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Future seminars
Seminar information archive ～04/22｜Today's seminar 04/23 | Future seminars 04/24～
2025/04/24
Seminar on Probability and Statistics
10:00-11:10 Room #126 (Graduate School of Math. Sci. Bldg.)
ハイブリッド開催
Stefano M. Iacus (Harvard University)
Inference for Ergodic Network Stochastic Differential Equations (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/cx7BR8oJSFGT42K4LY-fkQ
ハイブリッド開催
Stefano M. Iacus (Harvard University)
Inference for Ergodic Network Stochastic Differential Equations (English)
[ Abstract ]
We propose a novel framework for Network Stochastic Differential Equations (N-SDE), where each node in a network is governed by an SDE influenced by interactions with its neighbors. The evolution of each node is driven by the interplay of three key components: the node's intrinsic dynamics (momentum effect), feedback from neighboring nodes (network effect), and a "stochastic volatility” term modeled by Brownian motion.
Our objective is to estimate the parameters of the N-SDE system under two different schemas: high-frequency discrete-time observations and small noise continuous-time observations.
The motivation behind this model lies in its ability to analyze very high-dimensional time series by leveraging the inherent sparsity of the underlying network graph.
We consider two distinct scenarios: i) known network structure: the graph is fully specified, and we establish conditions under which the parameters can be identified, considering the quadratic growth of the parameter space with the number of edges. ii) unknown network structure: the graph must be inferred from the data. For this, we develop an iterative procedure using adaptive Lasso, tailored to a specific subclass of N-SDE models.
In this work, we assume the network graph is oriented, paving the way for novel applications of SDEs in causal inference, enabling the study of cause-effect relationships in dynamic systems.
Through simulation studies, we demonstrate the performance of our estimators across various graph topologies in high-dimensional settings. We also showcase the framework's applicability to real-world datasets, highlighting its potential for advancing the analysis of complex networked systems.
[ Reference URL ]We propose a novel framework for Network Stochastic Differential Equations (N-SDE), where each node in a network is governed by an SDE influenced by interactions with its neighbors. The evolution of each node is driven by the interplay of three key components: the node's intrinsic dynamics (momentum effect), feedback from neighboring nodes (network effect), and a "stochastic volatility” term modeled by Brownian motion.
Our objective is to estimate the parameters of the N-SDE system under two different schemas: high-frequency discrete-time observations and small noise continuous-time observations.
The motivation behind this model lies in its ability to analyze very high-dimensional time series by leveraging the inherent sparsity of the underlying network graph.
We consider two distinct scenarios: i) known network structure: the graph is fully specified, and we establish conditions under which the parameters can be identified, considering the quadratic growth of the parameter space with the number of edges. ii) unknown network structure: the graph must be inferred from the data. For this, we develop an iterative procedure using adaptive Lasso, tailored to a specific subclass of N-SDE models.
In this work, we assume the network graph is oriented, paving the way for novel applications of SDEs in causal inference, enabling the study of cause-effect relationships in dynamic systems.
Through simulation studies, we demonstrate the performance of our estimators across various graph topologies in high-dimensional settings. We also showcase the framework's applicability to real-world datasets, highlighting its potential for advancing the analysis of complex networked systems.
https://u-tokyo-ac-jp.zoom.us/meeting/register/cx7BR8oJSFGT42K4LY-fkQ
2025/04/25
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
Asuka Takatsu (Graduate School of Mathematical Sciences, The University of Tokyo)
Disintegrated optimal transport for metric fiber bundles (JAPANESE)
Asuka Takatsu (Graduate School of Mathematical Sciences, The University of Tokyo)
Disintegrated optimal transport for metric fiber bundles (JAPANESE)
[ Abstract ]
An optimal transport problem is a problem of finding a way to transport a matter with a minimal energy, formulated as a minimization problem on the space of probability measures. On a complete separable metric space, the problem induces a metric on the space of probability measures. In this talk, I will briefly review a recent application of this metric structure, and then explain the motivation to consider a disintegrated optimal transport for metric fiber bundles. This talk is based on joint work with Jun KITAGAWA (Michigan State University).
