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Seminar information archive
Seminar information archive ～01/17｜Today's seminar 01/18 | Future seminars 01/19～
FJ-LMI Seminar
14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jonathan Ditlevsen (The University of Tokyo)
Symmetry breaking operators for the pair (GL(n+1,R), GL(n,R)) (英語)
https://fj-lmi.cnrs.fr/seminars/
Jonathan Ditlevsen (The University of Tokyo)
Symmetry breaking operators for the pair (GL(n+1,R), GL(n,R)) (英語)
[ Abstract ]
In this talk, we construct explicit symmetry breaking operators (SBOs) between principal series representations of the group GL(n+1,R) and its subgroup GL(n,R). Using Bernstein–Sato identities, we find a holomorphic renormalization of a meromorphic family of SBOs. Finally, we identify certain differential SBOs as residues of this holomorphic family.
[ Reference URL ]In this talk, we construct explicit symmetry breaking operators (SBOs) between principal series representations of the group GL(n+1,R) and its subgroup GL(n,R). Using Bernstein–Sato identities, we find a holomorphic renormalization of a meromorphic family of SBOs. Finally, we identify certain differential SBOs as residues of this holomorphic family.
https://fj-lmi.cnrs.fr/seminars/
2024/12/03
Tuesday Seminar on Topology
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Jun-ichi Inoguchi (Hokkaido University)
Surfaces in 3-dimensional spaces and Integrable systems (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jun-ichi Inoguchi (Hokkaido University)
Surfaces in 3-dimensional spaces and Integrable systems (JAPANESE)
[ Abstract ]
Surfaces of constant mean curvature in hyperbolic 3-space have different aspects depending on the value of mean curvature. In particular, the class of surfaces of constant mean curvature $H<1$ has no Euclidean or spherical correspondents. I would explain how to construct surface of constant mean curvature $H<1$ in hyperbolic 3-space by the method of Integrable Systems (joint work with Josef F. Dorfmeister and Shinpei Kobayashi).
[ Reference URL ]Surfaces of constant mean curvature in hyperbolic 3-space have different aspects depending on the value of mean curvature. In particular, the class of surfaces of constant mean curvature $H<1$ has no Euclidean or spherical correspondents. I would explain how to construct surface of constant mean curvature $H<1$ in hyperbolic 3-space by the method of Integrable Systems (joint work with Josef F. Dorfmeister and Shinpei Kobayashi).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Valerio Proietti (Univ. Oslo)
The rational K-theory of ample groupoids
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Valerio Proietti (Univ. Oslo)
The rational K-theory of ample groupoids
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/12/02
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (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.
Shouhei Honda (The University of Tokyo)
Weyl’s law with Ricci curvature bounded below
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Shouhei Honda (The University of Tokyo)
Weyl’s law with Ricci curvature bounded below
[ Abstract ]
Weyl’s law on a closed manifold gives an asymptotic behavior of eigenvalues of the Laplace operator in terms of the size of the manifold. It was conjectured by Luigi Ambrosio (Scuola Normale Superiore), David Tewodrose (Vrije Universiteit Brussel) and myself such that Weyl’s law is valid for Gromov-Hausdorff limit spaces with a restriction of Ricci curvature. A joint work with Xianzhe Dai (UC Santa Barbara), Jiayin Pan (UC Santa Cruz) and Guofang Wei
(UC Santa Barbara) disproved the conjecture. We will discuss about these topics in this talk.
Weyl’s law on a closed manifold gives an asymptotic behavior of eigenvalues of the Laplace operator in terms of the size of the manifold. It was conjectured by Luigi Ambrosio (Scuola Normale Superiore), David Tewodrose (Vrije Universiteit Brussel) and myself such that Weyl’s law is valid for Gromov-Hausdorff limit spaces with a restriction of Ricci curvature. A joint work with Xianzhe Dai (UC Santa Barbara), Jiayin Pan (UC Santa Cruz) and Guofang Wei
(UC Santa Barbara) disproved the conjecture. We will discuss about these topics in this talk.
