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Seminar information archive
Seminar information archive ～04/22｜Today's seminar 04/23 | Future seminars 04/24～
2023/06/23
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Kohsuke Shibata (Tokyo Denki University)
Minimal log discrepnacies for quotient singularities
Kohsuke Shibata (Tokyo Denki University)
Minimal log discrepnacies for quotient singularities
[ Abstract ]
In this talk, I will discuss recent joint work with Yusuke Nakamura on minimal log discrepancies for quotient singularities. The minimal log discrepancy is an important invariant of singularities in birational geometry. The denominator of the minimal log discrepancy of a variety depends on the Gorenstein index. On the other hand, Shokurov conjectured that the Gorenstein index of a Q-Gorenstein germ can be bounded in terms of its dimension and minimal log discrepancy. In this talk, I will explain basic properties for quotient singularities and show Shokurov's index conjecture for quotient singularities.
In this talk, I will discuss recent joint work with Yusuke Nakamura on minimal log discrepancies for quotient singularities. The minimal log discrepancy is an important invariant of singularities in birational geometry. The denominator of the minimal log discrepancy of a variety depends on the Gorenstein index. On the other hand, Shokurov conjectured that the Gorenstein index of a Q-Gorenstein germ can be bounded in terms of its dimension and minimal log discrepancy. In this talk, I will explain basic properties for quotient singularities and show Shokurov's index conjecture for quotient singularities.
2023/06/22
Applied Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Jiwoong Jang (University of Wisconsin Madison)
Convergence rate of periodic homogenization of forced mean curvature flow of graphs in the laminar setting (English)
https://forms.gle/BTuFtcmUVnvCLieX9
Jiwoong Jang (University of Wisconsin Madison)
Convergence rate of periodic homogenization of forced mean curvature flow of graphs in the laminar setting (English)
[ Abstract ]
Mean curvature flow with a forcing term models the motion of a phase boundary through media with defects and heterogeneities. When the environment shows periodic patterns with small oscillations, an averaged behavior is exhibited as we zoom out, and providing mathematical treatment for the behavior has received a great attention recently. In this talk, we discuss the periodic homogenization of forced mean curvature flows, and we give a quantitative analysis for the flow starting from an entire graph in a laminated environment.
[ Reference URL ]Mean curvature flow with a forcing term models the motion of a phase boundary through media with defects and heterogeneities. When the environment shows periodic patterns with small oscillations, an averaged behavior is exhibited as we zoom out, and providing mathematical treatment for the behavior has received a great attention recently. In this talk, we discuss the periodic homogenization of forced mean curvature flows, and we give a quantitative analysis for the flow starting from an entire graph in a laminated environment.
https://forms.gle/BTuFtcmUVnvCLieX9
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
Lattice-based cryptography (Japanese)
Tatsuaki Okamoto (NTT)
Lattice-based cryptography (Japanese)
[ Abstract ]
Explanation of lattice-based cryptography
Explanation of lattice-based cryptography
2023/06/21
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Stefan Reppen (Stockholm University)
On moduli of principal bundles under non-connected reductive groups (英語)
Stefan Reppen (Stockholm University)
On moduli of principal bundles under non-connected reductive groups (英語)
[ Abstract ]
Let $C$ be a smooth, connected projective curve over an algebraically closed field $k$ of characteristic 0, and let $G$ be a non-connected reductive group over $k$. I will explain how to decompose the stack of $G$-bundles $\text{Bun}_G$ into open and closed substacks $X_i$ which admits finite torsors $\text{Bun}_{\mathcal{G}_i} \to X_i$, for some connected reductive group schemes $\mathcal{G}_i$ over $C$. I explain how to use this to obtain a projective good moduli space of semistable $G$-bundles over $C$, for a suitable notion of semistability. Finally, after stating a result concerning finite subgroups of connected reductive groups over $k$, I explain how to see that essentially finite $H$-bundles are not dense in the moduli space of semistable degree 0 $H$-bundles, for any connected reductive group $H$ not equal to a torus.
Let $C$ be a smooth, connected projective curve over an algebraically closed field $k$ of characteristic 0, and let $G$ be a non-connected reductive group over $k$. I will explain how to decompose the stack of $G$-bundles $\text{Bun}_G$ into open and closed substacks $X_i$ which admits finite torsors $\text{Bun}_{\mathcal{G}_i} \to X_i$, for some connected reductive group schemes $\mathcal{G}_i$ over $C$. I explain how to use this to obtain a projective good moduli space of semistable $G$-bundles over $C$, for a suitable notion of semistability. Finally, after stating a result concerning finite subgroups of connected reductive groups over $k$, I explain how to see that essentially finite $H$-bundles are not dense in the moduli space of semistable degree 0 $H$-bundles, for any connected reductive group $H$ not equal to a torus.