An optimal transport problem is a problem of finding a way to transport a matter with a minimal energy, formulated as a minimization problem on the space of probability measures. On a complete separable metric space, the problem induces a metric on the space of probability measures. In this talk, I will briefly review a recent application of this metric structure, and then explain the motivation to consider a disintegrated optimal transport for metric fiber bundles. This talk is based on joint work with Jun KITAGAWA (Michigan State University).
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (University of Tokyo)
Higher F-injective singularities
Tatsuro Kawakami (University of Tokyo)
Higher F-injective singularities
[ Abstract ]
The theory of F-singularities is a field that studies singularities in positive characteristic defined via the Frobenius morphism. A particularly well-known aspect of the theory is its correspondence, via reduction, with singularities that appear in birational geometry in characteristic zero.
In recent years, higher versions of such singularities in characteristic zero--such as higher Du Bois singularities--have been actively studied. In this talk, I will discuss how a higher analogue of F-singularity theory can be developed in positive characteristic by using the Cartier operator, which serves as a higher version of the Frobenius morphism.
In particular, I will introduce higher F-injective singularities, which correspond to higher Du Bois singularities, and focus on how the correspondence via reduction can be established.
This is joint work with Jakub Witaszek.
The theory of F-singularities is a field that studies singularities in positive characteristic defined via the Frobenius morphism. A particularly well-known aspect of the theory is its correspondence, via reduction, with singularities that appear in birational geometry in characteristic zero.
In recent years, higher versions of such singularities in characteristic zero--such as higher Du Bois singularities--have been actively studied. In this talk, I will discuss how a higher analogue of F-singularity theory can be developed in positive characteristic by using the Cartier operator, which serves as a higher version of the Frobenius morphism.
In particular, I will introduce higher F-injective singularities, which correspond to higher Du Bois singularities, and focus on how the correspondence via reduction can be established.
This is joint work with Jakub Witaszek.
Infinite Analysis Seminar Tokyo
17:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Naoto Okubo (Aoyama Gakuin University, College of Science and Engineering) 17:00-18:00
Cluster algebra and birational representations of affine Weyl groups (JAPANESE)
A generalization of the q-Garnier system with the aid of a birational representation of an affine Weyl group (JAPANESE)
Naoto Okubo (Aoyama Gakuin University, College of Science and Engineering) 17:00-18:00
Cluster algebra and birational representations of affine Weyl groups (JAPANESE)
[ Abstract ]
The cluster algebra (with the coefficients) was introduced by Fomin and Zelevinsky. It is a variety of commutative ring generated by the cluster variables. A set of all cluster variables is given by an operation called the mutation which acts on a triple of the quiver, the cluster variables and the coefficients. Then new cluster variables (resp. coefficients) are rational in original cluster variables and coefficients (resp. coefficients). In this talk, we discuss a systematic formulation of birational representations of affine Weyl groups with the aid of the mutation. These birational representations become sources of the q-Painleve equations as will be seen in the next talk. This talk is based on a collaboration with T. Suzuki (Kindai Univ.) and that with T. Masuda (Aoyama Gakuin Univ.) and T. Tsuda (Aoyama Gakuin Univ).
Takao Suzuki (Kindai University, Faculty of Science and Engineering) 18:00-19:00The cluster algebra (with the coefficients) was introduced by Fomin and Zelevinsky. It is a variety of commutative ring generated by the cluster variables. A set of all cluster variables is given by an operation called the mutation which acts on a triple of the quiver, the cluster variables and the coefficients. Then new cluster variables (resp. coefficients) are rational in original cluster variables and coefficients (resp. coefficients). In this talk, we discuss a systematic formulation of birational representations of affine Weyl groups with the aid of the mutation. These birational representations become sources of the q-Painleve equations as will be seen in the next talk. This talk is based on a collaboration with T. Suzuki (Kindai Univ.) and that with T. Masuda (Aoyama Gakuin Univ.) and T. Tsuda (Aoyama Gakuin Univ).
