Text only print
Full screen print
Seminar information archive
Seminar information archive ～07/01｜Today's seminar 07/02 | Future seminars 07/03～
FJ-LMI Seminar
15:45-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Giuseppe DITO (Université Bourgogne Europe)
Deformation quantization and Wightman distributions (英語)
https://fj-lmi.cnrs.fr/seminars/
Giuseppe DITO (Université Bourgogne Europe)
Deformation quantization and Wightman distributions (英語)
[ Abstract ]
Twisted $\hbar$-deformations by classical wave operators are introduced for a scalar field theory in Minkowski spacetime. These deformations are non-perturbative in the coupling constant. The corresponding Wightman $n$-functions are defined as evaluations at $0$ of the $n$-fold deformed products of classical solutions of the classical wave equation. We show that, in this setting, the $2$-point function is well-defined as a formal series in $\hbar$ of tempered distributions. Interestingly, these twisted deformations appear to possess an inherent renormalization scheme.
[ Reference URL ]Twisted $\hbar$-deformations by classical wave operators are introduced for a scalar field theory in Minkowski spacetime. These deformations are non-perturbative in the coupling constant. The corresponding Wightman $n$-functions are defined as evaluations at $0$ of the $n$-fold deformed products of classical solutions of the classical wave equation. We show that, in this setting, the $2$-point function is well-defined as a formal series in $\hbar$ of tempered distributions. Interestingly, these twisted deformations appear to possess an inherent renormalization scheme.
https://fj-lmi.cnrs.fr/seminars/
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
[ Abstract ]
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
2025/04/15
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yuji Ito (TOYOTA CENTRAL R&D LABS., INC.)
Control of uncertain and unknown systems (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yuji Ito (TOYOTA CENTRAL R&D LABS., INC.)
Control of uncertain and unknown systems (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
Harmonic maps and uniform degeneration of hyperbolic surfaces with boundary (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)
Harmonic maps and uniform degeneration of hyperbolic surfaces with boundary (JAPANESE)
[ Abstract ]
If holomorphic quadratic differentials on a punctured Riemann surface have poles of order >1 at the punctures, they correspond to hyperbolic surfaces with geodesic boundary via harmonic maps. This correspondence is known as the harmonic map parametrization of hyperbolic surfaces. In this talk, we use this parametrization to describe the degeneration of hyperbolic surfaces via Gromov-Hausdorff convergence. As an application, we study the limit of a one-parameter family of hyperbolic surfaces in the Thurston boundary of Teichmüller space.
[ Reference URL ]If holomorphic quadratic differentials on a punctured Riemann surface have poles of order >1 at the punctures, they correspond to hyperbolic surfaces with geodesic boundary via harmonic maps. This correspondence is known as the harmonic map parametrization of hyperbolic surfaces. In this talk, we use this parametrization to describe the degeneration of hyperbolic surfaces via Gromov-Hausdorff convergence. As an application, we study the limit of a one-parameter family of hyperbolic surfaces in the Thurston boundary of Teichmüller space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Room # ハイブリッド開催/128 (Graduate School of Math. Sci. Bldg.)
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Parth Shimpi (University of Glasgow)
Torsion pairs for McKay quivers (English)
[ Abstract ]
Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
[ Reference URL ]Classifying torsion classes in the module category has been a problem of much interest in the representation theory of preprojective algebras, owing to its immediate applications in the study of t-structures, bricks, and spherical objects in the derived category. When the preprojective algebra arises from a Dynkin quiver, all such torsion classes must lead to algebraic intermediate hearts— in particular, they arise from tilting modules and therefore admit a finite combinatorial description. Affine ADE quivers, on the other hand, produce infinitely many tilting modules and moreover have geometric hearts arising from the McKay correspondence. By realising the geometric hearts as `limits’ of algebraic ones, I will explain how all torsion pairs for affine preprojective algebras can be described using the above two possibilities; in particular a complete classification is achieved.
