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過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
2026年05月22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
Justin Sawon 氏 (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
Justin Sawon 氏 (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
[ 講演概要 ]
A Lagrangian fibration on a holomorphic symplectic manifold or variety is one whose general fibre is an abelian variety that is Lagrangian with respect to the symplectic form. Examples were constructed by Beauville/Mukai whose fibres are Jacobians of curves, and by Markushevich-Tikhomirov, Arbarella-Sacca-Ferretti, Matteini, S-Shen, and Brakkee-Camere-Grossi-Pertusi-Sacca-Viktorova whose fibres are Prym varieties of curves with involutions. In all of these examples the family of curves is a linear system on a K3 surface, suggesting the question: is this always the case? Markushevich answered this affirmatively in the genus two case: if the relative compactified Jacobian of a family of genus two curves is a Lagrangian fibration then the curves all lie on a K3 surface, and the Lagrangian fibration is a Beauville-Mukai system. In this talk I will describe our generalization of this result to higher genus, and also to relative Prym varieties of genus three covers with involutions (joint work with Xuqiang Qin).
A Lagrangian fibration on a holomorphic symplectic manifold or variety is one whose general fibre is an abelian variety that is Lagrangian with respect to the symplectic form. Examples were constructed by Beauville/Mukai whose fibres are Jacobians of curves, and by Markushevich-Tikhomirov, Arbarella-Sacca-Ferretti, Matteini, S-Shen, and Brakkee-Camere-Grossi-Pertusi-Sacca-Viktorova whose fibres are Prym varieties of curves with involutions. In all of these examples the family of curves is a linear system on a K3 surface, suggesting the question: is this always the case? Markushevich answered this affirmatively in the genus two case: if the relative compactified Jacobian of a family of genus two curves is a Lagrangian fibration then the curves all lie on a K3 surface, and the Lagrangian fibration is a Beauville-Mukai system. In this talk I will describe our generalization of this result to higher genus, and also to relative Prym varieties of genus three covers with involutions (joint work with Xuqiang Qin).
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
Evgeny Shinder 氏 (University of Sheffield / 東京大学大学院数理科学研究科)
Gromov's cancellation question in birational algebraic geometry
Evgeny Shinder 氏 (University of Sheffield / 東京大学大学院数理科学研究科)
Gromov's cancellation question in birational algebraic geometry
[ 講演概要 ]
Gromov's 1999 cancellation question is: given two open embeddings of a variety U into a variety X, do they always have isomorphic closed complements? In my joint work with Hsueh-Yung Lin we reformulate this question in terms of the structure of the Grothendieck ring of varieties and answer it in various situations. The answer will be positive or negative depending on the dimension of varieties and the ground field. Finally, I will present an application to the structure of the Cremona group of birational self-maps of the projective space.
Gromov's 1999 cancellation question is: given two open embeddings of a variety U into a variety X, do they always have isomorphic closed complements? In my joint work with Hsueh-Yung Lin we reformulate this question in terms of the structure of the Grothendieck ring of varieties and answer it in various situations. The answer will be positive or negative depending on the dimension of varieties and the ground field. Finally, I will present an application to the structure of the Cremona group of birational self-maps of the projective space.
2026年05月21日(木)
日仏数学拠点FJ-LMIセミナー
14:15-15:00 数理科学研究科棟(駒場) 号室
Julien ROUYER 氏 (École Centrale de Pékin, Beihang university, Beijing)
How to cross an intersection ?
Julien ROUYER 氏 (École Centrale de Pékin, Beihang university, Beijing)
How to cross an intersection ?
[ 講演概要 ]
Under certain constraints, we enumerate the different ways of simultaneously crossing a road intersection with alternating entries and exits, for a maximal number of vehicles. The problem reduces to the study of various types of non-crossing partitions of {1,…,n} and gives rise to new integer sequences. Standard combinatorial methods then lead to systems of polynomial equations, in which the unknowns are the generating functions of these sequences.
Under certain constraints, we enumerate the different ways of simultaneously crossing a road intersection with alternating entries and exits, for a maximal number of vehicles. The problem reduces to the study of various types of non-crossing partitions of {1,…,n} and gives rise to new integer sequences. Standard combinatorial methods then lead to systems of polynomial equations, in which the unknowns are the generating functions of these sequences.