A generalization of the q-Garnier system with the aid of a birational representation of an affine Weyl group (JAPANESE)
[ Abstract ]
The q-Garnier system was introduced by Sakai as the connection preserving deformation of a linear q-difference equation. Afterward, Nagao and Yamada investigated the q-Garnier system by using the Pade method in detail and gave its variations (regarded as q-analogues of the Schlesinger transformations). In this talk, we formulate the q-Garnier system and its variations systematically by using the birational representation given in the previous talk. If time permits, we discuss a Lax form and a particular solution in terms of the basic hypergeometric series. This talk is based on a collaboration with N. Okubo (Aoyama Gakuin Univ).
The q-Garnier system was introduced by Sakai as the connection preserving deformation of a linear q-difference equation. Afterward, Nagao and Yamada investigated the q-Garnier system by using the Pade method in detail and gave its variations (regarded as q-analogues of the Schlesinger transformations). In this talk, we formulate the q-Garnier system and its variations systematically by using the birational representation given in the previous talk. If time permits, we discuss a Lax form and a particular solution in terms of the basic hypergeometric series. This talk is based on a collaboration with N. Okubo (Aoyama Gakuin Univ).
2025/04/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Katsutoshi Yamanoi (Osaka Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
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.
Mitsuo Higaki (Kobe University)
ランダム粗面領域における粘性流体に対するナヴィエ壁法則
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Mitsuo Higaki (Kobe University)
ランダム粗面領域における粘性流体に対するナヴィエ壁法則
[ Abstract ]
粗面を伴う領域における粘性流体運動の有効近似を得る経験的な手法として、工学分野では壁法則が知られてきた [cf. Nikuradse 1933]。筒状粗面領域における定常層流に対しては、壁法則により、ナヴィエ滑り境界条件に従う速度場が得られる (ナヴィエ壁法則)。本講演では、これが実際に有効近似を与えることを数学的に厳密に証明する。より正確には、粗面領域全体の標本空間を考えた際に、ある種のエルゴード性の仮定の下で、最適な近似率が得られることを報告する。証明の鍵は、粗面付近の流体運動を記述する境界層の確定的/確率的評価である。ここで我々は楕円型方程式に対する定量的確率均質化のアイディアを用いる [cf. Armstrong-Smart, Armstrong-Kuusi-Mourrat, Gloria-Neukamm-Otto, Shen]。ただし、係数行列ではなく粗面領域の標本空間を考えていることに注意されたい。なお、上述のエルゴード性としては、確率変数に対する関数不等式 (対数ソボレフ不等式やスペクトルギャップ不等式など) の成立を採用する。本講演の内容は Jinping Zhuge 氏 (Morningside Center of Mathematics, China)、Yulong Lu 氏 (University of Minnesota, USA) との共同研究に基づく。
粗面を伴う領域における粘性流体運動の有効近似を得る経験的な手法として、工学分野では壁法則が知られてきた [cf. Nikuradse 1933]。筒状粗面領域における定常層流に対しては、壁法則により、ナヴィエ滑り境界条件に従う速度場が得られる (ナヴィエ壁法則)。本講演では、これが実際に有効近似を与えることを数学的に厳密に証明する。より正確には、粗面領域全体の標本空間を考えた際に、ある種のエルゴード性の仮定の下で、最適な近似率が得られることを報告する。証明の鍵は、粗面付近の流体運動を記述する境界層の確定的/確率的評価である。ここで我々は楕円型方程式に対する定量的確率均質化のアイディアを用いる [cf. Armstrong-Smart, Armstrong-Kuusi-Mourrat, Gloria-Neukamm-Otto, Shen]。ただし、係数行列ではなく粗面領域の標本空間を考えていることに注意されたい。なお、上述のエルゴード性としては、確率変数に対する関数不等式 (対数ソボレフ不等式やスペクトルギャップ不等式など) の成立を採用する。本講演の内容は Jinping Zhuge 氏 (Morningside Center of Mathematics, China)、Yulong Lu 氏 (University of Minnesota, USA) との共同研究に基づく。
Geometric Analysis Seminar
15:00-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Junrong Yan (Northeathtern University)
Heat Kernel Expansion and Weyl's Law for Schrödinger-Type Operators on Noncompact Manifolds (英語)
Junrong Yan (Northeathtern University)
Heat Kernel Expansion and Weyl's Law for Schrödinger-Type Operators on Noncompact Manifolds (英語)
[ Abstract ]
Motivated by the study of Landau-Ginzburg models in string theory from the viewpoint of index theorem, we explore the heat kernel expansion for Schrödinger-type operators on noncompact manifolds. This expansion leads to a local index theorem for such operators.