Zoom ID 813 0345 0035 Password 706679
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/04/14
FJ-LMI Seminar
17:00-18:00 Room #Main Lecture Hall (Graduate School of Math. Sci. Bldg.)
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal sheaf theory and elliptic pairs (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/03/Tokyo25Colloq.pdf
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal sheaf theory and elliptic pairs (英語)
[ Abstract ]
On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{D}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincar\'e index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann--Roch or the Atiyah--Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
[ Reference URL ]On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{D}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincar\'e index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann--Roch or the Atiyah--Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/03/Tokyo25Colloq.pdf
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hisashi Kasuya (Univ. of Nagoya)
Non-abelian Hodge correspondence and moduli spaces of flat bundles on Sasakian manifolds with fixed basic structures (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.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
[ Abstract ]
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
2025/04/08
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Masahito Hayashi (The Chinese University of Hong Kong, Shenzhen/Nagoya University)
Indefinite causal order strategy nor adaptive strategy does not improve the estimation of group action
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Masahito Hayashi (The Chinese University of Hong Kong, Shenzhen/Nagoya University)
Indefinite causal order strategy nor adaptive strategy does not improve the estimation of group action
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Asuka Takatsu (The University of Tokyo)
Concavity and Dirichlet heat flow (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Asuka Takatsu (The University of Tokyo)
Concavity and Dirichlet heat flow (JAPANESE)
[ Abstract ]
In a convex domain of Euclidean space, the Dirichlet heat flow transmits log-concavity from the initial time to any time. I first introduce a notion of generalized concavity and specify a concavity preserved by the Dirichlet heat flow. Then I show that in a totally convex domain of a Riemannian manifold, if some concavity is preserved by the Dirichlet heat flow, then the sectional curvature must vanish on the domain. The first part is based on joint work with Kazuhiro Ishige and Paolo Salani, and the second part is based on joint work with Kazuhiro Ishige and Haruto Tokunaga.
[ Reference URL ]In a convex domain of Euclidean space, the Dirichlet heat flow transmits log-concavity from the initial time to any time. I first introduce a notion of generalized concavity and specify a concavity preserved by the Dirichlet heat flow. Then I show that in a totally convex domain of a Riemannian manifold, if some concavity is preserved by the Dirichlet heat flow, then the sectional curvature must vanish on the domain. The first part is based on joint work with Kazuhiro Ishige and Paolo Salani, and the second part is based on joint work with Kazuhiro Ishige and Haruto Tokunaga.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/04/02
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Koji Matsushita (The University of Tokyo)
因子類群が$\mathbb{Z}^2$であるトーリック環の非可換クレパント特異点解消について (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Koji Matsushita (The University of Tokyo)
因子類群が$\mathbb{Z}^2$であるトーリック環の非可換クレパント特異点解消について (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/03/27
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Ryota Iitsuka (Nagoya University)
Reduction理論における変異が誘導する三角圏構造 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Ryota Iitsuka (Nagoya University)
Reduction理論における変異が誘導する三角圏構造 (Japanese)
[ Reference URL ]
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/03/21
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Wentao Teng (The University of Tokyo)
A positive product formula of integral kernels of $k$-Hankel transforms (English)
Wentao Teng (The University of Tokyo)
A positive product formula of integral kernels of $k$-Hankel transforms (English)
[ Abstract ]
Let $R$ be a root system in $\mathbb R^N$ and $G$ be the finite subgroup generated by the reflections associated to the root system.