2023/06/20
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.
Arnaud Maret (Sorbonne Université)
Moduli spaces of triangle chains (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Arnaud Maret (Sorbonne Université)
Moduli spaces of triangle chains (ENGLISH)
[ Abstract ]
In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.
[ Reference URL ]In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/06/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nobuhiro Honda (Tokyo University of Technology)
A new construction method for 3-dimensional indefinite Zoll manifolds
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Nobuhiro Honda (Tokyo University of Technology)
A new construction method for 3-dimensional indefinite Zoll manifolds
[ Abstract ]
The Penrose correspondence gives correspondences between special geometric structures on manifolds and complex manifolds, one of which is between Einstein-Weyl structures on 3-manifolds and complex surfaces. The latter complex surfaces are called mini-Twister spaces. In this talk, I will show that compact mini-Zeister spaces can be constructed in a natural way from hyperelliptic curves of arbitrary species, and that the resulting 3-manifolds have a remarkable geometric property called the Zoll property, which means that all geodesics are closed. A typical example is a sphere. The three-dimensional Einstein-Weyl manifold obtained in this study is indefinite, and the geodesics considered are spatial. These Einstein-Weyl manifolds can be regarded as generalizations of those given in arXiv:2208.13567.
Translated with www.DeepL.com/Translator (free version)
[ Reference URL ]The Penrose correspondence gives correspondences between special geometric structures on manifolds and complex manifolds, one of which is between Einstein-Weyl structures on 3-manifolds and complex surfaces. The latter complex surfaces are called mini-Twister spaces. In this talk, I will show that compact mini-Zeister spaces can be constructed in a natural way from hyperelliptic curves of arbitrary species, and that the resulting 3-manifolds have a remarkable geometric property called the Zoll property, which means that all geodesics are closed. A typical example is a sphere. The three-dimensional Einstein-Weyl manifold obtained in this study is indefinite, and the geodesics considered are spatial. These Einstein-Weyl manifolds can be regarded as generalizations of those given in arXiv:2208.13567.
Translated with www.DeepL.com/Translator (free version)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/06/15
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
Cryptosystems based on elliptic curves (Japanese)
Tatsuaki Okamoto (NTT)
Cryptosystems based on elliptic curves (Japanese)
[ Abstract ]
Explanation of crypto-systems based on elliptic curves
Explanation of crypto-systems based on elliptic curves
2023/06/14
Algebraic Geometry Seminar
14:00-15:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Wenliang Zhang (University of Illinois Chicago)
Vanishing of local cohomology modules
Wenliang Zhang (University of Illinois Chicago)
Vanishing of local cohomology modules
[ Abstract ]
Studying the vanishing of local cohomology modules has a long and rich history, and is still an active research area. In this talk, we will discuss classic theorems (due to Grothendieck, Hartshorne, Peskine-Szpiro, and Ogus), recent developments, and some open problems.
Studying the vanishing of local cohomology modules has a long and rich history, and is still an active research area. In this talk, we will discuss classic theorems (due to Grothendieck, Hartshorne, Peskine-Szpiro, and Ogus), recent developments, and some open problems.
2023/06/13
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Kan Kitamura (Univ. Tokyo)
Around homogeneous spaces of complex semisimple quantum groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Kan Kitamura (Univ. Tokyo)
Around homogeneous spaces of complex semisimple quantum groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Shunsuke Usuki (Kyoto University)
On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shunsuke Usuki (Kyoto University)
On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)
[ Abstract ]
Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.
[ Reference URL ]Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (The University of Tokyo)
Examples of discrete branching laws of derived functor modules (Japanese)
Yoshiki Oshima (The University of Tokyo)
Examples of discrete branching laws of derived functor modules (Japanese)
[ Abstract ]
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.
2023/06/08
Information Mathematics Seminar
16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuaki Okamoto (NTT)
Security, construction and proof of digital signatures (Japanese)
Tatsuaki Okamoto (NTT)
Security, construction and proof of digital signatures (Japanese)
[ Abstract ]
Explanation of security, construction and proof of digital signatures
Explanation of security, construction and proof of digital signatures
Discrete mathematical modelling seminar
18:15-19:15 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andy Hone (University of Kent)
Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andy Hone (University of Kent)
Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)
[ Abstract ]
Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.
Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.
2023/06/07
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Fuetaro Yobuko (Nagoya University)
Quasi-F-splitting and Hodge-Witt
Fuetaro Yobuko (Nagoya University)
Quasi-F-splitting and Hodge-Witt
[ Abstract ]
Quasi-F-splitting is an extension of F-splitting, which is defined for schemes in positive characteristic. On the other hand, Hodge-Wittness is defined for smooth proper schemes over a perfect field using the de Rham-Witt complex and ordinarity implies Hodge-Wittness. In this talk, I will explain (unexpected) relations between F-split/quasi-F-split and ordinary/Hodge-Witt via examples and properties.
Quasi-F-splitting is an extension of F-splitting, which is defined for schemes in positive characteristic. On the other hand, Hodge-Wittness is defined for smooth proper schemes over a perfect field using the de Rham-Witt complex and ordinarity implies Hodge-Wittness. In this talk, I will explain (unexpected) relations between F-split/quasi-F-split and ordinary/Hodge-Witt via examples and properties.
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Hirofumi Yamamoto (The University of Tokyo)
On the dimension of spaces of p-ordinary half-integral weight Siegel modular forms
of degree 2 (日本語)
Hirofumi Yamamoto (The University of Tokyo)
On the dimension of spaces of p-ordinary half-integral weight Siegel modular forms
of degree 2 (日本語)
[ Abstract ]
Hecke eigenforms whose eigenvalues at $p$ are $p$-adic units are called $p$-ordinary. The dimension of the spaces spanned by $p$-ordinary Siegel modular eigenforms is known to be bounded regardless of the power of $p$ of levels and weights. Furthermore, Hida showed that the degree is bounded in the case of half-integral weight modular forms, using the Shimura correspondence. In this talk, I will explain that a similar result holds for half-integral weight $p$-ordinary Siegel modular forms of degree 2. Let $F$ be a $p$-ordinary Hecke eigen cuspform, and $\pi_F$ be the corresponding cuspidal representation of $Mp_4(\mathbb{A}_\mathbb{Q})$. Then the weight of $F$ determines the Hecke eigenvalue of $\pi_F$ at $p$. Therefore, we can relate $F$ to $p$-ordinary integral weight Siegel modular forms or elliptic modular forms by using the local theta correspondence and the method of Ishimoto(Ibukiyama conjecture).
Hecke eigenforms whose eigenvalues at $p$ are $p$-adic units are called $p$-ordinary. The dimension of the spaces spanned by $p$-ordinary Siegel modular eigenforms is known to be bounded regardless of the power of $p$ of levels and weights. Furthermore, Hida showed that the degree is bounded in the case of half-integral weight modular forms, using the Shimura correspondence. In this talk, I will explain that a similar result holds for half-integral weight $p$-ordinary Siegel modular forms of degree 2. Let $F$ be a $p$-ordinary Hecke eigen cuspform, and $\pi_F$ be the corresponding cuspidal representation of $Mp_4(\mathbb{A}_\mathbb{Q})$. Then the weight of $F$ determines the Hecke eigenvalue of $\pi_F$ at $p$. Therefore, we can relate $F$ to $p$-ordinary integral weight Siegel modular forms or elliptic modular forms by using the local theta correspondence and the method of Ishimoto(Ibukiyama conjecture).
2023/06/06
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Maria Stella Adamo (Univ. Tokyo)
Wightman fields and their construction for a class of 2D CFTs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Maria Stella Adamo (Univ. Tokyo)
Wightman fields and their construction for a class of 2D CFTs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Hideyuki Azegami (Nagoya Industrial Science Research Institute)
Relation between regularity and numerical solutions of shape optimization problems
(Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Hideyuki Azegami (Nagoya Industrial Science Research Institute)
Relation between regularity and numerical solutions of shape optimization problems
(Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Tuesday Seminar of Analysis
17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Erik Skibsted (Aarhus University)
Stationary completeness; the many-body short-range case (English)
https://forms.gle/kWHDfb6J6kcjfSah8
Erik Skibsted (Aarhus University)
Stationary completeness; the many-body short-range case (English)
[ Abstract ]
For a general class of many-body Schr\"odinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. In fact this holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Derezi\'nski-Enss type. For short-range models we improve on the known \emph{weak continuity} statements in that we show that all non-threshold energies are \emph{stationary complete}, resolving in this case a recent conjecture. A consequence is that the above scattering quantities depend \emph{strongly continuously} on the energy parameter at all non-threshold energies (whence not only almost everywhere as previously demonstrated). Another consequence is that the scattering matrix is unitary at any such energy. Our procedure yields (as a side result) a new and purely stationary proof of asymptotic completeness for many-body short-range systems.