2024/11/27
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yumiharu Nakano (Institute of Science Tokyo)
Schrödinger problems and diffusion generative models (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yumiharu Nakano (Institute of Science Tokyo)
Schrödinger problems and diffusion generative models (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
FJ-LMI Seminar
14:30-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (英語)
https://fj-lmi.cnrs.fr/seminars/
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (英語)
[ Abstract ]
I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
[ Reference URL ]I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
https://fj-lmi.cnrs.fr/seminars/
FJ-LMI Seminar
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups. (英語)
https://fj-lmi.cnrs.fr/seminars/
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups. (英語)
[ Abstract ]
Let $G = \exp \mathfrak g$ be a connected and simply connected real nilpotent Lie group with Lie algebra $\mathfrak g$, $H = \exp \mathfrak h$ an analytic subgroup of $G$ with Lie algebra $\mathfrak h$, $\chi$ a unitary character of $H$ and $\tau = \text{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as ${\chi}_f$, where $\chi_f(\exp X) = e^{if(X)} (X \in \mathfrak h)$ with a certain $f \in {\mathfrak g}^*$ verifying $f([\mathfrak h,\mathfrak h]) = \{0\}$. Let $S(\mathfrak g)$ be the symmetric algebra of $\mathfrak g$ and ${\mathfrak a}_{\tau} = \{X + \sqrt{-1}f(X) ; X \in \mathfrak h\}.$ We regard $S(\mathfrak g)$ as the algebra of polynomial functions on ${\mathfrak g}^*$ by $X(\ell) = \sqrt{-1}\ell(X)$ for $X \in \mathfrak g, \ell \in {\mathfrak g}^*$. Now, $S(\mathfrak g)$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\} = [X,Y]$ if $X, Y$ are in $\mathfrak g$. Let us consider the algebra $(S(\mathfrak g)/S(\mathfrak g)\overline{{\mathfrak a}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace ${\Gamma}_{\tau} = \{\ell \in {\mathfrak g}^* : \ell(X) = f(X), X \in \mathfrak h\}$ of ${\mathfrak g}^*$. This inherits the Poisson structure from $S(\mathfrak g)$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
[ Reference URL ]Let $G = \exp \mathfrak g$ be a connected and simply connected real nilpotent Lie group with Lie algebra $\mathfrak g$, $H = \exp \mathfrak h$ an analytic subgroup of $G$ with Lie algebra $\mathfrak h$, $\chi$ a unitary character of $H$ and $\tau = \text{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as ${\chi}_f$, where $\chi_f(\exp X) = e^{if(X)} (X \in \mathfrak h)$ with a certain $f \in {\mathfrak g}^*$ verifying $f([\mathfrak h,\mathfrak h]) = \{0\}$. Let $S(\mathfrak g)$ be the symmetric algebra of $\mathfrak g$ and ${\mathfrak a}_{\tau} = \{X + \sqrt{-1}f(X) ; X \in \mathfrak h\}.$ We regard $S(\mathfrak g)$ as the algebra of polynomial functions on ${\mathfrak g}^*$ by $X(\ell) = \sqrt{-1}\ell(X)$ for $X \in \mathfrak g, \ell \in {\mathfrak g}^*$. Now, $S(\mathfrak g)$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\} = [X,Y]$ if $X, Y$ are in $\mathfrak g$. Let us consider the algebra $(S(\mathfrak g)/S(\mathfrak g)\overline{{\mathfrak a}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace ${\Gamma}_{\tau} = \{\ell \in {\mathfrak g}^* : \ell(X) = f(X), X \in \mathfrak h\}$ of ${\mathfrak g}^*$. This inherits the Poisson structure from $S(\mathfrak g)$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
https://fj-lmi.cnrs.fr/seminars/
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Kaito Masuzawa (University of Tokyo)
On the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}$ and its inner form (Japanese)
Kaito Masuzawa (University of Tokyo)
On the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}$ and its inner form (Japanese)
[ Abstract ]
Let $F$ be a nonarchimedean local field. The local Jacquet-Langlands correspondence is the one-to-one correspondence of essential square integrable representations of $\mathrm{GL}_n(F)$ and its inner form. It is known that this correspondence satisfies the character relation and preserves the simple supercuspidality. We assume the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}(F)$ and irreducible admissible representations of its inner form which satisfies the character relation. This is expected to exist by a standard argument using the theory of stable trace formula. In this talk, we show the simple supercuspidality is preserved under this correspondence. In addition, we can parametrize simple supercuspidal representations and describe the correspondence explicitly.