Unlike in the compact case, the heat kernel in the noncompact setting exhibits new behaviors. Obtaining its precise expansion and deriving a remainder estimate require careful analysis. We will first present our approach to establishing this expansion.
As a key application, we study Weyl’s law for such operators. In the compact case, such results follow from Karamata’s Tauberian theorem, but the standard Tauberian argument does not apply in the noncompact setting. To address this, we develop a new version of Karamata’s theorem.
This is joint work with Xianzhe Dai.
Motivated by the study of Landau-Ginzburg models in string theory from the viewpoint of index theorem, we explore the heat kernel expansion for Schrödinger-type operators on noncompact manifolds. This expansion leads to a local index theorem for such operators.
Unlike in the compact case, the heat kernel in the noncompact setting exhibits new behaviors. Obtaining its precise expansion and deriving a remainder estimate require careful analysis. We will first present our approach to establishing this expansion.
As a key application, we study Weyl’s law for such operators. In the compact case, such results follow from Karamata’s Tauberian theorem, but the standard Tauberian argument does not apply in the noncompact setting. To address this, we develop a new version of Karamata’s theorem.
This is joint work with Xianzhe Dai.
2025/05/01
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Sho KATAYAMA (The University of Tokyo)
Fundamental solution to the heat equation with a dynamical boundary condition (Japanese)
Sho KATAYAMA (The University of Tokyo)
Fundamental solution to the heat equation with a dynamical boundary condition (Japanese)
[ Abstract ]
We give an explicit representation of the fundamental solution to the heat equation on a half-space of R^N with the homogeneous dynamical boundary condition and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of R^N with the homogeneous dynamical boundary condition. This talk is based on a joint work with Kazuhiro Ishige (Univ. of Tokyo) and Tatsuki Kawakami (Ryukoku Univ.)
We give an explicit representation of the fundamental solution to the heat equation on a half-space of R^N with the homogeneous dynamical boundary condition and obtain upper and lower estimates of the fundamental solution. These enable us to obtain sharp decay estimates of solutions to the heat equation with the homogeneous dynamical boundary condition. Furthermore, as an application of our decay estimates, we identify the so-called Fujita exponent for a semilinear heat equation on the half-space of R^N with the homogeneous dynamical boundary condition. This talk is based on a joint work with Kazuhiro Ishige (Univ. of Tokyo) and Tatsuki Kawakami (Ryukoku Univ.)
2025/05/02
Discrete mathematical modelling seminar
16:45-17:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (BIMSA, Beijing)
On a positivity property of a solution of discrete Painlevé equations (English)
Anton Dzhamay (BIMSA, Beijing)
On a positivity property of a solution of discrete Painlevé equations (English)
[ Abstract ]
We consider a particular example of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich. Observing that this equation corresponds to a very special choice of parameters (root variables) in the Space of Initial Conditions for the differential Painlevé V equation, we show that some explicit special function solutions, written in terms of modified Bessel functions, for d-PV, yield the unique positive solution for some initial value problem for the discrete Painlevé equation needed for quantum minimal surfaces. This is a joint work with Peter Clarkson, Andy Hone, and Ben Mitchell.
We consider a particular example of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich. Observing that this equation corresponds to a very special choice of parameters (root variables) in the Space of Initial Conditions for the differential Painlevé V equation, we show that some explicit special function solutions, written in terms of modified Bessel functions, for d-PV, yield the unique positive solution for some initial value problem for the discrete Painlevé equation needed for quantum minimal surfaces. This is a joint work with Peter Clarkson, Andy Hone, and Ben Mitchell.
