非線型問題が，メッシュ節点数によらない K+1 次元の代数系に縮約されることを示す．曲線短縮流，面積保存曲線短縮流，曲線拡散流，ならびに面積・周長制約付き Helfrich 型流の数値例を通じて，時間精度，修正エネルギー散逸，制約を高精度に満たすこと，メッシュ品質および計算効率を検証する．
[ 参考URL ]曲率に駆動される平面閉曲線の時間発展をパラメトリック有限要素法で計算する際には，高階の幾何学的剛性に加え，節点の集中・疎化によるメッシュの劣化，さらに面積や酋長などの大域的制約に由来する非線型性を同時に扱う必要がある．本講演では，物理的な幾何エネルギーと人工的なメッシュ正則化エネルギーに対して，独立な2つの scalar auxiliary variable (SAV) を導入する安定化 dual-SAV パラメトリック有限要素法を紹介する．メッシュ正則化に対応する力を接線方向にのみ作用させることで，曲線の法線方向の幾何学的運動を変えることなく，節点の再配置を実現する．また，既知時刻の計量を凍結した半陰的離散化と，速度そのものに作用する零次安定化を組み合わせることにより，各時間ステップに現れる空間方向の問題を正定値対称な線型応答問題へと帰着させ，幾何 SAV エネルギーおよびメッシュ修正 SAV エネルギーに対する離散散逸則を導く．さらに，K 個の大域的制約を課す場合，ブロック消去によって残る非線型問題が，メッシュ節点数によらない K+1 次元の代数系に縮約されることを示す．曲線短縮流，面積保存曲線短縮流，曲線拡散流，ならびに面積・周長制約付き Helfrich 型流の数値例を通じて，時間精度，修正エネルギー散逸，制約を高精度に満たすこと，メッシュ品質および計算効率を検証する．
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2026年07月13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) 126号室
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
[ 講演概要 ]
It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
[ 参考URL ]It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
https://forms.gle/8ERsVDLuKHwbVzm57
2026年07月08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
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
https://vova-sosnilo.com/
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
[ 講演概要 ]
Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
[ 参考URL ]Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
https://vova-sosnilo.com/
東京名古屋代数セミナー
13:00-14:30 オンライン開催
髙谷 悠太 氏 (東京大学)
Characteristic-free approaches around Yu's construction (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
髙谷 悠太 氏 (東京大学)
Characteristic-free approaches around Yu's construction (Japanese)
[ 講演概要 ]
Yu's construction is one of the most wide-ranging constructions of supercuspidal representations. Recently, Fintzen, Kaletha, and Spice introduced a quadratic twist of this construction to build stable L-packets, which also appears in the geometric realization via positive-depth Deligne-Lusztig induction. In this talk, I will present a direct approach to twisted Yu's construction and explain how to remove technical conditions on small primes in the theory of Yu's construction and positive-depth Deligne-Lusztig induction.
Zoom ID 882 6509 3568 Password 616173
[ 参考URL ]Yu's construction is one of the most wide-ranging constructions of supercuspidal representations. Recently, Fintzen, Kaletha, and Spice introduced a quadratic twist of this construction to build stable L-packets, which also appears in the geometric realization via positive-depth Deligne-Lusztig induction. In this talk, I will present a direct approach to twisted Yu's construction and explain how to remove technical conditions on small primes in the theory of Yu's construction and positive-depth Deligne-Lusztig induction.
Zoom ID 882 6509 3568 Password 616173
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026年07月07日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
橋本七海 氏 (慶応大)
Equivalence of categories of KK-theory or E-theory for $C^*$-algebras over topological spaces by reflection functors
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
橋本七海 氏 (慶応大)
Equivalence of categories of KK-theory or E-theory for $C^*$-algebras over topological spaces by reflection functors
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
トポロジー火曜セミナー
16:00-17:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
[ 講演概要 ]
This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
[ 参考URL ]This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年07月06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) 126号室
Xiaojun Wu 氏 (筑波大学)
Generalised Ueda Obstruction Classes and Non-Semipositive Line Bundles (English)
https://forms.gle/8ERsVDLuKHwbVzm57
Xiaojun Wu 氏 (筑波大学)
Generalised Ueda Obstruction Classes and Non-Semipositive Line Bundles (English)
[ 講演概要 ]
Serre’s classical example provides a fundamental instance of a nef but non-semipositive line bundle and motivated the analytic definition of nefness introduced by Demailly–Peternell–Schneider. Building on subsequent developments by Koike, the classical Ueda obstruction classes provide a natural criterion for non-semipositivity. In this talk, we introduce a natural generalisation of the Ueda obstruction classes that is always well defined and for which the Chern curvature naturally determines representatives. As an application, we obtain an elementary and systematic method for constructing nef but non-semipositive line bundles.
