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Seminar information archive
Seminar information archive ～06/23｜Today's seminar 06/24 | Future seminars 06/25～
2026/05/29
Algebraic Geometry Seminar
13:15-14:45 Room #117 (Graduate School of Math. Sci. Bldg.)
Yuki Koto (Academia Sinica)
Towards a quantization of the Kirwan map via Fourier transform
Yuki Koto (Academia Sinica)
Towards a quantization of the Kirwan map via Fourier transform
[ Abstract ]
Quantum cohomology ring is a deformation of the ordinary cohomology ring defined using counts of rational curves (genus zero Gromov-Witten invariants). In this talk, I will propose a Fourier transform for the quantum cohomology of smooth projective GIT quotients, viewed as a quantum analogue of the Kirwan map in ordinary cohomology. I will present several examples where this Fourier transform can be constructed and discuss some applications. This talk is based on ongoing work.
Quantum cohomology ring is a deformation of the ordinary cohomology ring defined using counts of rational curves (genus zero Gromov-Witten invariants). In this talk, I will propose a Fourier transform for the quantum cohomology of smooth projective GIT quotients, viewed as a quantum analogue of the Kirwan map in ordinary cohomology. I will present several examples where this Fourier transform can be constructed and discuss some applications. This talk is based on ongoing work.
2026/05/27
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
ONISHI Haruto (University of Tokyo)
Geometric realization of the local Langlands and local Jacquet-Langlands correspondences for GL(4) in a partially ramified case
ONISHI Haruto (University of Tokyo)
Geometric realization of the local Langlands and local Jacquet-Langlands correspondences for GL(4) in a partially ramified case
[ Abstract ]
The local Langlands correspondence and the local Jacquet-Langlands correspondence are realized using Lubin-Tate spaces. However, only limited cases of the correspondence between supercuspidal representations and L-parameters have been geometrically realized by algebraic varieties defined by explicit equations. There are several works in which such algebraic varieties are obtained as reductions of special affinoids in the Lubin-Tate space at infinite level. Even in the essentially tame case, where the correspondence is explicitly described by Bushnell–Henniart, such affinoids had previously been constructed only in the unramified and totally ramified cases. In this talk, I will explain a result constructing such affinoids in a partially ramified case, under certain special assumptions.
The local Langlands correspondence and the local Jacquet-Langlands correspondence are realized using Lubin-Tate spaces. However, only limited cases of the correspondence between supercuspidal representations and L-parameters have been geometrically realized by algebraic varieties defined by explicit equations. There are several works in which such algebraic varieties are obtained as reductions of special affinoids in the Lubin-Tate space at infinite level. Even in the essentially tame case, where the correspondence is explicitly described by Bushnell–Henniart, such affinoids had previously been constructed only in the unramified and totally ramified cases. In this talk, I will explain a result constructing such affinoids in a partially ramified case, under certain special assumptions.
Tokyo-Nagoya Algebra Seminar
16:00-17:30 Online
Yuki Mizuno (Utrecht University)
Bondal–Orlov’s reconstruction theorem in noncommutative projective geometry (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Yuki Mizuno (Utrecht University)
Bondal–Orlov’s reconstruction theorem in noncommutative projective geometry (Japanese)
[ Abstract ]
The (derived) category of coherent sheaves on a scheme encodes rich
information about the underlying geometry. P. Gabriel showed that for
noetherian schemes X and Y, if Coh X and Coh Y are equivalent as abelian
categories, then X and Y are isomorphic. Furthermore, A. Bondal and D.
Orlov proved that for smooth projective schemes X and Y with
(anti-)ample canonical bundles, if D^b(Coh X) and D^b(Coh Y) are
equivalent as triangulated categories, then X and Y are isomorphic. On
the other hand, J.-P. Serre showed that the category of coherent sheaves
on a projective scheme can be described as the quotient category of
finitely generated graded modules over the homogeneous coordinate ring
by the subcategory of torsion modules. Motivated by the results of
Gabriel and Serre, the quotient category of finitely generated graded
modules over a (not necessarily commutative) graded ring by the
subcategory of torsion modules is called a noncommutative projective scheme.
In this talk, I will present an analogue of Bondal–Orlov’s
reconstruction theorem for noncommutative projective geometry.
Furthermore, if time permits, I will discuss recent progress on the
study of the derived autoequivalence groups of noncommutative projective
schemes. Specifically, I will mention a structure result for the derived
autoequivalence groups of certain noncommutative projective planes.