2026年05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
毛塚 由佳子 氏 (東京大学大学院数理科学研究科)
Special values of $L$-functions and the Birch and Swinnerton-Dyer conjecture for CM elliptic curves
https://www.ms.u-tokyo.ac.jp/~kezuka/
毛塚 由佳子 氏 (東京大学大学院数理科学研究科)
Special values of $L$-functions and the Birch and Swinnerton-Dyer conjecture for CM elliptic curves
[ 講演概要 ]
Elliptic curves with complex multiplication (CM) have long served as some of the most powerful examples for understanding the Birch and Swinnerton-Dyer (BSD) conjecture. In particular, a wide range of arithmetic phenomena has been observed in families of quadratic twists of these curves. In this talk, I will explain how CM elliptic curves have been used to advance our understanding of the conjecture, and discuss some current directions in this area, focusing in particular on Iwasawa theory and recent developments involving the Gross family of elliptic curves.
[ 参考URL ]Elliptic curves with complex multiplication (CM) have long served as some of the most powerful examples for understanding the Birch and Swinnerton-Dyer (BSD) conjecture. In particular, a wide range of arithmetic phenomena has been observed in families of quadratic twists of these curves. In this talk, I will explain how CM elliptic curves have been used to advance our understanding of the conjecture, and discuss some current directions in this area, focusing in particular on Iwasawa theory and recent developments involving the Gross family of elliptic curves.
https://www.ms.u-tokyo.ac.jp/~kezuka/
東京名古屋代数セミナー
13:00-14:30 オンライン開催
坂本 平蔵 氏 (東京大学)
アフィン型団代数のモノイダル圏化におけるアフィン量子群の実加群と虚加群の分類 (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
坂本 平蔵 氏 (東京大学)
アフィン型団代数のモノイダル圏化におけるアフィン量子群の実加群と虚加群の分類 (Japanese)
[ 講演概要 ]
アフィン量子群の有限次元表現$L$は、$L\otimes L$が既約のとき実加群、既約でないとき虚加群と呼ばれる。有限次元表現圏において部分圏$\mathcal{C}$を適切に取ることで、そのGrothendieck環$K(\mathcal{C})$が、団単項式が既約加群に対応するような団代数構造を持つようにできること（団代数の圏化）が知られている。団代数の圏化を与える$\mathcal{C}$において、既約表現が「団単項式と対応すること」と「実加群であること」は同値だと予想されている。この予想は、実加群の分類が表現論的に基本的課題であることや、表現論と組合せ論をつなぐ問であることなどから重要であるが、圏化される団代数が有限型の場合を除き一般に未解決である。本講演では、アフィン型団代数を圏化する部分圏を構成し、その圏において本予想が成立することを解説する。
Zoom ID 882 0676 3866 Password 289404
[ 参考URL ]アフィン量子群の有限次元表現$L$は、$L\otimes L$が既約のとき実加群、既約でないとき虚加群と呼ばれる。有限次元表現圏において部分圏$\mathcal{C}$を適切に取ることで、そのGrothendieck環$K(\mathcal{C})$が、団単項式が既約加群に対応するような団代数構造を持つようにできること（団代数の圏化）が知られている。団代数の圏化を与える$\mathcal{C}$において、既約表現が「団単項式と対応すること」と「実加群であること」は同値だと予想されている。この予想は、実加群の分類が表現論的に基本的課題であることや、表現論と組合せ論をつなぐ問であることなどから重要であるが、圏化される団代数が有限型の場合を除き一般に未解決である。本講演では、アフィン型団代数を圏化する部分圏を構成し、その圏において本予想が成立することを解説する。
Zoom ID 882 0676 3866 Password 289404
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026年05月19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
上川弘郎 氏 (京都大学)
The homotopy groups of the automorphism group of Kirchberg algebras with compact group actions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
上川弘郎 氏 (京都大学)
The homotopy groups of the automorphism group of Kirchberg algebras with compact group actions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 128号室
通常の会場と異なります。
浜向 直 氏 (北海道大学 大学院理学研究院)
対数凹関数に対するGagliardo-Nirenberg型不等式と非線形楕円型固有値問題への応用 (日本語)
通常の会場と異なります。
浜向 直 氏 (北海道大学 大学院理学研究院)
対数凹関数に対するGagliardo-Nirenberg型不等式と非線形楕円型固有値問題への応用 (日本語)
[ 講演概要 ]
Gagliardo-Nirenberg型不等式を、遠方で減衰する対数凹関数に対して導きます。証明では、関数から定まるエントロピーに対する上下からの評価が鍵となります。上からの評価には対数型ソボレフの不等式、下からの評価には関数の対数凹性を利用します。また、得られたGagliardo-Nirenberg型不等式における定数の精度についても議論します。さらに、完全非線形楕円型固有値問題の解に適用して、固有値に対する下からの評価を導きます。本講演の内容は、藤田安啓氏、五十嵐蓮氏との共同研究に基づきます。
Gagliardo-Nirenberg型不等式を、遠方で減衰する対数凹関数に対して導きます。証明では、関数から定まるエントロピーに対する上下からの評価が鍵となります。上からの評価には対数型ソボレフの不等式、下からの評価には関数の対数凹性を利用します。また、得られたGagliardo-Nirenberg型不等式における定数の精度についても議論します。さらに、完全非線形楕円型固有値問題の解に適用して、固有値に対する下からの評価を導きます。本講演の内容は、藤田安啓氏、五十嵐蓮氏との共同研究に基づきます。