Let $F$ be a nonarchimedean local field. The local Jacquet-Langlands correspondence is the one-to-one correspondence of essential square integrable representations of $\mathrm{GL}_n(F)$ and its inner form. It is known that this correspondence satisfies the character relation and preserves the simple supercuspidality. We assume the correspondence of simple supercuspidal representations of $\mathrm{GSp}_{2n}(F)$ and irreducible admissible representations of its inner form which satisfies the character relation. This is expected to exist by a standard argument using the theory of stable trace formula. In this talk, we show the simple supercuspidality is preserved under this correspondence. In addition, we can parametrize simple supercuspidal representations and describe the correspondence explicitly.
Lie Groups and Representation Theory
13:30-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI seminar
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups (English)
Joint with FJ-LMI seminar
Hidenori FUJIWARA (OCAMI, Kindai University)
Inductions and restrictions of unitary representations for exponential solvable Lie groups (English)
[ Abstract ]
Let $G=\exp{\mathfrak{g}}$ be a connected and simply connected real nilpotent Lie group with Lie algebra ${\mathfrak{g}}$, $H=\exp{\mathfrak{h}}$ an analytic subgroup of $G$ with Lie algebra ${\mathfrak{h}}$, $\chi$ a unitary character of $H$ and $\tau=\operatorname{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as $\chi_f$, where $\chi_f(\exp X)=e^{if(X)}$ $(X∈{\mathfrak{h}})$ with a certain $f∈{\mathfrak{g}}^{\ast}$ verifying $f([{\mathfrak{h}}, {\mathfrak{h}}])=\{0\}$. Let $S({\mathfrak{g}})$ be the symmetric algebra of ${\mathfrak{g}}$ and ${\mathfrak{a}}_{\tau}=\{X+\sqrt{-1} f(X) ; X∈{\mathfrak{h}}\}$. We regard $S({\mathfrak{g}})$ as the algebra of polynomial functions on ${\mathfrak{g}}^{\ast}$ by $X(\ell)=\sqrt{-1} \ell(X)$ for $X∈{\mathfrak{g}}$, $\ell ∈{\mathfrak{g}}^{\ast}$. Now, $S({\mathfrak{g}})$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\}=[X,Y]$ if $X$,$Y$ are in ${\mathfrak{g}}$. Let us consider the algebra $(S({\mathfrak{g}})/S({\mathfrak{g}})\overline{{\mathfrak{a}}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace $\Gamma_{\tau}=\{ℓ \in {\mathfrak{g}}^{\ast}:\ell(X)=f(X),X \in {\mathfrak{h}}\}$ of ${\mathfrak{g}}^{\ast}$. This inherits the Poisson structure from $S({\mathfrak{g}})$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
Let $G=\exp{\mathfrak{g}}$ be a connected and simply connected real nilpotent Lie group with Lie algebra ${\mathfrak{g}}$, $H=\exp{\mathfrak{h}}$ an analytic subgroup of $G$ with Lie algebra ${\mathfrak{h}}$, $\chi$ a unitary character of $H$ and $\tau=\operatorname{ind}_H^G \chi$ the monomial representation of $G$ induced from $\chi$. Let $D_{\tau}(G/H)$ be the algebra of the $G$-invariant differential operators on the line bundle over $G/H$ associated to the data $(H,\chi)$. We denote by $C_{\tau}$ the center of $D_{\tau}(G/H)$. We know that $\chi$ is written as $\chi_f$, where $\chi_f(\exp X)=e^{if(X)}$ $(X∈{\mathfrak{h}})$ with a certain $f∈{\mathfrak{g}}^{\ast}$ verifying $f([{\mathfrak{h}}, {\mathfrak{h}}])=\{0\}$. Let $S({\mathfrak{g}})$ be the symmetric algebra of ${\mathfrak{g}}$ and ${\mathfrak{a}}_{\tau}=\{X+\sqrt{-1} f(X) ; X∈{\mathfrak{h}}\}$. We regard $S({\mathfrak{g}})$ as the algebra of polynomial functions on ${\mathfrak{g}}^{\ast}$ by $X(\ell)=\sqrt{-1} \ell(X)$ for $X∈{\mathfrak{g}}$, $\ell ∈{\mathfrak{g}}^{\ast}$. Now, $S({\mathfrak{g}})$ possesses the Poisson structure $\{,\}$ well determined by the equality $\{X,Y\}=[X,Y]$ if $X$,$Y$ are in ${\mathfrak{g}}$. Let us consider the algebra $(S({\mathfrak{g}})/S({\mathfrak{g}})\overline{{\mathfrak{a}}_{\tau}})^H$ of the $H$-invariant polynomial functions on the affine subspace $\Gamma_{\tau}=\{ℓ \in {\mathfrak{g}}^{\ast}:\ell(X)=f(X),X \in {\mathfrak{h}}\}$ of ${\mathfrak{g}}^{\ast}$. This inherits the Poisson structure from $S({\mathfrak{g}})$. We denote by $Z_{\tau}$ its Poisson center. Michel Duflo asked: the two algebras $C_{\tau}$ and $Z_{\tau}$, are they isomorphic? Here we provide a positive answer to this question.
Lie Groups and Representation Theory
14:30-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Joint with FJ-LMI seminar
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (English)
Joint with FJ-LMI seminar
Ali BAKLOUTI (University of Sfax)
A proof of the Zariski closure conjecture for coadjoint orbits of exponential Lie groups (English)
[ Abstract ]
I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
I will begin by defining the Zariski Closure Conjecture for coadjoint orbits of exponential solvable Lie groups, examining some cases that have been solved, and addressing the ongoing challenges in resolving the conjecture fully. I will then introduce new approaches to explore the relationship between generating families of primitive ideals and the set of polynomials that vanish on the associated coadjoint orbits, ultimately aiming to advance toward a solution to the conjecture.
2024/11/26
Lectures
14:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Ohta (Arithmer Inc., Graduate School of Mathematical Sciences the University of Tokyo, The University of Tokyo Isotope Science Center)
社会に数学を活用するArithmerの活動
[ Reference URL ]
https://sgk2005.org/
Yoshihiro Ohta (Arithmer Inc., Graduate School of Mathematical Sciences the University of Tokyo, The University of Tokyo Isotope Science Center)
社会に数学を活用するArithmerの活動
[ Reference URL ]
https://sgk2005.org/
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Masaki Natori (The University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masaki Natori (The University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence (JAPANESE)
[ Abstract ]
The bulk-edge correspondence refers to the phenomenon typically found in topological insulators, where the topological restriction of the bulk (interior) determines the physical state, such as electric currents, at the edge (boundary). In this talk, we focus on the formulation by G. M. Graf and M. Porta and later by S. Hayashi and provide a new proof of bulk-edge correspondence. It is more direct compared to previous approaches. Behind the proof lies the Bott periodicity of K-theory. The proof of Bott periodicity has been approached from various perspectives. We provide a new proof of Bott periodicity. In the proof, we use Quot schemes in algebraic geometry as configuration spaces.