ミーティング ID: 828 6882 8074
パスコード: 131261
[ Reference URL ]The (derived) category of coherent sheaves on a scheme encodes rich
information about the underlying geometry. P. Gabriel showed that for
noetherian schemes X and Y, if Coh X and Coh Y are equivalent as abelian
categories, then X and Y are isomorphic. Furthermore, A. Bondal and D.
Orlov proved that for smooth projective schemes X and Y with
(anti-)ample canonical bundles, if D^b(Coh X) and D^b(Coh Y) are
equivalent as triangulated categories, then X and Y are isomorphic. On
the other hand, J.-P. Serre showed that the category of coherent sheaves
on a projective scheme can be described as the quotient category of
finitely generated graded modules over the homogeneous coordinate ring
by the subcategory of torsion modules. Motivated by the results of
Gabriel and Serre, the quotient category of finitely generated graded
modules over a (not necessarily commutative) graded ring by the
subcategory of torsion modules is called a noncommutative projective scheme.
In this talk, I will present an analogue of Bondal–Orlov’s
reconstruction theorem for noncommutative projective geometry.
Furthermore, if time permits, I will discuss recent progress on the
study of the derived autoequivalence groups of noncommutative projective
schemes. Specifically, I will mention a structure result for the derived
autoequivalence groups of certain noncommutative projective planes.
ミーティング ID: 828 6882 8074
パスコード: 131261
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026/05/26
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Takumi Nishihara (RIMS, Kyoto Univ.)
Compact group actions and $G$-kernels on von Neumann algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar-e.htm
Takumi Nishihara (RIMS, Kyoto Univ.)
Compact group actions and $G$-kernels on von Neumann algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar-e.htm
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Qin(Tim) Sheng (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Qin(Tim) Sheng (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
[ Abstract ]
This presentation addresses two main issues. First, we shall discuss recent advancements in both exponential and non-exponential splitting methods, with particular emphasis on their stability, accuracy and global error estimates. Second, we shall introduce a new splitting configuration for solving nonlinear Hideo Kawarada equations with mixed derivative terms. This approach leads to intercardinal splitting finite-difference schemes that provide efficient and accurate numerical approximations of the underlying solutions.
We shall further demonstrate that the resulting implicit methods are numerically stable, convergent, and efficient, while preserving key physical properties such as the positivity and monotonicity. The dynamic orders of accuracy of the proposed algorithms will be illustrated using generalized Milne devices. Simulation examples of the solution procedure will be presented and investigated, and several open problems will also be outlined.
[ Reference URL ]This presentation addresses two main issues. First, we shall discuss recent advancements in both exponential and non-exponential splitting methods, with particular emphasis on their stability, accuracy and global error estimates. Second, we shall introduce a new splitting configuration for solving nonlinear Hideo Kawarada equations with mixed derivative terms. This approach leads to intercardinal splitting finite-difference schemes that provide efficient and accurate numerical approximations of the underlying solutions.
We shall further demonstrate that the resulting implicit methods are numerically stable, convergent, and efficient, while preserving key physical properties such as the positivity and monotonicity. The dynamic orders of accuracy of the proposed algorithms will be illustrated using generalized Milne devices. Simulation examples of the solution procedure will be presented and investigated, and several open problems will also be outlined.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
On the large-scale geometry of k-multicurve graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
On the large-scale geometry of k-multicurve graphs (JAPANESE)
[ Abstract ]
Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
[ Reference URL ]Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Víctor Pérez-Valdés (The University of Tokyo)
On sporadic symmetry breaking operators from $S^3$ to $S^2$
Víctor Pérez-Valdés (The University of Tokyo)
On sporadic symmetry breaking operators from $S^3$ to $S^2$
[ Abstract ]
In this talk we construct and classify all differential symmetry breaking operators between certain principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$.
In this case, we also prove a localness theorem, namely, all symmetry breaking operators between the principal series representations in concern are necessarily differential operators.
In addition, we show that all these symmetry breaking operators are sporadic, that is, they cannot be obtained by residue formulas of meromorphic families of symmetry breaking operators.
In this talk we construct and classify all differential symmetry breaking operators between certain principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$.
In this case, we also prove a localness theorem, namely, all symmetry breaking operators between the principal series representations in concern are necessarily differential operators.
In addition, we show that all these symmetry breaking operators are sporadic, that is, they cannot be obtained by residue formulas of meromorphic families of symmetry breaking operators.