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) 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。
森田 陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (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。
森田 陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (JAPANESE)
[ 講演概要 ]
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the 'vector fields on sphere' problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
[ 参考URL ]Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the 'vector fields on sphere' problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie群論・表現論セミナー
17:30-18:30 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。
森田陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
トポロジー火曜セミナーと合同開催。
森田陽介 氏 (九州大学)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
[ 講演概要 ]
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the ‘vector fields on sphere’ problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the ‘vector fields on sphere’ problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
2026年05月18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
15:15〜 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。
行徳 義弘 氏 (東京大学)
Independence preservation property through web geometry
15:15〜 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。
行徳 義弘 氏 (東京大学)
Independence preservation property through web geometry
[ 講演概要 ]
The subclass [2:2] of quadrirational Yang–Baxter maps on (0,∞)² contains three involutions H⁺_I, H⁺_II, and H^A_III. The central object of study is the independence-preserving property: given a map F with F(X,Y) = (U,V), one seeks all distributions of an independent pair (X,Y) for which (U,V) is again an independent pair. This property stands in direct analogy with classical characterisation theorems — the Kac–Bernstein and Lukacs theorems, and the Matsumoto–Yor property — in which the independence of a prescribed transformation characterises a specific family of distributions. A uniform derivation of the complete characterisation for all three maps is obtained via the theory of planar webs: a Jacobian identity common to all three maps reduces the problem to the determination of Abelian relations of a planar 4-web, whereupon Bol's bound and an explicit basis of three relations yield the full three-parameter families — the generalised beta-prime laws for H⁺_I, the Kummer laws for H⁺_II, and the generalised inverse Gaussian laws for H^A_III.
The subclass [2:2] of quadrirational Yang–Baxter maps on (0,∞)² contains three involutions H⁺_I, H⁺_II, and H^A_III. The central object of study is the independence-preserving property: given a map F with F(X,Y) = (U,V), one seeks all distributions of an independent pair (X,Y) for which (U,V) is again an independent pair. This property stands in direct analogy with classical characterisation theorems — the Kac–Bernstein and Lukacs theorems, and the Matsumoto–Yor property — in which the independence of a prescribed transformation characterises a specific family of distributions. A uniform derivation of the complete characterisation for all three maps is obtained via the theory of planar webs: a Jacobian identity common to all three maps reduces the problem to the determination of Abelian relations of a planar 4-web, whereupon Bol's bound and an explicit basis of three relations yield the full three-parameter families — the generalised beta-prime laws for H⁺_I, the Kummer laws for H⁺_II, and the generalised inverse Gaussian laws for H^A_III.
