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Seminar information archive
Seminar information archive ～07/06｜Today's seminar 07/07 | Future seminars 07/08～
2023/01/18
Number Theory Seminar
17:00-18:00 Hybrid
Kestutis Cesnavicius (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
Kestutis Cesnavicius (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
[ Abstract ]
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.
2023/01/17
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Chenghan Zha (The Univesity of Tokyo)
Integral structures in the local algebra of a singularity (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Chenghan Zha (The Univesity of Tokyo)
Integral structures in the local algebra of a singularity (ENGLISH)
[ Abstract ]
We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
[ Reference URL ]We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2023/01/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Osaka Metropolitan University)
Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Takayuki Koike (Osaka Metropolitan University)
Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
[ Abstract ]
Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
[ Reference URL ]Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
https://forms.gle/hYT2hVhDE3q1wDSh6
2023/01/13
Discrete mathematical modelling seminar
13:15-14:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
Andy Hone (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
[ Abstract ]
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.
2023/01/12
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Theory of fault-tolerant quantum computing II (Japanese)
Yasunari Suzuki (NTT)
Theory of fault-tolerant quantum computing II (Japanese)
[ Abstract ]
To demonstrate reliable quantum computing, we need to integrate
quantum error correction techniques and achieve fault-tolerant quantum
computing. In this seminar, I will explain the basics of fault-tolerant quantum
computing and recent progress toward its experimental realization.
To demonstrate reliable quantum computing, we need to integrate
quantum error correction techniques and achieve fault-tolerant quantum
computing. In this seminar, I will explain the basics of fault-tolerant quantum
computing and recent progress toward its experimental realization.
Lectures
16:00-17:00 Online
Prof. Yi-Hsuan Lin (National Yang Ming Chiao Tung University, Taiwan)
The Calder'on problem for nonlocal parabolic operators (English)
https://u-tokyo-ac-jp.zoom.us/j/82806510515?pwd=NEk1RDlMVEFOTEg4WE1MekRySlJpdz09
Prof. Yi-Hsuan Lin (National Yang Ming Chiao Tung University, Taiwan)
The Calder'on problem for nonlocal parabolic operators (English)
[ Abstract ]
We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder'on problems, respectively.
This is a joint work with Ching-Lung Lin and Gunther Uhlmann.
[ Reference URL ]We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder'on problems, respectively.
This is a joint work with Ching-Lung Lin and Gunther Uhlmann.
https://u-tokyo-ac-jp.zoom.us/j/82806510515?pwd=NEk1RDlMVEFOTEg4WE1MekRySlJpdz09
2023/01/11
Discrete mathematical modelling seminar
13:15-16:45 Room #056 (Graduate School of Math. Sci. Bldg.)
Joe Harrow (University of Kent) 13:15-14:45
Determinantal expressions for Ohyama polynomials (English)
Discrete dynamics, continued fractions and hyperelliptic curves (English)
Joe Harrow (University of Kent) 13:15-14:45
Determinantal expressions for Ohyama polynomials (English)
[ Abstract ]
The Ohyama polynomials provide algebraic solutions of the D7 case of the Painleve III equation at a particular sequence of parameter values. It is known that many special function solutions of Painleve equations are expressed in terms of tau functions that can be written in the form of determinants, but until now such a representation for the Ohyama polynomials was not known. Here we present two different determinantal formulae for these polynomials: the first, in terms of Wronskian determinants related to a Darboux transformation for a Lax pair of KdV type; and the second, in terms of Hankel determinants, which is related to the Toda lattice. If time permits, then connections with orthogonal polynomials, and with the recent Riemann-Hilbert approach of Buckingham & Miller, will briefly be mentioned.
Andy Hone (University of Kent) 15:15-16:45The Ohyama polynomials provide algebraic solutions of the D7 case of the Painleve III equation at a particular sequence of parameter values. It is known that many special function solutions of Painleve equations are expressed in terms of tau functions that can be written in the form of determinants, but until now such a representation for the Ohyama polynomials was not known. Here we present two different determinantal formulae for these polynomials: the first, in terms of Wronskian determinants related to a Darboux transformation for a Lax pair of KdV type; and the second, in terms of Hankel determinants, which is related to the Toda lattice. If time permits, then connections with orthogonal polynomials, and with the recent Riemann-Hilbert approach of Buckingham & Miller, will briefly be mentioned.