2026/05/25
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Misa Ohashi (Nagoya Institute of Technology)
Geometric structures on Hirzebruch surfaces from the viewpoint of $S^{3} \times S^{3}$ (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
Misa Ohashi (Nagoya Institute of Technology)
Geometric structures on Hirzebruch surfaces from the viewpoint of $S^{3} \times S^{3}$ (Japanese)
[ Abstract ]
For a non-negative integer $m$, each Hirzebruch surface Wm is defined as a complex two-dimensional K\"ahler submanifold of the product of the complex projective line and the complex projective plane. It is known that Hirzebruch surfaces are all biregularly distinct. The purpose of this talk is to describe the complex structures on Hirzebruch surfaces from a differential geometric point of view. For each $m$, we show that the real two-dimensional torus bundle over a Hirzebruch surface is diffeomorphic to the product of two 3-spheres, $S^{3} \times S^{3}$. From this, we realize the complex structure as a global section (tensor field) on $S^{3} \times S^{3}$. We explain the construction of these diffeomorphisms and their properties. This talk is based on joint work with Hideya Hashimoto.
[ Reference URL ]For a non-negative integer $m$, each Hirzebruch surface Wm is defined as a complex two-dimensional K\"ahler submanifold of the product of the complex projective line and the complex projective plane. It is known that Hirzebruch surfaces are all biregularly distinct. The purpose of this talk is to describe the complex structures on Hirzebruch surfaces from a differential geometric point of view. For each $m$, we show that the real two-dimensional torus bundle over a Hirzebruch surface is diffeomorphic to the product of two 3-spheres, $S^{3} \times S^{3}$. From this, we realize the complex structure as a global section (tensor field) on $S^{3} \times S^{3}$. We explain the construction of these diffeomorphisms and their properties. This talk is based on joint work with Hideya Hashimoto.
https://forms.gle/8ERsVDLuKHwbVzm57
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Fumiya Okazaki (Science Tokyo)
非局所ディリクレ形式に関する調和写像の微分に付随する接束上のマルチンゲールについて
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Fumiya Okazaki (Science Tokyo)
非局所ディリクレ形式に関する調和写像の微分に付随する接束上のマルチンゲールについて
[ Abstract ]
リーマン多様体が高次のユークリッド空間に埋め込まれているという仮定の下では, その多様体に値を取る非局所ディリクレ形式に関する調和写像を変分原理に基づいて定義できる. 例えば分数冪ラプラシアンに関するディリクレ形式を考えた場合は, Da Lio-Rivière (2011)で導入された分数冪ラプラシアンに関する調和写像に対応する. 本研究では値域の多様体の幾何と調和写像の関係を見ることを目的として, 調和写像にある程度の正則性を課し, その微分を確率過程を通して考察する. まず接束上の不連続なセミマルチンゲールに対する伊藤解析を, 第2基本形式などを用いてジャンプを定めることで定式化し, それを用いて接束上の不連続なマルチンゲールを導入する. また写像の定義域の空間として別のリーマン多様体と, その上のあるKillingベクトル場による変換で不変なディリクレ形式を考え, そのKillingベクトル場による調和写像の微分から定まるジャンプ過程が接束上のマルチンゲールとなることを紹介する.
リーマン多様体が高次のユークリッド空間に埋め込まれているという仮定の下では, その多様体に値を取る非局所ディリクレ形式に関する調和写像を変分原理に基づいて定義できる. 例えば分数冪ラプラシアンに関するディリクレ形式を考えた場合は, Da Lio-Rivière (2011)で導入された分数冪ラプラシアンに関する調和写像に対応する. 本研究では値域の多様体の幾何と調和写像の関係を見ることを目的として, 調和写像にある程度の正則性を課し, その微分を確率過程を通して考察する. まず接束上の不連続なセミマルチンゲールに対する伊藤解析を, 第2基本形式などを用いてジャンプを定めることで定式化し, それを用いて接束上の不連続なマルチンゲールを導入する. また写像の定義域の空間として別のリーマン多様体と, その上のあるKillingベクトル場による変換で不変なディリクレ形式を考え, そのKillingベクトル場による調和写像の微分から定まるジャンプ過程が接束上のマルチンゲールとなることを紹介する.
2026/05/22
Algebraic Geometry Seminar
13:15-14:45 Room #117 (Graduate School of Math. Sci. Bldg.)