2026年05月14日(木)
幾何解析セミナー
14:00-16:20 数理科学研究科棟(駒場) 002号室
Jacob Bernstein 氏 (Johns Hopkins University) 14:00-15:00
Complexity of submanifolds and Colding-Minicozzi entropy (英語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Peter Topping 氏 (University of Warwick) 15:20-16:20
Unusual regularisation properties of curve shortening flow (英語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Jacob Bernstein 氏 (Johns Hopkins University) 14:00-15:00
Complexity of submanifolds and Colding-Minicozzi entropy (英語)
[ 講演概要 ]
Colding-Minicozzi entropy is a natural quantity associated to mean curvature flow which measures complexity of submanifolds of Euclidean space. We discuss some (nearly) optimal relationships between entropy and areas of (minimal) submanifolds of the sphere.
[ 参考URL ]Colding-Minicozzi entropy is a natural quantity associated to mean curvature flow which measures complexity of submanifolds of Euclidean space. We discuss some (nearly) optimal relationships between entropy and areas of (minimal) submanifolds of the sphere.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Peter Topping 氏 (University of Warwick) 15:20-16:20
Unusual regularisation properties of curve shortening flow (英語)
[ 講演概要 ]
Parabolic partial differential equations tend to improve regularity. Generally one can control strong norms (e.g. $C^k$) of a solution at time $t$ principally in terms of $t$ and a weak norm of the initial data. Curve shortening flow is a geometric flow for which the story is more weird and wonderful. I will explain some recent works with Arjun Sobnack from 2026 and before where this is manifest. I expect to be able to make the talk accessible to a relatively broad audience.
[ 参考URL ]Parabolic partial differential equations tend to improve regularity. Generally one can control strong norms (e.g. $C^k$) of a solution at time $t$ principally in terms of $t$ and a weak norm of the initial data. Curve shortening flow is a geometric flow for which the story is more weird and wonderful. I will explain some recent works with Arjun Sobnack from 2026 and before where this is manifest. I expect to be able to make the talk accessible to a relatively broad audience.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
2026年05月12日(火)
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。
Sanghoon Kwak 氏 (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
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。
Sanghoon Kwak 氏 (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
[ 講演概要 ]
Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
[ 参考URL ]Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
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) 126号室
Camila Sehnem 氏 (京大数理研)
Injective envelopes for partial $C^*$-dynamical systems
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Camila Sehnem 氏 (京大数理研)
Injective envelopes for partial $C^*$-dynamical systems
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 128号室
斎藤 秀司 氏 (東京大学)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
斎藤 秀司 氏 (東京大学)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
[ 講演概要 ]
We show that the cohomology of the structure sheaf of smooth and proper varieties over a complete non-archimedean field K with the ring R of integers of characteristic zero, can be refined to a birational cohomology theory of smooth (not necessarily proper) varieties over K with values in R-lattices, and the same holds for K of positive characteristic in dimensions at most 3.
As one application, we obtain that the automorphism group of the function field of a proper smooth variety X of dimension at most 3 over any field of positive characteristic acts quasi-unipotently on the cohomology of the canonical sheaf of X. The proof relies on some results from rigid analytic geometry on the cohomology of twisted integral rigid structure sheaves due to Bartenwerfer and van der Put.
This is a joint work with A. Merici and Kay Ruelling.
We show that the cohomology of the structure sheaf of smooth and proper varieties over a complete non-archimedean field K with the ring R of integers of characteristic zero, can be refined to a birational cohomology theory of smooth (not necessarily proper) varieties over K with values in R-lattices, and the same holds for K of positive characteristic in dimensions at most 3.
As one application, we obtain that the automorphism group of the function field of a proper smooth variety X of dimension at most 3 over any field of positive characteristic acts quasi-unipotently on the cohomology of the canonical sheaf of X. The proof relies on some results from rigid analytic geometry on the cohomology of twisted integral rigid structure sheaves due to Bartenwerfer and van der Put.
This is a joint work with A. Merici and Kay Ruelling.