Discrete dynamics, continued fractions and hyperelliptic curves (English)
[ Abstract ]
After reviewing some standard facts about continued fractions for quadratic irrationals, we switch from the real numbers to the field of Laurent series, and describe some classical and more recent results on continued fraction expansions for the square root of an even degree polynomial, and other functions defined on the associated hyperelliptic curve. In the latter case, we extend results of van der Poorten on continued fractions of Jacobi type (J-fractions), and explain the connection with a family of discrete integrable systems (including Quispel-Roberts-Thompson maps and Somos sequences), orthogonal polynomials, and the Toda lattice. If time permits, we will make some remarks on current work with John Roberts and Pol Vanhaecke, concerning expansions involving the square root of an odd degree polynomial, Stieltjes continued fractions, and the Volterra lattice.
After reviewing some standard facts about continued fractions for quadratic irrationals, we switch from the real numbers to the field of Laurent series, and describe some classical and more recent results on continued fraction expansions for the square root of an even degree polynomial, and other functions defined on the associated hyperelliptic curve. In the latter case, we extend results of van der Poorten on continued fractions of Jacobi type (J-fractions), and explain the connection with a family of discrete integrable systems (including Quispel-Roberts-Thompson maps and Somos sequences), orthogonal polynomials, and the Toda lattice. If time permits, we will make some remarks on current work with John Roberts and Pol Vanhaecke, concerning expansions involving the square root of an odd degree polynomial, Stieltjes continued fractions, and the Volterra lattice.
2023/01/10
Algebraic Geometry Seminar
10:30-12:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
Akihiro Higashitani (Osaka/Dept. of Inf. )
Toric Fano varieties arising from posets and their combinatorial mutation equivalence (日本語)
Akihiro Higashitani (Osaka/Dept. of Inf. )
Toric Fano varieties arising from posets and their combinatorial mutation equivalence (日本語)
[ Abstract ]
In 1986, Stanley introduced two polytopes arising from posets, called order polytopes and chain polytopes. Since then, those polytopes have been studied from viewpoints of combinatorics. Projective toric varieties arising from order polytopes are called Hibi toric varieties in these days. On the other hand, combinatorial mutations were introduced by Akhtar-Coates-Galkin-Kasprzyk in 2012 in the context of the classification problem of Fano varieties using mirror symmetry.
In this talk, after surveying two poset polytopes and combinatorial mutations, we discuss the combinatorial mutation equivalence of two poset polytopes. Those equivalence implies qG-deformation equivalence of projective toric varieties arising from two poset polytopes.
Moreover, it turns out that order polytopes, chain polytopes and their intermediate polytopes correspond to some toric Fano varieties.
In 1986, Stanley introduced two polytopes arising from posets, called order polytopes and chain polytopes. Since then, those polytopes have been studied from viewpoints of combinatorics. Projective toric varieties arising from order polytopes are called Hibi toric varieties in these days. On the other hand, combinatorial mutations were introduced by Akhtar-Coates-Galkin-Kasprzyk in 2012 in the context of the classification problem of Fano varieties using mirror symmetry.
In this talk, after surveying two poset polytopes and combinatorial mutations, we discuss the combinatorial mutation equivalence of two poset polytopes. Those equivalence implies qG-deformation equivalence of projective toric varieties arising from two poset polytopes.
Moreover, it turns out that order polytopes, chain polytopes and their intermediate polytopes correspond to some toric Fano varieties.
Lectures
16:00-17:00 Online
Professor Salah-Eddine CHORFI (Cadi Ayyad University, Faculty of Sciences, Morocco)
Logarithmic convexity of semigroups and inverse problems for parabolic equations (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
Professor Salah-Eddine CHORFI (Cadi Ayyad University, Faculty of Sciences, Morocco)
Logarithmic convexity of semigroups and inverse problems for parabolic equations (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Takeru Asaka (The Univesity of Tokyo)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takeru Asaka (The Univesity of Tokyo)
Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
[ Abstract ]
Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
[ Reference URL ]Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Seminar on Probability and Statistics
10:50-11:30 Room # (Graduate School of Math. Sci. Bldg.)
井口優雅 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
井口優雅 (University College London)
Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions
[ Abstract ]
Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
[ Reference URL ]Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
(現地参加) https://forms.gle/qwssLccVgsAWcfps7 (Zoom参加) (1/8迄) https://docs.google.com/forms/d/e/1FAIpQLSe7OYeMDfaZ7pTLO42k43Tn5dWKpsyw
2023/01/04
Number Theory Seminar
17:00-18:00 Hybrid
Kazuhiro Ito (The University of Tokyo, Kavli IPMU)
G-displays over prisms and deformation theory (Japanese)
Kazuhiro Ito (The University of Tokyo, Kavli IPMU)
G-displays over prisms and deformation theory (Japanese)
[ Abstract ]
The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.
The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.