Justin Sawon (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
Justin Sawon (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
[ Abstract ]
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).
Colloquium
15:30-16:30 Room #NISSAY Lecture Hall (Graduate School of Math. Sci. Bldg.)
Evgeny Shinder (University of Sheffield / University of Tokyo)
Gromov's cancellation question in birational algebraic geometry
Evgeny Shinder (University of Sheffield / University of Tokyo)
Gromov's cancellation question in birational algebraic geometry
[ Abstract ]
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.
2026/05/21
FJ-LMI Seminar
14:15-15:00 Room # (Graduate School of Math. Sci. Bldg.)
Julien ROUYER (École Centrale de Pékin, Beihang university, Beijing)
How to cross an intersection ?
Julien ROUYER (École Centrale de Pékin, Beihang university, Beijing)
How to cross an intersection ?
[ Abstract ]
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.
2026/05/20
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Yukako Kezuka (University of Tokyo)
Special values of $L$-functions and the Birch and Swinnerton-Dyer conjecture for CM elliptic curves
https://www.ms.u-tokyo.ac.jp/~kezuka/
Yukako Kezuka (University of Tokyo)
Special values of $L$-functions and the Birch and Swinnerton-Dyer conjecture for CM elliptic curves
[ Abstract ]
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.
[ Reference 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/
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Heizo Sakamoto (University of Tokyo)
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)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Heizo Sakamoto (University of Tokyo)
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)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026/05/19
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroro Kamikawa (Kyoto Univ.)
The homotopy groups of the automorphism group of Kirchberg algebras with compact group actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Hiroro Kamikawa (Kyoto Univ.)
The homotopy groups of the automorphism group of Kirchberg algebras with compact group actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Nao Hamamuki (Faculty of Science, Hokkaido University)
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。 (日本語)
Nao Hamamuki (Faculty of Science, Hokkaido University)
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。 (日本語)
[ Abstract ]
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。
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (JAPANESE)
[ Abstract ]
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.
[ Reference 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 Groups and Representation Theory
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
Joint with Tuesday Seminar on Topology.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (Japanese)
[ Abstract ]
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.
2026/05/18
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yoshihiro Gyotoku (The University of Tokyo)
Independence preservation property through web geometry
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yoshihiro Gyotoku (The University of Tokyo)
Independence preservation property through web geometry
[ Abstract ]
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.
2026/05/14
Geometric Analysis Seminar
14:00-16:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Jacob Bernstein (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 (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 (Johns Hopkins University) 14:00-15:00
Complexity of submanifolds and Colding-Minicozzi entropy (英語)
[ Abstract ]
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.
[ Reference 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 (University of Warwick) 15:20-16:20
Unusual regularisation properties of curve shortening flow (英語)
[ Abstract ]
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.
[ Reference 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/
2026/05/12
Tuesday Seminar on Topology
16:00-17:00 Online
Pre-registration required. See our seminar webpage.
Sanghoon Kwak (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
Pre-registration required. See our seminar webpage.
Sanghoon Kwak (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
[ Abstract ]
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.
[ Reference 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
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Camila Sehnem (RIMS, Kyoto Univ.)
Injective envelopes for partial $C^*$-dynamical systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Camila Sehnem (RIMS, Kyoto Univ.)
Injective envelopes for partial $C^*$-dynamical systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Algebraic Geometry Seminar
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuji Saito (University of Tokyo)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
Shuji Saito (University of Tokyo)
Birational lattices in the cohomology of the structure sheaf over non-archimedean fields
[ Abstract ]
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.
2026/05/11
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI seminar
Luc Pirio (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
https://forms.gle/8ERsVDLuKHwbVzm57
Joint with FJ-LMI seminar
Luc Pirio (CNRS/Université Paris–Saclay)
From Cauchy and Abel to Hyperlogarithmic Functional Identities on Del Pezzo Surfaces (English)
[ Abstract ]
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.
[ Reference 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
2026/05/07
Applied Analysis
16:00-17:30 Room # 002 (Graduate School of Math. Sci. Bldg.)
Kenta Kumagai (the University of Tokyo)
Large-time behavior and grow-up rates of inhomogeneous semilinear heat equations, via the bifurcation structure of the stationary problem (Japanese)
Kenta Kumagai (the University of Tokyo)
Large-time behavior and grow-up rates of inhomogeneous semilinear heat equations, via the bifurcation structure of the stationary problem (Japanese)
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