2026年05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) 126号室
日仏数学拠点FJ-LMIセミナーとの共同開催
Luc Pirio 氏 (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
https://forms.gle/8ERsVDLuKHwbVzm57
日仏数学拠点FJ-LMIセミナーとの共同開催
Luc Pirio 氏 (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
[ 講演概要 ]
Polylogarithms are special functions with many remarkable properties, notably their functional identities. The most interesting identities of this kind involve several variables and are known only in low weights. In weights 1 and 2, there is essentially one fundamental identity in each case: Cauchy’s equation for the logarithm and Abel’s five-term identity for the dilogarithm.
After introducing the subject, I will present natural generalizations, up to weight 6, of Cauchy’s and Abel’s identities. The new identities are no longer merely polylogarithmic, but hyperlogarithmic, and they arise naturally from the geometry of del Pezzo surfaces.
In the second part of the talk, I will discuss a generalization of an approach due to Gelfand and MacPherson in the weight 2 case, leading to a more canonical viewpoint on these hyperlogarithmic functional equations.
The first part of the talk is based on joint work with Ana-Maria Castravet.
[ 参考URL ]Polylogarithms are special functions with many remarkable properties, notably their functional identities. The most interesting identities of this kind involve several variables and are known only in low weights. In weights 1 and 2, there is essentially one fundamental identity in each case: Cauchy’s equation for the logarithm and Abel’s five-term identity for the dilogarithm.
After introducing the subject, I will present natural generalizations, up to weight 6, of Cauchy’s and Abel’s identities. The new identities are no longer merely polylogarithmic, but hyperlogarithmic, and they arise naturally from the geometry of del Pezzo surfaces.
In the second part of the talk, I will discuss a generalization of an approach due to Gelfand and MacPherson in the weight 2 case, leading to a more canonical viewpoint on these hyperlogarithmic functional equations.
The first part of the talk is based on joint work with Ana-Maria Castravet.
https://forms.gle/8ERsVDLuKHwbVzm57
2026年05月07日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
熊谷 健太 氏 (東京大学)
Large-time behavior and grow-up rates of inhomogeneous semilinear heat equations, via the bifurcation structure of the stationary problem (Japanese)
熊谷 健太 氏 (東京大学)
Large-time behavior and grow-up rates of inhomogeneous semilinear heat equations, via the bifurcation structure of the stationary problem (Japanese)
[ 講演概要 ]
球領域上における指数型非線形項と非斉次項を伴う半線型熱方程式, およびその定常問題を考察する. 非斉次項を伴わない場合，定常問題の分岐構造は空間10次元を境に変化することが知られている. これに起因して熱方程式の解の漸近挙動も変化し，特に10次元以上では無限時間爆発（grow-up）が生じる.
本講演では，空間次元が10以上の場合に限り，非斉次項がある閾値を超えると，定常問題の分岐構造が従来とは異なる型へと変化することを示す. さらに，この変化に対応して，熱方程式における解の無限時間爆発現象が消失することを明らかにする. また，解の爆発レートを明示的に導出することにより，この消失現象に対する定量的理解を与える. 特に，吸収項が閾値に一致する臨界的状況では，爆発レートは対数型へと変化し，11次元においてはさらに log–log 型の第二項が現れる.
これら一連の現象の変化は，いずれも定常問題における特異解によって支配されている.
本研究は東北大学の岡優丞氏との共同研究に基づく.
球領域上における指数型非線形項と非斉次項を伴う半線型熱方程式, およびその定常問題を考察する. 非斉次項を伴わない場合，定常問題の分岐構造は空間10次元を境に変化することが知られている. これに起因して熱方程式の解の漸近挙動も変化し，特に10次元以上では無限時間爆発（grow-up）が生じる.
本講演では，空間次元が10以上の場合に限り，非斉次項がある閾値を超えると，定常問題の分岐構造が従来とは異なる型へと変化することを示す. さらに，この変化に対応して，熱方程式における解の無限時間爆発現象が消失することを明らかにする. また，解の爆発レートを明示的に導出することにより，この消失現象に対する定量的理解を与える. 特に，吸収項が閾値に一致する臨界的状況では，爆発レートは対数型へと変化し，11次元においてはさらに log–log 型の第二項が現れる.
