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Seminar information archive
Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～
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
Lie Groups and Representation Theory
15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
Masatoshi KITAGAWA (Institute of Mathematics for Industry, Kyushu University)
On the restriction of good filtration in the branching problem of reductive Lie groups (Japanese)
[ Abstract ]
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
In arXiv:2405.10382, a Cartan subalgebra related to the branching problem of reductive Lie groups was defined. It is considered to control the size and shape of the continuous spectrum in irreducible decompositions, and is defined using the support of the action of the center of the universal enveloping algebra. Except in special cases, direct computations from the definition of this Cartan subalgebra are difficult.
In this talk, I will present results on restrictions of good filtrations and show a relation between the associated varieties of representations and the Cartan subalgebra.
I will also discuss applications to the necessary condition for discrete decomposability and related conjectures by T. Kobayashi.
2025/05/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Yasufuku (Waseda Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2025/05/16
Seminar on Probability and Statistics
13:30-14:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Maud Delattre (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
Maud Delattre (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
[ Abstract ]
Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
[ Reference URL ]Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
[ Abstract ]
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
2025/05/15
Geometric Analysis Seminar
15:30-16:30 Room #123 (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.
2025/05/14
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Eamon Quinlan (University of Utah)
Introduction to the Bernstein-Sato polynomial in positive characteristic
https://eamonqg.github.io/
Eamon Quinlan (University of Utah)
Introduction to the Bernstein-Sato polynomial in positive characteristic
[ Abstract ]
The Bernstein-Sato polynomial of a holomorphic function is an invariant that originated in complex analysis, and with now strong applications to birational geometry and singularity theory over the complex numbers. For example, it detects the log-canonical threshold as well as the eigenvalues of the monodromy action on nearby cycles. In this talk I will define a characteristic-p analogue of this invariant, I will survey some of its basic properties, and I will illustrate how its behavior reflects arithmetic phenomena. This will serve as an introduction to the talk by Hiroki Kato.
[ Reference URL ]The Bernstein-Sato polynomial of a holomorphic function is an invariant that originated in complex analysis, and with now strong applications to birational geometry and singularity theory over the complex numbers. For example, it detects the log-canonical threshold as well as the eigenvalues of the monodromy action on nearby cycles. In this talk I will define a characteristic-p analogue of this invariant, I will survey some of its basic properties, and I will illustrate how its behavior reflects arithmetic phenomena. This will serve as an introduction to the talk by Hiroki Kato.
https://eamonqg.github.io/
Number Theory Seminar
18:10-19:10 Room #117 (Graduate School of Math. Sci. Bldg.)
Hiroki Kato (IHES)
Bernstein--Sato theory in positive characteristic and unit root nearby cycles.
Hiroki Kato (IHES)
Bernstein--Sato theory in positive characteristic and unit root nearby cycles.
[ Abstract ]
I will talk about how to formulate (and outline an idea of a proof of) a positive characteristic analogue of the theorem of Kashiwara and Malgrange about the relationship, in characteristic zero, between the Bernstein-Sato polynomial and the eigenvalues of the monodromy action on nearby cycles. It will/is expected to give a cohomological explanation for some of the arithmetic phenomena that will be presented in the talk by Eamon Quinlan. This is a joint work in progress with him and Daichi Takeuchi.
I will talk about how to formulate (and outline an idea of a proof of) a positive characteristic analogue of the theorem of Kashiwara and Malgrange about the relationship, in characteristic zero, between the Bernstein-Sato polynomial and the eigenvalues of the monodromy action on nearby cycles. It will/is expected to give a cohomological explanation for some of the arithmetic phenomena that will be presented in the talk by Eamon Quinlan. This is a joint work in progress with him and Daichi Takeuchi.