We establish a positive radial product formula for the integral kernels $B_{k,1}(x,y)$ of $(k,1)$-generalized Fourier transforms (or the $k$-Hankel transforms) $F_{k,1}$
$$B_{k,1}(x,z)j_{2\left\langle k\right\rangle+N-2}\left(2\sqrt{t\left|z\right|}\right)=\int_{\mathbb R^N} B_{k,1}(\xi,z)\,d\sigma_{x,t}^{k,1}(\xi),$$
where $j_{\lambda}$ is the normalized Bessel function, and $\sigma_{x,t}^{k,1}(\xi)$ is the unique probability measure. Such a product formula is equivalent to the following representation of the generalized spherical mean operator $f\mapsto M_f,\;f\in C_b(\mathbb{R}^N)$ in $(k,1)$-generalized Fourier analysis
\begin{align*} M_f(x,t)=\int_{\mathbb{R}^N}f\,d\sigma_{x,t}^{k,1},\;(x,t)\in\mathbb{R}^N\times{\mathbb{R}}_+.\end{align*}
We will then analyze the representing measure $\sigma_{x,t}^{k,1}(\xi)$ and show that the support of the measure is contained in
$$\left\{\xi\in\mathbb{R}^N:\sqrt{\vert\xi\vert}\geq\vert\sqrt{\vert x\vert}-\sqrt t\vert\right\}\cap\left(\bigcup_{g\in G}\{\xi\in\mathbb{R}^N:d(\xi,gx)\leq\sqrt t\}\right),$$
where $d\left(x,y\right)=\sqrt{\left|x\right|+\left|y\right|-\sqrt{2\left(\left|x\right|\left|y\right|+\left\langle x,y\right\rangle\right)}}$.
Based on the support of the representing measure $\sigma_{x,t}^{k,1}$, we will get a weak Huygens's principle for the deformed wave equation in $(k,1)$-generalized Fourier analysis.
Moreover, for $N\geq 2$, if we assume that $F_{k,1}\left(\mathcal S(\mathbb{R}^N)\right)$ consists of rapidly decreasing functions at infinity, then we get two different results on $\text{supp}\sigma_{x,t}^{k,1}$, which indirectly denies such assumption.
Let $R$ be a root system in $\mathbb R^N$ and $G$ be the finite subgroup generated by the reflections associated to the root system.
We establish a positive radial product formula for the integral kernels $B_{k,1}(x,y)$ of $(k,1)$-generalized Fourier transforms (or the $k$-Hankel transforms) $F_{k,1}$
$$B_{k,1}(x,z)j_{2\left\langle k\right\rangle+N-2}\left(2\sqrt{t\left|z\right|}\right)=\int_{\mathbb R^N} B_{k,1}(\xi,z)\,d\sigma_{x,t}^{k,1}(\xi),$$
where $j_{\lambda}$ is the normalized Bessel function, and $\sigma_{x,t}^{k,1}(\xi)$ is the unique probability measure. Such a product formula is equivalent to the following representation of the generalized spherical mean operator $f\mapsto M_f,\;f\in C_b(\mathbb{R}^N)$ in $(k,1)$-generalized Fourier analysis
\begin{align*} M_f(x,t)=\int_{\mathbb{R}^N}f\,d\sigma_{x,t}^{k,1},\;(x,t)\in\mathbb{R}^N\times{\mathbb{R}}_+.\end{align*}
We will then analyze the representing measure $\sigma_{x,t}^{k,1}(\xi)$ and show that the support of the measure is contained in
$$\left\{\xi\in\mathbb{R}^N:\sqrt{\vert\xi\vert}\geq\vert\sqrt{\vert x\vert}-\sqrt t\vert\right\}\cap\left(\bigcup_{g\in G}\{\xi\in\mathbb{R}^N:d(\xi,gx)\leq\sqrt t\}\right),$$
where $d\left(x,y\right)=\sqrt{\left|x\right|+\left|y\right|-\sqrt{2\left(\left|x\right|\left|y\right|+\left\langle x,y\right\rangle\right)}}$.
Based on the support of the representing measure $\sigma_{x,t}^{k,1}$, we will get a weak Huygens's principle for the deformed wave equation in $(k,1)$-generalized Fourier analysis.
Moreover, for $N\geq 2$, if we assume that $F_{k,1}\left(\mathcal S(\mathbb{R}^N)\right)$ consists of rapidly decreasing functions at infinity, then we get two different results on $\text{supp}\sigma_{x,t}^{k,1}$, which indirectly denies such assumption.