Lectures
17:00-18:00 Online
Professor Debora Presti (Messina University)
On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09
Professor Debora Presti (Messina University)
On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09
2022/12/27
Lectures
16:00-17:00 Online
Professor Salah-Eddine CHORFI (Cadi Ayyad University, Faculty of Sciences, Morocco)
Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
Professor Salah-Eddine CHORFI (Cadi Ayyad University, Faculty of Sciences, Morocco)
Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09
2022/12/22
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasunari Suzuki (NTT)
Theory of fault-tolerant quantum computing I (Japanese)
Yasunari Suzuki (NTT)
Theory of fault-tolerant quantum computing I (Japanese)
[ Abstract ]
To demonstrate reliable quantum computing, we need to integrate quantum error correction techniques and achieve fault-tolerant quantum computing. In this seminar, I will explain the basic of fault-tolerant quantum computing and recent progress towards its experimental realization.
To demonstrate reliable quantum computing, we need to integrate quantum error correction techniques and achieve fault-tolerant quantum computing. In this seminar, I will explain the basic of fault-tolerant quantum computing and recent progress towards its experimental realization.
2022/12/21
Algebraic Geometry Seminar
13:00-14:00 or 14:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
The room is different from the usual place. This is a joint seminar with Kyoto University.
Hsueh-Yung Lin (NTU)
Towards a geometric origin of the dynamical filtrations (English)
The room is different from the usual place. This is a joint seminar with Kyoto University.
Hsueh-Yung Lin (NTU)
Towards a geometric origin of the dynamical filtrations (English)
[ Abstract ]
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.
2022/12/20
Algebraic Geometry Seminar
9:30-10:30 Room #オンラインZoom (Graduate School of Math. Sci. Bldg.)
Takumi Murayama (Purdue)
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)
Takumi Murayama (Purdue)
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)
[ Abstract ]
In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.
In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.
In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.
In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.
Tuesday Seminar of Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
KATAOKA Kiyoomi (The University of Tokyo)
A commentary on J. Boman's recent two related results about the support of a distribution and its analyticity, and a special relationship between Radon transformations and ellipsoidal regions (Japanese)
https://forms.gle/BpciRTzKh9FPUV8D7
KATAOKA Kiyoomi (The University of Tokyo)
A commentary on J. Boman's recent two related results about the support of a distribution and its analyticity, and a special relationship between Radon transformations and ellipsoidal regions (Japanese)
[ Abstract ]
Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
[ Reference URL ]Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
https://forms.gle/BpciRTzKh9FPUV8D7
Operator Algebra Seminars
16:45-18:15 Online
Yosuke Kubota (Shinshu Univ.)
Band width and the Rosenberg index
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yosuke Kubota (Shinshu Univ.)
Band width and the Rosenberg index
[ Abstract ]
Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.
In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.
[ Reference URL ]Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.
In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2022/12/13
Algebraic Geometry Seminar
10:30-11:30 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
The speaker will give his talk by Zoom
山岸亮 (NTU)
Moduli of G-constellations and crepant resolutions (日本語)
The speaker will give his talk by Zoom
山岸亮 (NTU)
Moduli of G-constellations and crepant resolutions (日本語)
[ Abstract ]
For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.
For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.
Operator Algebra Seminars
16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
Entropy in QFT
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Feng Xu (UC Riverside)
Entropy in QFT
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:30-18:30 Online
Pre-registration required. See our seminar webpage.
Kota Hattori (Keio University)
Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kota Hattori (Keio University)
Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
[ Abstract ]
In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
[ Reference URL ]In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Tuesday Seminar of Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
TADANO Yukihide (Tokyo University of Science)
Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)
https://forms.gle/CRha8hydEuXzh71S7
TADANO Yukihide (Tokyo University of Science)
Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)
[ Abstract ]
We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).
[ Reference URL ]We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).
https://forms.gle/CRha8hydEuXzh71S7
2022/12/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takahiro Inayama (Tokyo University of Science)
$L^2$-extension index and its applications (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Takahiro Inayama (Tokyo University of Science)
$L^2$-extension index and its applications (Japanese)
[ Abstract ]
In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.
[ Reference URL ]In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022/12/08
Information Mathematics Seminar
16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)
Suguru Endo (NTT)
Near-term quantum algorithms and quantum error mitigation (Japanese)
Suguru Endo (NTT)
Near-term quantum algorithms and quantum error mitigation (Japanese)
[ Abstract ]
The current or near-term quantum computing devices are still small and noisy. In this talk, I will near-term quantum algorithms and quantum error mitigation for improving computation accuracy.
The current or near-term quantum computing devices are still small and noisy. In this talk, I will near-term quantum algorithms and quantum error mitigation for improving computation accuracy.
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