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Seminar information archive
Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～
2022/04/19
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Kei Ito (Univ. Tokyo)
Cartan subalgebras of $C^*$-algebras associated to dynamical systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Kei Ito (Univ. Tokyo)
Cartan subalgebras of $C^*$-algebras associated to dynamical systems
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:30-18:30 Online
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Toshihisa Kubo (Ryukoku University)
On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Toshihisa Kubo (Ryukoku University)
On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces (JAPANESE)
[ Abstract ]
Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a differential symmetry breaking operator (differential SBO for short) ([T.~Kobayashi, Differential Geom. Appl. (2014)]).
In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$. In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.
[ Reference URL ]Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a differential symmetry breaking operator (differential SBO for short) ([T.~Kobayashi, Differential Geom. Appl. (2014)]).
In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$. In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:30-18:30 Room #online (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Toshihisa Kubo (Ryukoku University)
On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces
(Japanese)
Joint with Tuesday Seminar on Topology
Toshihisa Kubo (Ryukoku University)
On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces
(Japanese)
[ Abstract ]
Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a \emph{differential symmetry breaking operator} (differential SBO for short)
([T. Kobayashi, Differential Geom. Appl. (2014)]).
In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard
Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$.
In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.
Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a \emph{differential symmetry breaking operator} (differential SBO for short)
([T. Kobayashi, Differential Geom. Appl. (2014)]).
In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard
Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$.
In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.
2022/04/18
Seminar on Geometric Complex Analysis
10:30-12:00 Online
Takeo Ohasawa (Nagoya University)
Approximation and bundle convexity on complex manifolds of pseudo convex type (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Takeo Ohasawa (Nagoya University)
Approximation and bundle convexity on complex manifolds of pseudo convex type (Japanese)
[ Abstract ]
An approximation theorem will be proved for the space of holomorphic sections of vector bundles on certain Zariski open sets of weakly 1-complete manifolds. As an existence result on such manifolds, a solution of the bundle-valued version of the Levi problem will be given by a variant of a method of Hoermander.
[ Reference URL ]An approximation theorem will be proved for the space of holomorphic sections of vector bundles on certain Zariski open sets of weakly 1-complete manifolds. As an existence result on such manifolds, a solution of the bundle-valued version of the Levi problem will be given by a variant of a method of Hoermander.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/04/14
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computers II (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computers II (Japanese)
[ Abstract ]
Explanation on the fundamental notion of quantum calculation.
Explanation on the fundamental notion of quantum calculation.
2022/04/13
Tokyo-Nagoya Algebra Seminar
10:30-12:00 Online
Please see the reference URL for details on the online seminar.
Yuta Kimura (Osaka Metropolitan University)
Tilting ideals of deformed preprojective algebras
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the reference URL for details on the online seminar.
Yuta Kimura (Osaka Metropolitan University)
Tilting ideals of deformed preprojective algebras
[ Abstract ]
Let $K$ be a field and $Q$ a finite quiver. For a weight $\lambda \in K^{|Q_0|}$, the deformed preprojective algebra $\Pi^{\lambda}$ was introduced by Crawley-Boevey and Holland to study deformations of Kleinian singularities. If $\lambda = 0$, then $\Pi^{0}$ is the preprojective algebra introduced by Gelfand-Ponomarev, and appears many areas of mathematics. Among interesting properties of $\Pi^{0}$, the classification of tilting ideals of $\Pi^{0}$, shown by Buan-Iyama-Reiten-Scott, is fundamental and important. They constructed a bijection between the set of tilting ideals of $\Pi^{0}$ and the Coxeter group $W_Q$ of $Q$.
In this talk, when $Q$ is non-Dynkin, we see that $\Pi^{\lambda}$ is a $2$-Calabi-Yau algebra, and show that there exists a bijection between tilting ideals and a Coxeter group. However $W_Q$ does not appear, since $\Pi^{\lambda}$ is not necessary basic. Instead of $W_Q$, we consider the Ext-quiver of rigid simple modules, and use its Coxeter group. When $Q$ is an extended Dynkin quiver, we see that the Ext-quiver is finite and this has an information of singularities of a representation space of semisimple modules.
This is joint work with William Crawley-Boevey.