2025/03/20
Lectures
13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー その可能性の中心 --- カナダ出発に際しての置き土産
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー その可能性の中心 --- カナダ出発に際しての置き土産
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
2025/03/17
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tokyo-Nagoya Algebra Seminar
14:30-16:00 Online
Junyang Liu (University of Science and Technology of China)
On Amiot's conjecture (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Junyang Liu (University of Science and Technology of China)
On Amiot's conjecture (English)
[ Abstract ]
In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau categories with cluster-tilting object must come from quivers with potential. This would extend a structure theorem obtained by Keller-Reiten in the case where the endomorphism algebra of the cluster-tilting object is hereditary. Many other classes of examples are also known. We will report on the proof of the conjecture in the general case for categories with *algebraic* 2-Calabi-Yau structure. This result has been obtained in joint work with Bernhard Keller and is based on Van den Bergh's structure theorem for complete Calabi-Yau algebras. We also generalize his structure theorem to the relative case and use it to prove a relative variant of the conjecture.
ミーティング ID: 853 1951 5047
パスコード: 900788
[ Reference URL ]In 2010, Claire Amiot conjectured that algebraic 2-Calabi-Yau categories with cluster-tilting object must come from quivers with potential. This would extend a structure theorem obtained by Keller-Reiten in the case where the endomorphism algebra of the cluster-tilting object is hereditary. Many other classes of examples are also known. We will report on the proof of the conjecture in the general case for categories with *algebraic* 2-Calabi-Yau structure. This result has been obtained in joint work with Bernhard Keller and is based on Van den Bergh's structure theorem for complete Calabi-Yau algebras. We also generalize his structure theorem to the relative case and use it to prove a relative variant of the conjecture.
ミーティング ID: 853 1951 5047
パスコード: 900788
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025/02/21
Operator Algebra Seminars
13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
The day of the week, the time slot and the room are different from the usual ones.
David O'Connell (OIST)
Colimits of $C^*$-algebras in Quantum Field Theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week, the time slot and the room are different from the usual ones.
David O'Connell (OIST)
Colimits of $C^*$-algebras in Quantum Field Theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/02/20
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
The day of the week is different from the usual one.
Christoph Schweigert (Univ. Hamburg)
Nakayama functors, relative Serre functors and some applications
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week is different from the usual one.
Christoph Schweigert (Univ. Hamburg)
Nakayama functors, relative Serre functors and some applications
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Discrete mathematical modelling seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
Integrable maps associated with Stieltjes fractions and the Volterra lattice
Andy Hone (University of Kent)
Integrable maps associated with Stieltjes fractions and the Volterra lattice
[ Abstract ]
Quite recently, a classification of birational maps in 4D that have a Lagrangian structure and are Liouville integrable was derived by Gubbiotti, building on earlier results obtained with Joshi, Tran and Viallet. Here we show that the first member in this family naturally arises from the Stieltjes continued fraction expansion of a meromorphic function on a genus 2 curve, and is associated with special solutions of the Volterra lattice hierarchy. This construction extends to hyperelliptic curves of all genera, producing a family of Poisson maps on an affine space of Lax matrices, with explicit Hankel determinant expressions for the tau functions. In particular, in the genus 1 case one finds elliptic solutions of the Volterra lattice, obtained from a QRT map whose tau functions satisfy the Somos-5 relation. We also observe that the other 4D maps in Gubbiotti's classification correspond to genus 2 solutions of two distinct forms of the modified Voltera lattice. If time permits, we will also mention the connection with families of orthogonal polynomials. This is joint work with John Roberts, Pol Vanhaecke and Federico Zullo.
Quite recently, a classification of birational maps in 4D that have a Lagrangian structure and are Liouville integrable was derived by Gubbiotti, building on earlier results obtained with Joshi, Tran and Viallet. Here we show that the first member in this family naturally arises from the Stieltjes continued fraction expansion of a meromorphic function on a genus 2 curve, and is associated with special solutions of the Volterra lattice hierarchy. This construction extends to hyperelliptic curves of all genera, producing a family of Poisson maps on an affine space of Lax matrices, with explicit Hankel determinant expressions for the tau functions. In particular, in the genus 1 case one finds elliptic solutions of the Volterra lattice, obtained from a QRT map whose tau functions satisfy the Somos-5 relation. We also observe that the other 4D maps in Gubbiotti's classification correspond to genus 2 solutions of two distinct forms of the modified Voltera lattice. If time permits, we will also mention the connection with families of orthogonal polynomials. This is joint work with John Roberts, Pol Vanhaecke and Federico Zullo.