Seminar on Probability and Statistics
13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Shunsuke Imai (Kyoto University)
General Bayesian Semiparametric Inference with Hyvärinen Score (Japanese)
https://us06web.zoom.us/meeting/register/3XxtsHwaQVSN7BuINu6E8g
Shunsuke Imai (Kyoto University)
General Bayesian Semiparametric Inference with Hyvärinen Score (Japanese)
[ Abstract ]
This paper proposes a novel framework for semiparametric Bayesian inference on finite-dimensional parameters under existence of nuisance functions. Based on a pseudo-model defined by (profiled) loss functions for the finite dimensional parameters and the Hyv\"arinen score, we propose a general posterior distribution, named semiparametric Hyv\"arinen (SH) posterior. The SH posterior enables us to make inference on the parameters of interest with taking account of uncertainty in the estimation/selection of tuning parameters in estimating the unknown nuisance functions. We establish its theoretical justification of the SH posterior under large samples, and provide posterior computation algorithm. As concrete examples, we provide the posterior inference of partial linear models and single index models, and demonstrate the performance through simulation.
[ Reference URL ]This paper proposes a novel framework for semiparametric Bayesian inference on finite-dimensional parameters under existence of nuisance functions. Based on a pseudo-model defined by (profiled) loss functions for the finite dimensional parameters and the Hyv\"arinen score, we propose a general posterior distribution, named semiparametric Hyv\"arinen (SH) posterior. The SH posterior enables us to make inference on the parameters of interest with taking account of uncertainty in the estimation/selection of tuning parameters in estimating the unknown nuisance functions. We establish its theoretical justification of the SH posterior under large samples, and provide posterior computation algorithm. As concrete examples, we provide the posterior inference of partial linear models and single index models, and demonstrate the performance through simulation.
https://us06web.zoom.us/meeting/register/3XxtsHwaQVSN7BuINu6E8g
2025/05/09
Geometric Analysis Seminar
10:00-11:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Paolo Salani (Università degli Studi di Firenze) -
Preservation of concavity properties by the Dirichlet heat flow and applications (英語)
The Gaussian correlation inequality for centered convex sets (英語)
Paolo Salani (Università degli Studi di Firenze) -
Preservation of concavity properties by the Dirichlet heat flow and applications (英語)
[ Abstract ]
This talk is based on joint works with K. Ishige, Q. Liu and A. Takatsu.
It is well known that heat flow preserves the log-concavity of the initial datum, in the following sense: if $\phi\geq0$ is log-concave (i.e., $\log\phi$ is concave), and u is the (bounded) solution of $u_t=\Delta u$ in $R^n\times(0,+\infty)$ with $u(x,0)=\phi$, then $u(\cdot,t)$ is log-concave for every $t\geq 0$.
Together with Ishige and Takatsu, we investigated on the optimality of this property and considered the more general concept of F-.concavity, discovering that, in a suitable sense, log-concavity is the weakest concavity property preserved by the heat flow, while the strongest is what we call "hot concavity".
For our investigation we use only pdes techniques, while the original proof of the preservation of log-concavity by the heat flow, due to Brascamp and Lieb, is easily obtained as an application of a functional-geometric inequality known as Prekòpa-Leindler inequality. It is interesting to notice that is is also possible to do the way back, retrieving PL inequality (and the whole family opf Borell-Brascamp-Lieb inequalities) thanks to the concavity preservation properties of parabolic equations, so establishing a perfect equivalence between these two apparently separated worlds. This investigation was done in collaboration with Ishige and Liu.
Hiroshi Tsuji (Saitama University) 11:30-12:30This talk is based on joint works with K. Ishige, Q. Liu and A. Takatsu.
It is well known that heat flow preserves the log-concavity of the initial datum, in the following sense: if $\phi\geq0$ is log-concave (i.e., $\log\phi$ is concave), and u is the (bounded) solution of $u_t=\Delta u$ in $R^n\times(0,+\infty)$ with $u(x,0)=\phi$, then $u(\cdot,t)$ is log-concave for every $t\geq 0$.
Together with Ishige and Takatsu, we investigated on the optimality of this property and considered the more general concept of F-.concavity, discovering that, in a suitable sense, log-concavity is the weakest concavity property preserved by the heat flow, while the strongest is what we call "hot concavity".