[ Reference URL ]Let $K$ be a field and $Q$ a finite quiver. For a weight $\lambda \in K^{|Q_0|}$, the deformed preprojective algebra $\Pi^{\lambda}$ was introduced by Crawley-Boevey and Holland to study deformations of Kleinian singularities. If $\lambda = 0$, then $\Pi^{0}$ is the preprojective algebra introduced by Gelfand-Ponomarev, and appears many areas of mathematics. Among interesting properties of $\Pi^{0}$, the classification of tilting ideals of $\Pi^{0}$, shown by Buan-Iyama-Reiten-Scott, is fundamental and important. They constructed a bijection between the set of tilting ideals of $\Pi^{0}$ and the Coxeter group $W_Q$ of $Q$.
In this talk, when $Q$ is non-Dynkin, we see that $\Pi^{\lambda}$ is a $2$-Calabi-Yau algebra, and show that there exists a bijection between tilting ideals and a Coxeter group. However $W_Q$ does not appear, since $\Pi^{\lambda}$ is not necessary basic. Instead of $W_Q$, we consider the Ext-quiver of rigid simple modules, and use its Coxeter group. When $Q$ is an extended Dynkin quiver, we see that the Ext-quiver is finite and this has an information of singularities of a representation space of semisimple modules.
This is joint work with William Crawley-Boevey.
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/04/12
Tuesday Seminar of Analysis
16:00-17:30 Online
Amru Hussein (Technische Universität Kaiserslautern)
Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)
https://forms.gle/QbQKex12dbQrt2Lw6
Amru Hussein (Technische Universität Kaiserslautern)
Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)
[ Abstract ]
Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.
This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962
[ Reference URL ]Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.
This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962
https://forms.gle/QbQKex12dbQrt2Lw6
2022/04/07
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Design and control of quantum computers (Japanese)
Yasunari Suzuki (NTT)
Design and control of quantum computers (Japanese)
[ Abstract ]
Explanation on the design and control of quantum computers
Explanation on the design and control of quantum computers
2022/04/05
Lie Groups and Representation Theory
17:00-17:30 Room #online (Graduate School of Math. Sci. Bldg.)
Toshiyuki KOBAYASHI (The University of Tokyo)
Note on the restriction of minimal representations with respect to reductive symmetric pairs (Japanese)
Toshiyuki KOBAYASHI (The University of Tokyo)
Note on the restriction of minimal representations with respect to reductive symmetric pairs (Japanese)
[ Abstract ]
I discuss briefly some abstract feature of branching problems with focus on the restriction of minimal representations with respect to reductive symmetric pairs.
I discuss briefly some abstract feature of branching problems with focus on the restriction of minimal representations with respect to reductive symmetric pairs.
Lie Groups and Representation Theory
17:30-18:30 Room #online (Graduate School of Math. Sci. Bldg.)
Junko INOUE (Tottori University)
Estimate of the norm of the $L^p$-Fourier transform on compact extensions of locally compact groups
(Japanese)
Junko INOUE (Tottori University)
Estimate of the norm of the $L^p$-Fourier transform on compact extensions of locally compact groups
(Japanese)
[ Abstract ]
The classical Hausdorff-Young theorem for locally compact abelian groups is generalized by Kunze for unimodular locally compact groups.
When the group $G$ is of type I, the abstract Plancherel theorem gives a decomposition of the regular representation into a direct integral of irreducible representations through the Fourier transform;
By the Hausdorff-Young theorem generalized by Kunze, for exponents $p$ $(1 < p \leq 2)$ and ${p'}=p/(p-1)$, the Fourier transform yields a bounded operator $\mathcal{F}^p:L^p(G)\to L^{p'}(\widehat{G})$, where $L^{p'}(\widehat{G})$ is the $L^{p'}$ space of measurable fields of the Schatten class operators on the unitary dual $\widehat{G}$ of $G$.
Under this setting, we are concerned with the norm $\|\mathcal{F}^p(G)\|$ of the $L^p$-Fourier transform $\mathcal{F}^p$.
Let $G$ be a separable unimodular locally compact group of type I,and $N$ be a type I, unimodular, closed normal subgroup of $G$. Suppose $G/N$ is compact. Then we show the inequality $\|\mathcal{F}^p(G)\|\leq\|\mathcal F^p(N)\|$ for $1< p \leq 2$.