[ Reference URL ]For a general class of many-body Schr\"odinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. In fact this holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Derezi\'nski-Enss type. For short-range models we improve on the known \emph{weak continuity} statements in that we show that all non-threshold energies are \emph{stationary complete}, resolving in this case a recent conjecture. A consequence is that the above scattering quantities depend \emph{strongly continuously} on the energy parameter at all non-threshold energies (whence not only almost everywhere as previously demonstrated). Another consequence is that the scattering matrix is unitary at any such energy. Our procedure yields (as a side result) a new and purely stationary proof of asymptotic completeness for many-body short-range systems.
https://forms.gle/kWHDfb6J6kcjfSah8
Lie Groups and Representation Theory
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures
(Japanese)
Joint with Tuesday Seminar on Topology
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures
(Japanese)
[ Abstract ]
Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.
This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.
This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
Tuesday Seminar on Topology
17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures (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.
Atsumu Sasaki (Tokai University)
Visible actions on reductive spherical homogeneous spaces and their invariant measures (JAPANESE)
[ Abstract ]
Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property. This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
[ Reference URL ]Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property. This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.
In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/06/05
Colloquium
15:30-16:30 Online
Curtis T McMullen (Harvard University)
Billiards and Moduli Spaces (ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD
Curtis T McMullen (Harvard University)
Billiards and Moduli Spaces (ENGLISH)
[ Abstract ]
The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.
In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.
A variety of open problems will be mentioned along the way.
[ Reference URL ]The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.
In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.
A variety of open problems will be mentioned along the way.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD
Tokyo Probability Seminar
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
福山克司 (神戸大学)
大きな公比を持つ等比数列の差異量の重複対数の法則について (日本語)
福山克司 (神戸大学)
大きな公比を持つ等比数列の差異量の重複対数の法則について (日本語)
2023/05/31
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Daichi Takeuchi (RIKEN)
Quadratic $\ell$-adic sheaf and its Heisenberg group (日本語)
Daichi Takeuchi (RIKEN)
Quadratic $\ell$-adic sheaf and its Heisenberg group (日本語)
[ Abstract ]
Quadratic Gauss sums are usually defined only for finite fields of odd characteristic. However, it is known that there is a reformulation in which one can uniformly treat the case of even characteristic. In this talk, I will introduce a new class of $\ell$-adic sheaf, which I call quadratic sheaf. This is a sheaf-theoretic enhancement of the reformulation of quadratic Gauss sum, in the sense of the function-sheaf dictionary. After explaining its cohomological properties and consequences, such as a version of Hasse-Davenport relation, I will show that a certain finite Heisenberg group naturally acts on a quadratic sheaf. I will also report various results that can be deduced from this action.
Quadratic Gauss sums are usually defined only for finite fields of odd characteristic. However, it is known that there is a reformulation in which one can uniformly treat the case of even characteristic. In this talk, I will introduce a new class of $\ell$-adic sheaf, which I call quadratic sheaf. This is a sheaf-theoretic enhancement of the reformulation of quadratic Gauss sum, in the sense of the function-sheaf dictionary. After explaining its cohomological properties and consequences, such as a version of Hasse-Davenport relation, I will show that a certain finite Heisenberg group naturally acts on a quadratic sheaf. I will also report various results that can be deduced from this action.
2023/05/30
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.
Yuya Kodama (Tokyo Metropolitan University)
p-colorable subgroup of Thompson's group F (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yuya Kodama (Tokyo Metropolitan University)
p-colorable subgroup of Thompson's group F (JAPANESE)
[ Abstract ]
Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.
[ Reference URL ]Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (The University of Tokyo)
Discrete branching laws of derived functor modules (Japanese)
Yoshiki Oshima (The University of Tokyo)
Discrete branching laws of derived functor modules (Japanese)
[ Abstract ]
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In this talk, we would like to discuss how to obtain explicit branching formulas for some examples.
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In this talk, we would like to discuss how to obtain explicit branching formulas for some examples.
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