For our investigation we use only pdes techniques, while the original proof of the preservation of log-concavity by the heat flow, due to Brascamp and Lieb, is easily obtained as an application of a functional-geometric inequality known as Prekòpa-Leindler inequality. It is interesting to notice that is is also possible to do the way back, retrieving PL inequality (and the whole family opf Borell-Brascamp-Lieb inequalities) thanks to the concavity preservation properties of parabolic equations, so establishing a perfect equivalence between these two apparently separated worlds. This investigation was done in collaboration with Ishige and Liu.
The Gaussian correlation inequality for centered convex sets (英語)
[ Abstract ]
This talk is based on a joint work with Shohei Nakamura. The Gaussian correlation inequality, a result known in probability theory and convex geometry, gives a comparison between the Gaussian measure of the intersection of two symmetric convex sets and the product of the Gaussian measures of each set. This inequality was proven by Pitt in the case $n=2$ and later extended to all dimensions by Royen. Recently E. Milman gave another simple proof by the observation that the Gaussian correlation inequality may be regarded as an example of the inverse Brascamp—Lieb inequality.
In this talk, building on Milman's observation, we prove that the Gaussian correlation inequality holds true for centered convex sets. Furthermore we give an extension of the Gaussian correlation inequality formulated by Szarek—Werner.
This talk is based on a joint work with Shohei Nakamura. The Gaussian correlation inequality, a result known in probability theory and convex geometry, gives a comparison between the Gaussian measure of the intersection of two symmetric convex sets and the product of the Gaussian measures of each set. This inequality was proven by Pitt in the case $n=2$ and later extended to all dimensions by Royen. Recently E. Milman gave another simple proof by the observation that the Gaussian correlation inequality may be regarded as an example of the inverse Brascamp—Lieb inequality.
In this talk, building on Milman's observation, we prove that the Gaussian correlation inequality holds true for centered convex sets. Furthermore we give an extension of the Gaussian correlation inequality formulated by Szarek—Werner.
2025/05/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuho Kanda (Univ. of Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shuho Kanda (Univ. of Tokyo)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/13
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Ikhan Choi (the University of Tokyo)
Haagerup's problems on normal weights
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ikhan Choi (the University of Tokyo)
Haagerup's problems on normal weights
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie Groups and Representation Theory
15:45-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)
Mamoru UEDA (The University of Tokyo)
Affine Yangians and non-rectangular W-algebras of type A (Japanese)
Mamoru UEDA (The University of Tokyo)
Affine Yangians and non-rectangular W-algebras of type A (Japanese)
[ Abstract ]
The Yangian is a quantum group introduced by Drinfeld and is a deformation of the current Lie algebra in finite setting. Yangians are actively used for studies of one kind of vertex algebra called a W-algebra. One of the representative results is that Brundan and Kleshchev wrote down a finite W-algebra of type A as a quotient algebra of the shifted Yangian. The shifted Yangian contains a finite Yangian of type A as a subalgebra. De Sole, Kac, and Valeri constructed a homomorphism from this subalgebra to the finite W-algebra of type A by using the Lax operator.
In this talk, I will explain how to construct a homomorphism from the affine Yangian of type A to a non-rectangular W-algebra of type A, which can be regarded as an affine version of the result of De Sole-Kac-Valeri. This homomorphism is expected to lead to a generalization of the AGT conjecture.
The Yangian is a quantum group introduced by Drinfeld and is a deformation of the current Lie algebra in finite setting. Yangians are actively used for studies of one kind of vertex algebra called a W-algebra. One of the representative results is that Brundan and Kleshchev wrote down a finite W-algebra of type A as a quotient algebra of the shifted Yangian. The shifted Yangian contains a finite Yangian of type A as a subalgebra. De Sole, Kac, and Valeri constructed a homomorphism from this subalgebra to the finite W-algebra of type A by using the Lax operator.
In this talk, I will explain how to construct a homomorphism from the affine Yangian of type A to a non-rectangular W-algebra of type A, which can be regarded as an affine version of the result of De Sole-Kac-Valeri. This homomorphism is expected to lead to a generalization of the AGT conjecture.