This result is a joint work with Ali Baklouti
(J. Fourier Anal. Appl. 26 (2020), Paper No. 26).
The classical Hausdorff-Young theorem for locally compact abelian groups is generalized by Kunze for unimodular locally compact groups.
When the group $G$ is of type I, the abstract Plancherel theorem gives a decomposition of the regular representation into a direct integral of irreducible representations through the Fourier transform;
By the Hausdorff-Young theorem generalized by Kunze, for exponents $p$ $(1 < p \leq 2)$ and ${p'}=p/(p-1)$, the Fourier transform yields a bounded operator $\mathcal{F}^p:L^p(G)\to L^{p'}(\widehat{G})$, where $L^{p'}(\widehat{G})$ is the $L^{p'}$ space of measurable fields of the Schatten class operators on the unitary dual $\widehat{G}$ of $G$.
Under this setting, we are concerned with the norm $\|\mathcal{F}^p(G)\|$ of the $L^p$-Fourier transform $\mathcal{F}^p$.
Let $G$ be a separable unimodular locally compact group of type I,and $N$ be a type I, unimodular, closed normal subgroup of $G$. Suppose $G/N$ is compact. Then we show the inequality $\|\mathcal{F}^p(G)\|\leq\|\mathcal F^p(N)\|$ for $1< p \leq 2$.
This result is a joint work with Ali Baklouti
(J. Fourier Anal. Appl. 26 (2020), Paper No. 26).
2022/03/26
Colloquium
16:00-17:00 Online
Registration is closed.
Masahiko Kanai (Graduate School of Mathematical Sciences, The University of Tokyo) -
Tetsuji Tokihiro (Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00
Registration is closed.
Masahiko Kanai (Graduate School of Mathematical Sciences, The University of Tokyo) -
Tetsuji Tokihiro (Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00
2022/03/11
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Please see the URL below for details on the online seminar.
Shigeo Koshitani (Chiba University)
Modular representation theory of finite groups – local versus global II (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Shigeo Koshitani (Chiba University)
Modular representation theory of finite groups – local versus global II (English)
[ Abstract ]
We are going to talk about representation theory of finite groups. In the 1st part it will be on "Equivalences of categories ” showing up for block theory in modular representation theory, and it should be kind of introductory lecture/talk. So the audience is supposed to have knowledge only of definitions of groups, rings, fields, modules, and so on. In the 2nd part we will discuss kind of local—global conjectures in modular representation theory of finite groups, that originally and essentially are due to Richard Brauer (1901–77).
[ Reference URL ]We are going to talk about representation theory of finite groups. In the 1st part it will be on "Equivalences of categories ” showing up for block theory in modular representation theory, and it should be kind of introductory lecture/talk. So the audience is supposed to have knowledge only of definitions of groups, rings, fields, modules, and so on. In the 2nd part we will discuss kind of local—global conjectures in modular representation theory of finite groups, that originally and essentially are due to Richard Brauer (1901–77).
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/03/09
Tokyo-Nagoya Algebra Seminar
13:00-14:30 Online
Please see the URL below for details on the online seminar.
Shigeo Koshitani (Chiba University)
Modular representation theory of finite groups – local versus global I (English)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Please see the URL below for details on the online seminar.
Shigeo Koshitani (Chiba University)
Modular representation theory of finite groups – local versus global I (English)
[ Abstract ]
We are going to talk about representation theory of finite groups. In the 1st part it will be on "Equivalences of categories ” showing up for block theory in modular representation theory, and it should be kind of introductory lecture/talk. So the audience is supposed to have knowledge only of definitions of groups, rings, fields, modules, and so on. In the 2nd part we will discuss kind of local—global conjectures in modular representation theory of finite groups, that originally and essentially are due to Richard Brauer (1901–77).
[ Reference URL ]We are going to talk about representation theory of finite groups. In the 1st part it will be on "Equivalences of categories ” showing up for block theory in modular representation theory, and it should be kind of introductory lecture/talk. So the audience is supposed to have knowledge only of definitions of groups, rings, fields, modules, and so on. In the 2nd part we will discuss kind of local—global conjectures in modular representation theory of finite groups, that originally and essentially are due to Richard Brauer (1901–77).