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
Seminar on Probability and Statistics
13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Takeshi Emura (School of Informatics and Data Science, Hiroshima University)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
Takeshi Emura (School of Informatics and Data Science, Hiroshima University)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
[ Abstract ]
Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
[ Reference URL ]Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
FJ-LMI Seminar
14:30-15:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Matthew CELLOT (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
https://fj-lmi.cnrs.fr/seminars/
Matthew CELLOT (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
[ Abstract ]
Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
[ Reference URL ]Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
https://fj-lmi.cnrs.fr/seminars/
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
Tokyo Probability Seminar
14:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Hirofumi Osada (Chubu University) 14:00-15:30
クーロン点過程の対数微分に対する明示表現とその応用 (Explicit formula to logarithmic derivatives of Coulomb random point fields and their applications)
GUE fluctuations near the time axis of the one-sided ballistic deposition model
Hirofumi Osada (Chubu University) 14:00-15:30
クーロン点過程の対数微分に対する明示表現とその応用 (Explicit formula to logarithmic derivatives of Coulomb random point fields and their applications)
[ Abstract ]
Coulomb点過程とは、d次元Coulomb ポテンシャルで相互作用するd次元空間の無限粒子系である。対数微分とは、個々の粒子が、相互作用によって、他の（無限個の）粒子から受ける力を表すベクトル場である。各粒子は対数微分に従って運動する。一般に、対数微分が存在すれば、確率力学が存在することが共著者によって証明されている。本講演は、クーロン点過程の対数微分の存在を証明し、更に、明示表現を構築する。明示表現の応用として、対応する無限次元確率微分方程式のパスワイズ一意の強解の存在を証明する。これを、2次元以上のすべての次元の、すべての正の逆温度に対して行う。
Gibbs測度の理論は、1970年ごろ、DLR方程式を基に確立した。しかし、Ruelle族という、遠方での可積分性を持つ干渉ポテンシャルに適用範囲が限られていた。自然界の最も基本的なポテンシャルであるCoulombポテンシャルが、Gibbs測度の理論からずっと長い間、除外されてきた。本明示表現の応用として、Coulombポテンシャルを含む、強い遠距離相互作用を持つ点過程の広いクラスに対して有効な、干渉ポテンシャルと点過程を結び付ける方程式（定式化）を与える。これは、DLR方程式の役割を、CoulombやRieszポテンシャルという、遠距離強相互作用に対して果たすものである。
Alejandro Ramirez (NYU Shanghai) 16:15-17:45Coulomb点過程とは、d次元Coulomb ポテンシャルで相互作用するd次元空間の無限粒子系である。対数微分とは、個々の粒子が、相互作用によって、他の（無限個の）粒子から受ける力を表すベクトル場である。各粒子は対数微分に従って運動する。一般に、対数微分が存在すれば、確率力学が存在することが共著者によって証明されている。本講演は、クーロン点過程の対数微分の存在を証明し、更に、明示表現を構築する。明示表現の応用として、対応する無限次元確率微分方程式のパスワイズ一意の強解の存在を証明する。これを、2次元以上のすべての次元の、すべての正の逆温度に対して行う。
Gibbs測度の理論は、1970年ごろ、DLR方程式を基に確立した。しかし、Ruelle族という、遠方での可積分性を持つ干渉ポテンシャルに適用範囲が限られていた。自然界の最も基本的なポテンシャルであるCoulombポテンシャルが、Gibbs測度の理論からずっと長い間、除外されてきた。本明示表現の応用として、Coulombポテンシャルを含む、強い遠距離相互作用を持つ点過程の広いクラスに対して有効な、干渉ポテンシャルと点過程を結び付ける方程式（定式化）を与える。これは、DLR方程式の役割を、CoulombやRieszポテンシャルという、遠距離強相互作用に対して果たすものである。
GUE fluctuations near the time axis of the one-sided ballistic deposition model
[ Abstract ]
Ballistic deposition is a model of interface growth introduced by Vold in 1959, which has remained largely mathematically intractable. It is believed that it is in the KPZ universality class. We introduce the one-sided ballistic deposition model, in which vertically falling blocks can only stick to the top or the upper right corner of growing columns, but not to the upper left corners of growing columns as in ballistic deposition. We establish that strong KPZ universality holds near the time axis, proving that the fluctuations of the height function there are given by the Tracy-Widom GUE distribution. The proof is based on a graphical construction of the process in terms of a last passage percolation model. This is a joint work with Pablo Groisman, Santiago Saglietti and Sebastián Zaninovich.