これら一連の現象の変化は，いずれも定常問題における特異解によって支配されている.
本研究は東北大学の岡優丞氏との共同研究に基づく.
2026年04月28日(火)
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
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。
佐野 岳人 氏 (理化学研究所数理創造研究センター)
A y-ification of Khovanov homology (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。
佐野 岳人 氏 (理化学研究所数理創造研究センター)
A y-ification of Khovanov homology (JAPANESE)
[ 講演概要 ]
In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
[ 参考URL ]In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
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) 126号室
Roozbeh Hazrat 氏 (Western Sydney University)
An attempt to classify combinatorial algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Roozbeh Hazrat 氏 (Western Sydney University)
An attempt to classify combinatorial algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
[ 講演概要 ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
日仏数学拠点FJ-LMIセミナー
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
https://fj-lmi.cnrs.fr/seminars/
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
[ 講演概要 ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
[ 参考URL ]This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
https://fj-lmi.cnrs.fr/seminars/
2026年04月27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
大野 高志 氏 (京大数理研)
Manton’s Exotic Vortex Equations (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
大野 高志 氏 (京大数理研)
Manton’s Exotic Vortex Equations (Japanese)
[ 講演概要 ]
The vortex equation is a second-order PDE on a Riemann surface, defined in terms of a triple consisting of a holomorphic line bundle, a section, and a Hermitian metric. Its solutions are closely related to Hermitian–Einstein metrics and to geometric structures such as metrics with conical singularities. In https://arxiv.org/abs/1612.06710, Manton introduced several generalizations of the vortex equation, leading to five distinct types of vortex equations, which we refer to as Manton’s exotic vortex equations. In this talk, I will introduce these equations and discuss the existence of their solutions. I will also explain how these solutions can be obtained via dimensional reduction of a solution of Hermitian–Einstein equation.
[ 参考URL ]The vortex equation is a second-order PDE on a Riemann surface, defined in terms of a triple consisting of a holomorphic line bundle, a section, and a Hermitian metric. Its solutions are closely related to Hermitian–Einstein metrics and to geometric structures such as metrics with conical singularities. In https://arxiv.org/abs/1612.06710, Manton introduced several generalizations of the vortex equation, leading to five distinct types of vortex equations, which we refer to as Manton’s exotic vortex equations. In this talk, I will introduce these equations and discuss the existence of their solutions. I will also explain how these solutions can be obtained via dimensional reduction of a solution of Hermitian–Einstein equation.
https://forms.gle/8ERsVDLuKHwbVzm57
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。15:30~ 教室126でTea timeを行います。ぜひこちらにもご参加ください。
Clément Cosco 氏 (Université Paris Dauphine) 14:00-15:30
The maximum of 2d directed polymers. (Joint work with Shuta Nakajima and Ofer Zeitouni.)
Gaussian fluctuations for spin systems and point processes: near-optimal rates via quantitative Marcinkiewicz's theorem
講演の開始が早くなっています。15:30~ 教室126でTea timeを行います。ぜひこちらにもご参加ください。
Clément Cosco 氏 (Université Paris Dauphine) 14:00-15:30
The maximum of 2d directed polymers. (Joint work with Shuta Nakajima and Ofer Zeitouni.)
[ 講演概要 ]
Directed polymers can be described as a tilting of the simple random walk, where some local random noise can attract or repel the trajectory of the walk. In the subcritical regime of the two-dimensional model, the partition function is known to be asymptotically approximated by a Gaussian log-correlated field. In a work in collaboration with Shuta Nakajima and Ofer Zeitouni, we could refine this result by proving that the maximum of the partition function field converges to that of a branching Brownian motion, which is the source of the log-correlation. In this talk, I will introduce the model as well as the objects related to it and present our result.
Subhro Ghosh 氏 (National University of Singapore) 16:00-17:30Directed polymers can be described as a tilting of the simple random walk, where some local random noise can attract or repel the trajectory of the walk. In the subcritical regime of the two-dimensional model, the partition function is known to be asymptotically approximated by a Gaussian log-correlated field. In a work in collaboration with Shuta Nakajima and Ofer Zeitouni, we could refine this result by proving that the maximum of the partition function field converges to that of a branching Brownian motion, which is the source of the log-correlation. In this talk, I will introduce the model as well as the objects related to it and present our result.