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2022/03/08
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Masatoshi Kitagawa (Waseda University)
On the structure of Hamiltonian G-varieties (Japanese)
Masatoshi Kitagawa (Waseda University)
On the structure of Hamiltonian G-varieties (Japanese)
[ Abstract ]
I will talk about a result by I. Losev (Math. Z. 2009) on the structure of Hamiltonian G-varieties.
In particular, I will explain how to reduce the result to central-nilpotent cases.
I will give an application of the result to branching laws.
I will talk about a result by I. Losev (Math. Z. 2009) on the structure of Hamiltonian G-varieties.
In particular, I will explain how to reduce the result to central-nilpotent cases.
I will give an application of the result to branching laws.
2022/02/22
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Hiroyoshi Tamori (Hokkaido University)
On a long exact sequence of the Schwartz homology (Japanese)
Hiroyoshi Tamori (Hokkaido University)
On a long exact sequence of the Schwartz homology (Japanese)
[ Abstract ]
For a smooth Fr\’{e}chet representation of moderate growth of an almost linear Nash group, Chen-Sun introduced a homology (called Schwartz homology) equipped with certain topology. Given a short exact sequence of such representations, we can construct a long exact sequence of Schwartz homology groups via the natural isomorphism with relative Lie algebra homology. We give an example of a long exact sequence where the connecting homomorphism is not continuous.
For a smooth Fr\’{e}chet representation of moderate growth of an almost linear Nash group, Chen-Sun introduced a homology (called Schwartz homology) equipped with certain topology. Given a short exact sequence of such representations, we can construct a long exact sequence of Schwartz homology groups via the natural isomorphism with relative Lie algebra homology. We give an example of a long exact sequence where the connecting homomorphism is not continuous.
2022/02/16
Seminar on Probability and Statistics
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Teppei Ogihara (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform
Teppei Ogihara (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We study the estimation problem of the parametric model for ergodic jump-diffusion processes. Shimizu and Yoshida (Stat. Inference Stoch. Process. 2006) proposed a quasi-maximum-likelihood estimator based on a thresholding likelihood function that detects the existence of jumps.
In this talk, we consider the efficiency of estimators by using local asymptotic normality (LAN). To show the LAN property, we need to specify the asymptotic behavior of log-likelihood ratios, which is complicated for the jump-diffusion model because the transition probability for no jump is quite different from that for the presence of jumps. We develop techniques to show the LAN property based on transition density approximation. By applying these techniques to the thresholding likelihood function, we obtain the LAN property for the jump-diffusion model. Moreover, we have the asymptotic efficiency of
the quasi-maximum-likelihood estimator in Shimizu and Yoshida (2006) and a Bayes-type estimator proposed in Ogihara and Yoshida (Stat.Inference Stoch. Process. 2011). This is a joint work with Yuma Uehara (Kansai University).
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
We study the estimation problem of the parametric model for ergodic jump-diffusion processes. Shimizu and Yoshida (Stat. Inference Stoch. Process. 2006) proposed a quasi-maximum-likelihood estimator based on a thresholding likelihood function that detects the existence of jumps.
In this talk, we consider the efficiency of estimators by using local asymptotic normality (LAN). To show the LAN property, we need to specify the asymptotic behavior of log-likelihood ratios, which is complicated for the jump-diffusion model because the transition probability for no jump is quite different from that for the presence of jumps. We develop techniques to show the LAN property based on transition density approximation. By applying these techniques to the thresholding likelihood function, we obtain the LAN property for the jump-diffusion model. Moreover, we have the asymptotic efficiency of
the quasi-maximum-likelihood estimator in Shimizu and Yoshida (2006) and a Bayes-type estimator proposed in Ogihara and Yoshida (Stat.Inference Stoch. Process. 2011). This is a joint work with Yuma Uehara (Kansai University).
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform
2022/02/15
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Kazuki Kannaka (RIKEN iTHEMS)
Deformations of standard compact Clifford-Klein forms (Japanese)
Kazuki Kannaka (RIKEN iTHEMS)
Deformations of standard compact Clifford-Klein forms (Japanese)
[ Abstract ]
Let Γ be a discontinuous group for a homogeneous manifold G/H of reductive type.