Ballistic deposition is a model of interface growth introduced by Vold in 1959, which has remained largely mathematically intractable. It is believed that it is in the KPZ universality class. We introduce the one-sided ballistic deposition model, in which vertically falling blocks can only stick to the top or the upper right corner of growing columns, but not to the upper left corners of growing columns as in ballistic deposition. We establish that strong KPZ universality holds near the time axis, proving that the fluctuations of the height function there are given by the Tracy-Widom GUE distribution. The proof is based on a graphical construction of the process in terms of a last passage percolation model. This is a joint work with Pablo Groisman, Santiago Saglietti and Sebastián Zaninovich.
Tokyo-Nagoya Algebra Seminar
15:30-17:00 Online
Yuya Otake (Nagoya University)
Auslander近似理論を用いたMartsinkovsky不変量へのアプローチ (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Yuya Otake (Nagoya University)
Auslander近似理論を用いたMartsinkovsky不変量へのアプローチ (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/05/09
Geometric Analysis Seminar
10:00-12:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Paolo Salani (Università degli Studi di Firenze) 10:00-11:00
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) 10:00-11:00
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.
2025/05/07
Tokyo Probability Seminar
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
The lecture is on Wednesday morning (10:00 – 11:30am). No Tea Time today.
Ivan Corwin (Columbia University)
How Yang-Baxter unravels Kardar-Parisi-Zhang.
The lecture is on Wednesday morning (10:00 – 11:30am). No Tea Time today.
Ivan Corwin (Columbia University)
How Yang-Baxter unravels Kardar-Parisi-Zhang.
[ Abstract ]
Over the past few decades, physicists and then mathematicians have sought to uncover the (conjecturally) universal long time and large space scaling limit for the so-called Kardar-Parisi-Zhang (KPZ) class of stochastically growing interfaces in (1+1)-dimensions. Progress has been marked by several breakthroughs, starting with the identification of a few free-fermionic integrable models in this class and their single-point limiting distributions, widening the field to include non-free-fermionic integrable representatives, evaluating their asymptotics distributions at various levels of generality, constructing the conjectural full space-time scaling limit, known as the directed landscape, and checking convergence to it for a few of the free-fermion representatives.
In this talk, I will describe a method that should prove convergence for all known integrable representatives of the KPZ class to this universal scaling limit. The method has been fully realized for the Asymmetric Simple Exclusion Process and the Stochastic Six Vertex Model. It relies on the Yang-Baxter equation as its only input and unravels the rich complexity of the KPZ class and its asymptotics from first principles. This is based on three works involving Amol Aggarwal, Alexei Borodin, Milind Hegde, Jiaoyang Huang and me.
Over the past few decades, physicists and then mathematicians have sought to uncover the (conjecturally) universal long time and large space scaling limit for the so-called Kardar-Parisi-Zhang (KPZ) class of stochastically growing interfaces in (1+1)-dimensions. Progress has been marked by several breakthroughs, starting with the identification of a few free-fermionic integrable models in this class and their single-point limiting distributions, widening the field to include non-free-fermionic integrable representatives, evaluating their asymptotics distributions at various levels of generality, constructing the conjectural full space-time scaling limit, known as the directed landscape, and checking convergence to it for a few of the free-fermion representatives.
In this talk, I will describe a method that should prove convergence for all known integrable representatives of the KPZ class to this universal scaling limit. The method has been fully realized for the Asymmetric Simple Exclusion Process and the Stochastic Six Vertex Model. It relies on the Yang-Baxter equation as its only input and unravels the rich complexity of the KPZ class and its asymptotics from first principles. This is based on three works involving Amol Aggarwal, Alexei Borodin, Milind Hegde, Jiaoyang Huang and me.