Gaussian fluctuations for spin systems and point processes: near-optimal rates via quantitative Marcinkiewicz's theorem
[ 講演概要 ]
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates.
For spin models, we demonstrate Gaussian asymptotics for the magnetization (i.e., the total spin) for a wide class of ferromagnetic spin systems on Euclidean lattices, in particular those with continuous spins. Specific applications include, in particular, the celebrated XY and Heisenberg models under ferromagnetic conditions, and more broadly, systems with very general rotationally invariant spins in arbitrary dimensions. We address both the setting of free boundary conditions and a large class of ferromagnetic boundary conditions, and our CLTs are endowed with near-optimal rate of O(log |Λ| · |Λ|−1/2) in the Kolmogorov-Smirnov distance, where the system size is |Λ|. Our approach leverages the classical Lee-Yang theory for the zeros of partition functions, and subsumes as a special case results of Lebowitz, Ruelle, Pittel and Speer on CLTs in discrete statistical mechanical models for which we obtain sharper convergence rates.
In a different direction, we obtain CLTs for linear statistics of a wide class of point processes known as α-determinantal point processes which interpolate between negatively and positively associated random point fields (including the usual determinantal, permanental and Poisson point processes).
We contribute a unified approach to CLTs in such models (agnostic to the parameter α that modulates the nature of association). Our methods are able to address a broad class of kernels including in particular those with slow spatial decay (such as the Bessel kernel in general dimensions). Significantly, our approach is able to analyse such processes in dimensions ≥ 3, where structural alternatives such as connections to random matrix theory are not available, and obtain explicit rates for fast convergence in a wide spectrum of models.
A key ingredient of our approach is a broad, quantitative extension of the classical Marcinkiewicz Theorem that holds under the limited condition that the characteristic function is non-vanishing only on a bounded disk. This technique complements classical work of Ostrovskii, Linnik, Zimogljad and others, as well as recent work of Michelen and Sahasrabudhe, and Eremenko and Fryntov. In spite of the general applicability of the results, including to heavy-tailed setups, our rates for the CLT match the classic Berry- Esseen bounds for independent sums up to a log factor.
Based on joint work with T.C. Dinh, H.S. Tran and M.H. Tran. Under revision at Annals of Applied Probability.
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates.
For spin models, we demonstrate Gaussian asymptotics for the magnetization (i.e., the total spin) for a wide class of ferromagnetic spin systems on Euclidean lattices, in particular those with continuous spins. Specific applications include, in particular, the celebrated XY and Heisenberg models under ferromagnetic conditions, and more broadly, systems with very general rotationally invariant spins in arbitrary dimensions. We address both the setting of free boundary conditions and a large class of ferromagnetic boundary conditions, and our CLTs are endowed with near-optimal rate of O(log |Λ| · |Λ|−1/2) in the Kolmogorov-Smirnov distance, where the system size is |Λ|. Our approach leverages the classical Lee-Yang theory for the zeros of partition functions, and subsumes as a special case results of Lebowitz, Ruelle, Pittel and Speer on CLTs in discrete statistical mechanical models for which we obtain sharper convergence rates.
In a different direction, we obtain CLTs for linear statistics of a wide class of point processes known as α-determinantal point processes which interpolate between negatively and positively associated random point fields (including the usual determinantal, permanental and Poisson point processes).
We contribute a unified approach to CLTs in such models (agnostic to the parameter α that modulates the nature of association). Our methods are able to address a broad class of kernels including in particular those with slow spatial decay (such as the Bessel kernel in general dimensions). Significantly, our approach is able to analyse such processes in dimensions ≥ 3, where structural alternatives such as connections to random matrix theory are not available, and obtain explicit rates for fast convergence in a wide spectrum of models.
