## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

### 2023/01/11

#### Discrete mathematical modelling seminar

13:15-16:45 Room #056 (Graduate School of Math. Sci. Bldg.)

Determinantal expressions for Ohyama polynomials (English)

Discrete dynamics, continued fractions and hyperelliptic curves (English)

**Joe Harrow**(University of Kent) 13:15-14:45Determinantal 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.

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) 15:15-16:45Discrete 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.)

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

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.

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.)

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

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

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

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.)

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.

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.)

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.)

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

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

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.)

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.

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.)

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.)

$L^2$-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.)

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.

### 2022/12/06

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Equivariant covering spaces of quantum homogeneous spaces

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Mao Hoshino**(Univ. Tokyo)Equivariant covering spaces of quantum homogeneous spaces

[ 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.

Torsion in the abelianization of the Johnson kernel (ENGLISH)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Quentin Faes**(The Univesity of Tokyo)Torsion in the abelianization of the Johnson kernel (ENGLISH)

[ Abstract ]

The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.

[ Reference URL ]The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2022/12/05

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Shota Kikuchi**(National Institute of Technology, Suzuka College)On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)

[ Abstract ]

Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.

In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.

[ Reference URL ]Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.

In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.

https://forms.gle/hYT2hVhDE3q1wDSh6

#### Seminar on Probability and Statistics

14:40-15:50 Room # (Graduate School of Math. Sci. Bldg.)

A binary branching model with Moran-type interactions (English)

(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5

**Michael Choi**(National University of Singapore and Yale-NUS College)A binary branching model with Moran-type interactions (English)

[ Abstract ]

Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).

[ Reference URL ]Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).

(Zoom参加) 12/1締切https://docs.google.com/forms/d/e/1FAIpQLSdyluSozvNOGmDcXzGv496v2AQNiPePqIerLaBN9pD4wxEmnw/viewform (現地参加) 先着20名https://forms.gle/rS9rjhL2jXo6eGgt5

### 2022/12/01

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Quantum Computing and Cryptography (Japanese)

**Takashi Yamakawa**(NTT)Quantum Computing and Cryptography (Japanese)

[ Abstract ]

I explain several topics on quantum computing and cryptography including Shor’s algorithm for factoring and discrete logarithm, quantum money, and verification of quantum computation based on cryptography.

I explain several topics on quantum computing and cryptography including Shor’s algorithm for factoring and discrete logarithm, quantum money, and verification of quantum computation based on cryptography.

### 2022/11/30

#### Number Theory Seminar

17:00-18:00 Hybrid

The modularity of elliptic curves over some number fields (English)

**Xinyao Zhang**(University of Tokyo)The modularity of elliptic curves over some number fields (English)

[ Abstract ]

As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.

As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176 Next >