Seminar on Probability and Statistics
13:00-14:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Evgeny Spodarev (Universität Ulm)
Non-ergodic statistics for stationary-increment harmonizable stable processes (English)
https://docs.google.com/forms/d/e/1FAIpQLSd5_4NM3xazVUAARMhyv_e55RsYZFyfpOHqC0oGYasM2NLOqQ/viewform
Evgeny Spodarev (Universität Ulm)
Non-ergodic statistics for stationary-increment harmonizable stable processes (English)
[ Abstract ]
We consider the class of stationary-increment harmonizable stable processes $𝑋=\{ 𝑋(𝑡): 𝑡\in \mathbb{R} \}$ defined by $$𝑋(𝑡)=𝑅𝑒\left( \int_{\mathbb{R}} (𝑒^{𝑖𝑡𝑥}−1) \Psi (𝑥) 𝑀_{\alpha}(𝑑𝑥) \right), \quad 𝑡\in\mathbb{R},$$ where $𝑀_{\alpha}$ is an isotropic complex symmetric $\alpha$-stable (𝑆$\alpha$𝑆) random measure with Lebesgue control measure. This class contains real harmonizable fractional stable motions, which are a generalization of the harmonizable representation of fractional Brownian motions to the stable regime, when $\Psi(𝑥)=|𝑥|−𝐻−1/\alpha, 𝑥\in\mathbb{R}$. We give conditions for the integrability of the path of $𝑋$ with respect to a finite, absolutely continuous measure, and show that the convolution with a suitable measure yields a real stationary harmonizable 𝑆$\alpha$𝑆 process with finite control measure. Such a process admits a LePage type series representation consisting of sine and cosine functions with random amplitudes and frequencies, which can be estimated consistently using the periodogram. Combined with kernel density estimation, this allows us to construct consistent estimators for the index of stability $\alpha$ as well as the kernel function $\Psi$ in the integral representation of $𝑋$ (up to a constant factor). For real harmonizable fractional stable motions consistent estimators for the index of stability $\alpha$ and its Hurst parameter $𝐻$ are given, which are computed directly from the periodogram frequency estimates.
[ Reference URL ]We consider the class of stationary-increment harmonizable stable processes $𝑋=\{ 𝑋(𝑡): 𝑡\in \mathbb{R} \}$ defined by $$𝑋(𝑡)=𝑅𝑒\left( \int_{\mathbb{R}} (𝑒^{𝑖𝑡𝑥}−1) \Psi (𝑥) 𝑀_{\alpha}(𝑑𝑥) \right), \quad 𝑡\in\mathbb{R},$$ where $𝑀_{\alpha}$ is an isotropic complex symmetric $\alpha$-stable (𝑆$\alpha$𝑆) random measure with Lebesgue control measure. This class contains real harmonizable fractional stable motions, which are a generalization of the harmonizable representation of fractional Brownian motions to the stable regime, when $\Psi(𝑥)=|𝑥|−𝐻−1/\alpha, 𝑥\in\mathbb{R}$. We give conditions for the integrability of the path of $𝑋$ with respect to a finite, absolutely continuous measure, and show that the convolution with a suitable measure yields a real stationary harmonizable 𝑆$\alpha$𝑆 process with finite control measure. Such a process admits a LePage type series representation consisting of sine and cosine functions with random amplitudes and frequencies, which can be estimated consistently using the periodogram. Combined with kernel density estimation, this allows us to construct consistent estimators for the index of stability $\alpha$ as well as the kernel function $\Psi$ in the integral representation of $𝑋$ (up to a constant factor). For real harmonizable fractional stable motions consistent estimators for the index of stability $\alpha$ and its Hurst parameter $𝐻$ are given, which are computed directly from the periodogram frequency estimates.
https://docs.google.com/forms/d/e/1FAIpQLSd5_4NM3xazVUAARMhyv_e55RsYZFyfpOHqC0oGYasM2NLOqQ/viewform
2025/02/13
Infinite Analysis Seminar Tokyo
13:30-17:00 Room #118, hybrid seminar (Graduate School of Math. Sci. Bldg.)