[ Reference URL ]The bulk-edge correspondence refers to the phenomenon typically found in topological insulators, where the topological restriction of the bulk (interior) determines the physical state, such as electric currents, at the edge (boundary). In this talk, we focus on the formulation by G. M. Graf and M. Porta and later by S. Hayashi and provide a new proof of bulk-edge correspondence. It is more direct compared to previous approaches. Behind the proof lies the Bott periodicity of K-theory. The proof of Bott periodicity has been approached from various perspectives. We provide a new proof of Bott periodicity. In the proof, we use Quot schemes in algebraic geometry as configuration spaces.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/25
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.
Leon Frober (Grand Valley State University)
Free energy and ground state of the spiked SSK spin-glass model
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Leon Frober (Grand Valley State University)
Free energy and ground state of the spiked SSK spin-glass model
[ Abstract ]
Spin-glasses are essentially mathematical models of particle interactions, and were originally describing magnetic states characterized by randomness in condensed matter physics. Due to the versatility of these types of models, however, they are now studied much more broadly for various complex systems such as statistical inference problems, weather/climate models or even neural networks. In this talk we will lay out the basic concepts of spin-glass models, while then focusing on the spiked SSK variant and its free energy as well as ground state energy. Furthermore we will discuss how one can determine these quantities including their lower order fluctuations with a so called "TAP approach" that was in this comprehensive form introduced in 2016 by N. Kistler and D. Belius, and what its benefits are compared to the earlier established "Parisi approach".
Spin-glasses are essentially mathematical models of particle interactions, and were originally describing magnetic states characterized by randomness in condensed matter physics. Due to the versatility of these types of models, however, they are now studied much more broadly for various complex systems such as statistical inference problems, weather/climate models or even neural networks. In this talk we will lay out the basic concepts of spin-glass models, while then focusing on the spiked SSK variant and its free energy as well as ground state energy. Furthermore we will discuss how one can determine these quantities including their lower order fluctuations with a so called "TAP approach" that was in this comprehensive form introduced in 2016 by N. Kistler and D. Belius, and what its benefits are compared to the earlier established "Parisi approach".
2024/11/22
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroshi Iritani (Kyoto University)
Quantum cohomology of blowups
Hiroshi Iritani (Kyoto University)
Quantum cohomology of blowups
[ Abstract ]
I will discuss a decomposition theorem for the quantum cohomology of a smooth projective variety blown up along a smooth subvariety. I will start with a general relationship between decomposition of quantum cohomology and extremal contractions, and then specialize to the case of blowups. Applications to birational geometry of this result have been announced by Katzarkov, Kontsevich, Pantev and Yu.
I will discuss a decomposition theorem for the quantum cohomology of a smooth projective variety blown up along a smooth subvariety. I will start with a general relationship between decomposition of quantum cohomology and extremal contractions, and then specialize to the case of blowups. Applications to birational geometry of this result have been announced by Katzarkov, Kontsevich, Pantev and Yu.
2024/11/19
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryosuke Sato (Chuo Univ.)
The quantum de Finetti theorem and operator-valued Martin boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryosuke Sato (Chuo Univ.)
The quantum de Finetti theorem and operator-valued Martin boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Operator Algebra Seminars
15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Roozbeh Hazrat (Western Sydney University)
Monoids, Dynamics and Leavitt path algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Roozbeh Hazrat (Western Sydney University)
Monoids, Dynamics and Leavitt path algebras
[ 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.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Bruno Scárdua (Federal University of Rio de Janeiro)
On real center singularities of complex vector fields on surfaces (ENGLISH)
[ Abstract ]
One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
[ Reference URL ]One of the various versions of the classical Lyapunov-Poincaré center theorem states that a nondegenerate real analytic center type planar vector field singularity admits an analytic first integral. In a more proof of this result, R. Moussu establishes important connection between this result and the theory of singularities of holomorphic foliations ([2]). In this paper we consider generalizations for two main frameworks: (i) planar real analytic vector fields with "many" periodic orbits near the singularity and
(ii) germs of holomorphic foliations having a suitable singularity in dimension two.