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yuichi Ike (The University of Tokyo)
Interleaving distance for sheaves and its application to symplectic geometry (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yuichi Ike (The University of Tokyo)
Interleaving distance for sheaves and its application to symplectic geometry (JAPANESE)
[ Abstract ]
The Interleaving distance was first introduced in the context of the stability of persistent homology and is now used in various fields. It was adapted to sheaves by the pioneering work of Curry, and later in the derived setting by Kashiwara and Schapira. In this talk, I will explain that the interleaving distance for sheaves is related to the energy of Hamiltonian actions on cotangent bundles. Moreover, I will show that the derived interleaving distance is complete, which enables us to treat non-smooth objects in symplectic geometry using sheaf-theoretic methods. This is based on joint work with Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, and Claude Viterbo.
[ Reference URL ]The Interleaving distance was first introduced in the context of the stability of persistent homology and is now used in various fields. It was adapted to sheaves by the pioneering work of Curry, and later in the derived setting by Kashiwara and Schapira. In this talk, I will explain that the interleaving distance for sheaves is related to the energy of Hamiltonian actions on cotangent bundles. Moreover, I will show that the derived interleaving distance is complete, which enables us to treat non-smooth objects in symplectic geometry using sheaf-theoretic methods. This is based on joint work with Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, and Claude Viterbo.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/05/15
Geometric Analysis Seminar
15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Kobe Marshall-Stevens (Johns Hopkins University)
Gradient flow of phase transitions with fixed contact angle (英語)
Kobe Marshall-Stevens (Johns Hopkins University)
Gradient flow of phase transitions with fixed contact angle (英語)
[ Abstract ]
The Allen-Cahn equation is closely related to the area functional on hypersurfaces and provides a means to investigate both its critical points (minimal hypersurfaces) and gradient flow (mean curvature flow). I will discuss various properties of the gradient flow of the Allen-Cahn equation with a fixed boundary contact angle condition, which is used to gain insight into an appropriate formulation for mean curvature flow with fixed boundary contact angle. This is based on joint work with M. Takada, Y. Tonegawa, and M. Workman.
The Allen-Cahn equation is closely related to the area functional on hypersurfaces and provides a means to investigate both its critical points (minimal hypersurfaces) and gradient flow (mean curvature flow). I will discuss various properties of the gradient flow of the Allen-Cahn equation with a fixed boundary contact angle condition, which is used to gain insight into an appropriate formulation for mean curvature flow with fixed boundary contact angle. This is based on joint work with M. Takada, Y. Tonegawa, and M. Workman.
2025/05/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Yasufuku (Waseda Univ.)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Yasufuku (Waseda Univ.)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/20
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Futaba Sato (the University of Tokyo)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Futaba Sato (the University of Tokyo)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/05/26
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Tohoku Univ.)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Shin-ichi Matsumura (Tohoku Univ.)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/06/03
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Takehiko Mori (Chiba University)
Application of Operator Theory for the Collatz Conjecture
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Takehiko Mori (Chiba University)
Application of Operator Theory for the Collatz Conjecture
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/06/05
Geometric Analysis Seminar
14:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Chao Li (New York University) -
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
TBA (英語)
Chao Li (New York University) -
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
[ Abstract ]
Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
Ruobing Zhang (University of Wisconsin–Madison) 15:30-16:30Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
TBA (英語)
[ Abstract ]
TBA
TBA
2025/06/10
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Nobuyuki Oshima (Faculty of Engineering, Hokkaido Univsersity)
Immersed-boundary Navier-Stokes equation and its application to image data (Japanese)
Nobuyuki Oshima (Faculty of Engineering, Hokkaido Univsersity)
Immersed-boundary Navier-Stokes equation and its application to image data (Japanese)
2025/06/17
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Hikaru Awazu (University of Tokyo)
Amenability of group actions on compact spaces and the associated Banach algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Hikaru Awazu (University of Tokyo)
Amenability of group actions on compact spaces and the associated Banach algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/06/24
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
George Elliott (Univ. Toronto)
TBA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
George Elliott (Univ. Toronto)
TBA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/07/01
Operator Algebra Seminars
16:45-18:15 Room #117 (Graduate School of Math. Sci. Bldg.)
Mao Hoshino (Univ. Tokyo)
A tensor categorical aspect of quantum group actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Mao Hoshino (Univ. Tokyo)
A tensor categorical aspect of quantum group actions
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