Genki Shibukawa (Kobe University) 13:30-15:00
Basics and developments of the $\mu$-function (First part) (日本語)
Basics and developments of the $\mu$-function (Second part) (日本語)
Genki Shibukawa (Kobe University) 13:30-15:00
Basics and developments of the $\mu$-function (First part) (日本語)
[ Abstract ]
First part (speaker: Genki Shibukawa) Starting from a short introduction to the original Zwegers' $\mu$ function, we explain some basic tools of $q$-special functions ( $q$-hypergeometric functions) and $q$-analysis ($q$-difference equations, $q$-Borel and $q$-Laplace transformations) which are necessary to give a special function theoretic interpretation of the $\mu $-function. In these settings, we introduce the generalized $\mu $-function which is a one-parameter deformation of the Zwegers' $\mu $-function, and derive its basic properties such as symmetry, explicit formulas, difference relations, and connection formulas. In particular, we explain the relationship between the generalized $\mu $-function and $q$-Hermite polynomial (function).
Satoshi Tsuchimi (Kobe University) 15:30-17:00First part (speaker: Genki Shibukawa) Starting from a short introduction to the original Zwegers' $\mu$ function, we explain some basic tools of $q$-special functions ( $q$-hypergeometric functions) and $q$-analysis ($q$-difference equations, $q$-Borel and $q$-Laplace transformations) which are necessary to give a special function theoretic interpretation of the $\mu $-function. In these settings, we introduce the generalized $\mu $-function which is a one-parameter deformation of the Zwegers' $\mu $-function, and derive its basic properties such as symmetry, explicit formulas, difference relations, and connection formulas. In particular, we explain the relationship between the generalized $\mu $-function and $q$-Hermite polynomial (function).
Basics and developments of the $\mu$-function (Second part) (日本語)
[ Abstract ]
Second part (speaker: Satoshi Tsuchimi)
In this part, we present some advanced topics of the $\mu$ function. First, we show that the $\mu$-functions naturally appear in special solutions of factorized higher-order $q$-difference equations. Next, by applying the above $q$-analytic methods, we introduce a multivariate analogue of the generalized $\mu$-function and give some formulas. Finally, by similar methods, we construct another generalization of the $\mu$-function from the Kontsevich function which is an important function in knot invariants. This generalization of the $\mu$-function is related to the big $q$-Hermite polynomial (function) which is a 1 parameter deform of the $q$-Hermite polynomial.
Second part (speaker: Satoshi Tsuchimi)
In this part, we present some advanced topics of the $\mu$ function. First, we show that the $\mu$-functions naturally appear in special solutions of factorized higher-order $q$-difference equations. Next, by applying the above $q$-analytic methods, we introduce a multivariate analogue of the generalized $\mu$-function and give some formulas. Finally, by similar methods, we construct another generalization of the $\mu$-function from the Kontsevich function which is an important function in knot invariants. This generalization of the $\mu$-function is related to the big $q$-Hermite polynomial (function) which is a 1 parameter deform of the $q$-Hermite polynomial.
2025/02/07
Seminar on Probability and Statistics
14:00-15:10 Room #128 (Graduate School of Math. Sci. Bldg.)