The Clifford-Klein form Γ\G/H is standard if Γ is contained in a reductive subgroup of G acting properly on G/H.
For 12 series of standard compact Clifford-Klein forms given by Kobayashi-Yoshino, we discuss in this talk whether or not there exist (1) locally rigid ones, (2) non-standard deformations, and (3) Zariski-dense deformations in G.
After briefly explaining Kobayashi's work and Kassel's work on these
questions, we will explain the new results.
Let Γ be a discontinuous group for a homogeneous manifold G/H of reductive type.
The Clifford-Klein form Γ\G/H is standard if Γ is contained in a reductive subgroup of G acting properly on G/H.
For 12 series of standard compact Clifford-Klein forms given by Kobayashi-Yoshino, we discuss in this talk whether or not there exist (1) locally rigid ones, (2) non-standard deformations, and (3) Zariski-dense deformations in G.
After briefly explaining Kobayashi's work and Kassel's work on these
questions, we will explain the new results.
2022/01/28
thesis presentations
13:00-14:15 Online
Xiaobing Sheng (Graduate School of Mathematical Sciences University of Tokyo)
Geometric and combinatorial properties of some generalisations of Thompson's groups
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
Xiaobing Sheng (Graduate School of Mathematical Sciences University of Tokyo)
Geometric and combinatorial properties of some generalisations of Thompson's groups
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
13:00-14:15 Online
Erbol Zhanpeisov (Graduate School of Mathematical Sciences University of Tokyo)
Local existence and blow-up rate of solutions to nonlinear parabolic equations
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
Erbol Zhanpeisov (Graduate School of Mathematical Sciences University of Tokyo)
Local existence and blow-up rate of solutions to nonlinear parabolic equations
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
13:00-14:15 Online
Kentaro Kameoka (Graduate School of Mathematical Sciences University of Tokyo)
Studies on semiclassical analysis and resonance theory
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
Kentaro Kameoka (Graduate School of Mathematical Sciences University of Tokyo)
Studies on semiclassical analysis and resonance theory
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
13:00-14:15 Online
Teppei Takamatsu (Graduate School of Mathematical Sciences University of Tokyo)
On the arithmetic finiteness of irreducible symplectic varieties
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
Teppei Takamatsu (Graduate School of Mathematical Sciences University of Tokyo)
On the arithmetic finiteness of irreducible symplectic varieties
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
11:00-12:15 Online
Yujiro Takeishi (Graduate School of Mathematical Sciences University of Tokyo)
Optimal decay estimates for Schrödinger heat semigroups with inverse square potential in Lorentz spaces
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
Yujiro Takeishi (Graduate School of Mathematical Sciences University of Tokyo)
Optimal decay estimates for Schrödinger heat semigroups with inverse square potential in Lorentz spaces
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
11:00-12:15 Online
Kengo Takei (Graduate School of Mathematical Sciences University of Tokyo)
Some asymptotic problems for systems of Hamilton-Jacobi-Bellman equations
[ Reference URL ]
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Kengo Takei (Graduate School of Mathematical Sciences University of Tokyo)
Some asymptotic problems for systems of Hamilton-Jacobi-Bellman equations
[ Reference URL ]
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thesis presentations
9:15-10:30 Online
Shota Fukushima (Graduate School of Mathematical Sciences University of Tokyo)
Microlocal construction and analysis of the Schrödinger propagators on manifolds
[ Reference URL ]
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Shota Fukushima (Graduate School of Mathematical Sciences University of Tokyo)
Microlocal construction and analysis of the Schrödinger propagators on manifolds
[ Reference URL ]
https://forms.gle/bdsntP4pZ4TMaehF9
thesis presentations
11:00-12:15 Online
Yuki Yamamoto (Graduate School of Mathematical Sciences University of Tokyo)
On the restrictions of supercuspidal representations for inner forms of GL_N
[ Reference URL ]
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Yuki Yamamoto (Graduate School of Mathematical Sciences University of Tokyo)
On the restrictions of supercuspidal representations for inner forms of GL_N
[ Reference URL ]
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