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Eric Chen (École Polytechnique Fédérale de Lausanne (EPFL))
Hanany–Witten transition and Rankin–Selberg periods
https://sites.google.com/view/eric-yen-yo-chen-math/homepage
Eric Chen (École Polytechnique Fédérale de Lausanne (EPFL))
Hanany–Witten transition and Rankin–Selberg periods
[ Abstract ]
Given a manifold decorated with defects separating the bulk into regions with varying gauge theories, it is often convenient to first simplify the topological picture into model configurations. One of the simplest examples of such operations are the transition moves introduced by Hanany and Witten, which describes the crossing of an NS5 and a D5 brane. In this talk, we will describe how these ideas lead to identities between Rankin—Selberg type integrals over moduli spaces of bundles, and consequences of S-duality, or relative Langlands duality, in this setup.
[ Reference URL ]Given a manifold decorated with defects separating the bulk into regions with varying gauge theories, it is often convenient to first simplify the topological picture into model configurations. One of the simplest examples of such operations are the transition moves introduced by Hanany and Witten, which describes the crossing of an NS5 and a D5 brane. In this talk, we will describe how these ideas lead to identities between Rankin—Selberg type integrals over moduli spaces of bundles, and consequences of S-duality, or relative Langlands duality, in this setup.
https://sites.google.com/view/eric-yen-yo-chen-math/homepage
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Sebastian Opper (Universeity of Tokyo)
Autoequivalences of triangulated categories via Hochschild cohomology (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Sebastian Opper (Universeity of Tokyo)
Autoequivalences of triangulated categories via Hochschild cohomology (English)
[ Abstract ]
I will talk about a general tool which allows one to study symmetries of (enhanced) triangulated categories in the form of their derived Picard groups. In general, these groups are rather elusive to computations which require a rather good understanding of the category at hand. A result of Keller shows that the Lie algebra of the derived Picard group of an algebra can be identified with its Hochschild cohomology equipped with the Gerstenhaber Lie bracket. Mimicking the classical relationship between Lie groups and their Lie algebras, I will explain how to "integrate" elements in the Hochschild cohomology of a dg category over fields of characteristic zero to elements in the derived Picard group via a generalized exponential map. Afterwards we discuss properties of this exponential and a few applications. This includes necessary conditions for the uniqueness of enhancements of triangulated functors and uniqueness of Fourier-Mukai kernels. Other applications concern derived Picard groups of categories arising in algebra and geometry: derived categories of graded gentle algebras and their corresponding partially wrapped Fukaya categories or stacky nodal curves as well as Fukaya categories of cotangent bundles and their plumbings.
Zoom ID 822 3531 1702 Password 596657
[ Reference URL ]I will talk about a general tool which allows one to study symmetries of (enhanced) triangulated categories in the form of their derived Picard groups. In general, these groups are rather elusive to computations which require a rather good understanding of the category at hand. A result of Keller shows that the Lie algebra of the derived Picard group of an algebra can be identified with its Hochschild cohomology equipped with the Gerstenhaber Lie bracket. Mimicking the classical relationship between Lie groups and their Lie algebras, I will explain how to "integrate" elements in the Hochschild cohomology of a dg category over fields of characteristic zero to elements in the derived Picard group via a generalized exponential map. Afterwards we discuss properties of this exponential and a few applications. This includes necessary conditions for the uniqueness of enhancements of triangulated functors and uniqueness of Fourier-Mukai kernels. Other applications concern derived Picard groups of categories arising in algebra and geometry: derived categories of graded gentle algebras and their corresponding partially wrapped Fukaya categories or stacky nodal curves as well as Fukaya categories of cotangent bundles and their plumbings.
Zoom ID 822 3531 1702 Password 596657
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
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
2025/05/01
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.)
2025/04/28
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。
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