ハイブリッド開催
Juho Leppänen (Tokai University)
A multivariate Berry–Esseen theorem for deterministic dynamical systems (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/lmbyLgO6RNi1GnoovqW_Sg
ハイブリッド開催
Juho Leppänen (Tokai University)
A multivariate Berry–Esseen theorem for deterministic dynamical systems (English)
[ Abstract ]
Many chaotic deterministic dynamical systems with a random initial state satisfy limit theorems similar to those of independent random variables. A classical example is the Central Limit Theorem, which, for a broad class of ergodic measure-preserving systems, is known to follow from a sufficiently rapid decay of correlations. Much work has also been done on the rate of convergence in the CLT. Results in this area typically rely on additional structure, such as suitable martingale approximation schemes or a spectral gap for the Perron–Frobenius operator.
In this talk, we present an adaptation of Stein's method for multivariate normal approximation of deterministic dynamical systems. For vector-valued processes generated by a class of fibred systems with good distortion properties (Gibbs–Markov maps), we derive bounds on the convex distance between the distribution of scaled partial sums and a multivariate normal distribution. These bounds, which are deduced as a consequence of certain correlation decay criteria, involve a multiplicative constant whose dependence on the dimension and dynamical quantities is explicit.
[ Reference URL ]Many chaotic deterministic dynamical systems with a random initial state satisfy limit theorems similar to those of independent random variables. A classical example is the Central Limit Theorem, which, for a broad class of ergodic measure-preserving systems, is known to follow from a sufficiently rapid decay of correlations. Much work has also been done on the rate of convergence in the CLT. Results in this area typically rely on additional structure, such as suitable martingale approximation schemes or a spectral gap for the Perron–Frobenius operator.
In this talk, we present an adaptation of Stein's method for multivariate normal approximation of deterministic dynamical systems. For vector-valued processes generated by a class of fibred systems with good distortion properties (Gibbs–Markov maps), we derive bounds on the convex distance between the distribution of scaled partial sums and a multivariate normal distribution. These bounds, which are deduced as a consequence of certain correlation decay criteria, involve a multiplicative constant whose dependence on the dimension and dynamical quantities is explicit.
https://u-tokyo-ac-jp.zoom.us/meeting/register/lmbyLgO6RNi1GnoovqW_Sg
2025/02/06
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.
Jacek Wesolowski (Warsaw University of Technology)
Asymptotics of random Motzkin paths
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Jacek Wesolowski (Warsaw University of Technology)
Asymptotics of random Motzkin paths
[ Abstract ]
We study Motzkin paths of length L with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as L becomes large. Macroscopic limits of the resulting processes (under two different asymptotic regimes) appear to be non-Brownian parts of stationary measures for the KPZ equation and hypothetical KPZ fixed point on the half-line. The talk is based on a joint paper with W. Bryc (Univ. of Cincinnati) and A. Kuztetsov (York Univ., Toronto) - to appear in IMRN, available also on arXiv: https://arxiv.org/abs/2402.00265
We study Motzkin paths of length L with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as L becomes large. Macroscopic limits of the resulting processes (under two different asymptotic regimes) appear to be non-Brownian parts of stationary measures for the KPZ equation and hypothetical KPZ fixed point on the half-line. The talk is based on a joint paper with W. Bryc (Univ. of Cincinnati) and A. Kuztetsov (York Univ., Toronto) - to appear in IMRN, available also on arXiv: https://arxiv.org/abs/2402.00265
2025/01/24
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
MAO Tianle (Graduate School of Mathematical Sciences University of Tokyo)
Stability conditions on the canonical line bundle of P^3
(射影空間P^3の標準束の安定性条件）
MAO Tianle (Graduate School of Mathematical Sciences University of Tokyo)
Stability conditions on the canonical line bundle of P^3
(射影空間P^3の標準束の安定性条件）
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
ITO Kei (Graduate School of Mathematical Sciences University of Tokyo)
Structure of Kajiwara-Watatani algebras and their Cartan subalgebras
(梶原-綿谷代数の構造とそのカルタン部分代数）
ITO Kei (Graduate School of Mathematical Sciences University of Tokyo)
Structure of Kajiwara-Watatani algebras and their Cartan subalgebras
(梶原-綿谷代数の構造とそのカルタン部分代数）
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197 Next >