A key ingredient of our approach is a broad, quantitative extension of the classical Marcinkiewicz Theorem that holds under the limited condition that the characteristic function is non-vanishing only on a bounded disk. This technique complements classical work of Ostrovskii, Linnik, Zimogljad and others, as well as recent work of Michelen and Sahasrabudhe, and Eremenko and Fryntov. In spite of the general applicability of the results, including to heavy-tailed setups, our rates for the CLT match the classic Berry- Esseen bounds for independent sums up to a log factor.
Based on joint work with T.C. Dinh, H.S. Tran and M.H. Tran. Under revision at Annals of Applied Probability.
2026年04月24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(大講義室)号室
毛塚由佳子 氏 (東京大学大学院数理科学研究科)
Birch–Swinnerton-Dyer予想のdichotomy (日本語)
毛塚由佳子 氏 (東京大学大学院数理科学研究科)
Birch–Swinnerton-Dyer予想のdichotomy (日本語)
[ 講演概要 ]
本講演では, Birch–Swinnerton-Dyer予想を一つの「dichotomy」として捉える視点を紹介し, その枠組みのもとでBSD予想の内容をどのように捉え直せるかを考察する. この枠組みにおいては, 楕円曲線の解析的階数とMordell–Weil群の階数の一致や, Tate–Shafarevich群の有限性といった性質を個別に仮定しない. むしろ, これらの性質が互いに強く結びついており, 一方が成り立たないときには他方もまた特定の形で成り立たなくなる, という相関に着目する. 講演では, この考えに至る動機として, (1) 岩澤理論との類似, (2) 楕円曲線に関する既知の結果との関連, (3) 函数体の場合との対比, という三つの観点から説明する.
本講演の内容はDon Zagier氏(MPIM Bonn)との共同研究に基づく.
本講演では, Birch–Swinnerton-Dyer予想を一つの「dichotomy」として捉える視点を紹介し, その枠組みのもとでBSD予想の内容をどのように捉え直せるかを考察する. この枠組みにおいては, 楕円曲線の解析的階数とMordell–Weil群の階数の一致や, Tate–Shafarevich群の有限性といった性質を個別に仮定しない. むしろ, これらの性質が互いに強く結びついており, 一方が成り立たないときには他方もまた特定の形で成り立たなくなる, という相関に着目する. 講演では, この考えに至る動機として, (1) 岩澤理論との類似, (2) 楕円曲線に関する既知の結果との関連, (3) 函数体の場合との対比, という三つの観点から説明する.
本講演の内容はDon Zagier氏(MPIM Bonn)との共同研究に基づく.
2026年04月22日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
通常の曜日と異なります。
吉岡 秀和 氏 (北陸先端科学技術大学院大学)
水圏環境を深く理解するための非標準的な数理モデル (日本語)
通常の曜日と異なります。
吉岡 秀和 氏 (北陸先端科学技術大学院大学)
水圏環境を深く理解するための非標準的な数理モデル (日本語)
[ 講演概要 ]
水に関わる環境や生物を対象とした研究では，教科書的な数理モデルでは記述できないかもしれない現象が数多く存在する．この講演では，まず，講演者が対象としてきた理論・フィールド研究事例を概観する．つぎに，以下の２研究の成果を紹介する：① (Musielak-)Orlicz空間を用いた長記憶的な河川流況の不確実性のモデル化，② 係数が爆発する確率微分方程式に基づく回遊魚の遡上現象の理論構築．この講演を通して，私たちに身近な環境には数理的によくわからない対象がたくさん存在することを知って頂ければ幸いである．
水に関わる環境や生物を対象とした研究では，教科書的な数理モデルでは記述できないかもしれない現象が数多く存在する．この講演では，まず，講演者が対象としてきた理論・フィールド研究事例を概観する．つぎに，以下の２研究の成果を紹介する：① (Musielak-)Orlicz空間を用いた長記憶的な河川流況の不確実性のモデル化，② 係数が爆発する確率微分方程式に基づく回遊魚の遡上現象の理論構築．この講演を通して，私たちに身近な環境には数理的によくわからない対象がたくさん存在することを知って頂ければ幸いである．
2026年04月21日(火)
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。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (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。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
[ 講演概要 ]
Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
[ 参考URL ]Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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