In this talk we discuss some versions of Poincaré-Lyapunov center theorem, including for the case of holomorphic vector fields. We also give some applications, hinting that there is much more to be explored in this framework.
References
[1] V. León, B. Scárdua, On a Theorem of Lyapunov-Poincaré in Higher Dimensions, July 2021, Arnold Mathematical Journal 7(3) DOI:10.1007/s40598-021-00183-x.
[2] R. Moussu: Une démonstration géométrique d’un théorème de Lyapunov-Poincaré. Astérisque, tome 98-99 (1982), p. 216-223.
[3] A. Lyapunov: Etude d’un cas particulier du problème de la stabilité du mouvement. Mat. Sbornik 17 (1893) pages 252-333 (Russe).
[4] H. Poincaré: Mémoire sur les courbes définies par une équation différentielle (I), Journal de mathématiques pures et appliquées 3e série, tome 7 (1881), p. 375-422.
[5] Minoru Urabe and Yasutaka Sibuya; On Center of Higher Dimensions; Journal of Science of the Hiroshima University, Ser. A, . Vol. 19, No. I, July, 1955.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/11/18
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/15
Colloquium
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
https://forms.gle/DcsJVYS4fvMLfPEM8
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
[ Abstract ]
Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
[ Reference URL ]Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
https://forms.gle/DcsJVYS4fvMLfPEM8
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Sho Tanimoto (Nagoya University)
The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto (Nagoya University)
The spaces of rational curves on del Pezzo surfaces via conic bundles
[ Abstract ]
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
2024/11/13
Lie Groups and Representation Theory
17:30-18:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Richard Stanley (MIT)
Some combinatorial aspects of cyclotomic polynomials
Richard Stanley (MIT)
Some combinatorial aspects of cyclotomic polynomials
[ Abstract ]
Euler showed that the number of partitions of n into distinct parts is equal to the number of partitions of n into odd parts. MacMahon showed that the number of partitions of n for which no part occurs exactly once is equal to the number of partitions of n into parts divisible by 2 or 3. Both these results are instances of a general phenomenon based on the fact that certain polynomials are the product of cyclotomic polynomials. After discussing this assertion, we explain how it can be extended to such topics as counting certain polynomials over finite fields and obtaining Dirichlet series generating functions for certain classes of integers.
Euler showed that the number of partitions of n into distinct parts is equal to the number of partitions of n into odd parts. MacMahon showed that the number of partitions of n for which no part occurs exactly once is equal to the number of partitions of n into parts divisible by 2 or 3. Both these results are instances of a general phenomenon based on the fact that certain polynomials are the product of cyclotomic polynomials. After discussing this assertion, we explain how it can be extended to such topics as counting certain polynomials over finite fields and obtaining Dirichlet series generating functions for certain classes of integers.
FJ-LMI Seminar
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
https://fj-lmi.cnrs.fr/seminars/
Stefano OLLA (Université de Paris Dauphine - PSL Research University)
Diffusive behaviour in extended completely integrable dynamics (英語)
[ Abstract ]
On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
[ Reference URL ]On a diffusive space-time scaling, density fluctuations behave very differently in extended completely integrable systems with respect to chaotic systems. I will expose some recent results concerning the one dimensional hard rods infinite dynamics and the box-ball cellular automata (an ultradiscretization of the KdV equation). Joint works with Pablo Ferrari, Makiko Sasada, Hayate Suda.
https://fj-lmi.cnrs.fr/seminars/
2024/11/12
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
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups (JAPANESE)
[ Abstract ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
[ Reference URL ]From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie Groups and Representation Theory
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
Joint with Tuesday Seminar on Topology
Junko Inoue (Tottori University)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
[ Abstract ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
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