[ 参考URL ]Serre’s classical example provides a fundamental instance of a nef but non-semipositive line bundle and motivated the analytic definition of nefness introduced by Demailly–Peternell–Schneider. Building on subsequent developments by Koike, the classical Ueda obstruction classes provide a natural criterion for non-semipositivity. In this talk, we introduce a natural generalisation of the Ueda obstruction classes that is always well defined and for which the Chern curvature naturally determines representatives. As an application, we obtain an elementary and systematic method for constructing nef but non-semipositive line bundles.
https://forms.gle/8ERsVDLuKHwbVzm57
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
舟木直久 氏 (北京雁栖湖応用数学研究院)
Interface motion from non-gradient Glauber-Kawasaki dynamics
15:20〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
舟木直久 氏 (北京雁栖湖応用数学研究院)
Interface motion from non-gradient Glauber-Kawasaki dynamics
[ 講演概要 ]
Motivated by the problem of dynamic phase transitions, we study the derivation of interface motion from non-gradient Glauber-Kawasaki dynamics. In the balanced case, the limiting interface evolves according to the anisotropic curvature flow, while in the unbalanced case it is governed by a geometric Hamilton-Jacobi equation. We establish this result as a quantitative hydrodynamic limit and, by applying the method of quantitative homogenization, obtain convergence rates. We also investigate fluctuations of the interface and derive a linear stochastic partial differential equation. This talk is partially based on several joint works with Chenlin Gu (Tsinghua U), Han Wang (Tsinghua U), Shuhan Zhou (Peking U), Hyunjoon Park (Meiji U), Claudio Landim (IMPA), Sunder Sethuraman (U Arizona).
Motivated by the problem of dynamic phase transitions, we study the derivation of interface motion from non-gradient Glauber-Kawasaki dynamics. In the balanced case, the limiting interface evolves according to the anisotropic curvature flow, while in the unbalanced case it is governed by a geometric Hamilton-Jacobi equation. We establish this result as a quantitative hydrodynamic limit and, by applying the method of quantitative homogenization, obtain convergence rates. We also investigate fluctuations of the interface and derive a linear stochastic partial differential equation. This talk is partially based on several joint works with Chenlin Gu (Tsinghua U), Han Wang (Tsinghua U), Shuhan Zhou (Peking U), Hyunjoon Park (Meiji U), Claudio Landim (IMPA), Sunder Sethuraman (U Arizona).
2026年07月03日(金)
代数幾何学セミナー
13:15-14:45 数理科学研究科棟(駒場) 117号室
吉川 翔 氏 (東京科学大学)
Hodge–Tate splitting and Akizuki–Nakano vanishing
吉川 翔 氏 (東京科学大学)
Hodge–Tate splitting and Akizuki–Nakano vanishing
[ 講演概要 ]
Akizuki–Nakano vanishing theorem は、Kodaira vanishing theorem を微分形式係数のコホモロジーへ拡張する基本的な消滅定理であり、複素代数幾何においてコホモロジーの制御や変形理論に重要な役割を果たす。一方、正標数ではこの定理は一般には成立せず、どのような幾何学的条件の下で同様の消滅定理が成り立つかは、自然かつ重要な問題である。
この方向の出発点として、Deligne–Illusie は、滑らかな固有多様体がW_2-lift をもち、かつその次元が標数より小さい場合に、de Rham complex の分解を用いて Akizuki–Nakano vanishing を証明した。近年、Petrov は quasi-F-split 多様体に対して、次元に関する制限なしに Akizuki–Nakano vanishing が従うことを証明した。
本講演では、これらの結果を統一的に捉える枠組みとして Hodge–Tate splitting という条件を考察し、この条件から Akizuki–Nakano vanishing が導かれることを説明する。また、この結果の混標数における類似についても紹介したい。
本講演は石塚彾氏との共同研究に基づく。
Akizuki–Nakano vanishing theorem は、Kodaira vanishing theorem を微分形式係数のコホモロジーへ拡張する基本的な消滅定理であり、複素代数幾何においてコホモロジーの制御や変形理論に重要な役割を果たす。一方、正標数ではこの定理は一般には成立せず、どのような幾何学的条件の下で同様の消滅定理が成り立つかは、自然かつ重要な問題である。
この方向の出発点として、Deligne–Illusie は、滑らかな固有多様体がW_2-lift をもち、かつその次元が標数より小さい場合に、de Rham complex の分解を用いて Akizuki–Nakano vanishing を証明した。近年、Petrov は quasi-F-split 多様体に対して、次元に関する制限なしに Akizuki–Nakano vanishing が従うことを証明した。
本講演では、これらの結果を統一的に捉える枠組みとして Hodge–Tate splitting という条件を考察し、この条件から Akizuki–Nakano vanishing が導かれることを説明する。また、この結果の混標数における類似についても紹介したい。
本講演は石塚彾氏との共同研究に基づく。
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