## Seminar information archive

Seminar information archive ～08/18｜Today's seminar 08/19 | Future seminars 08/20～

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Classification of Mukai pairs with corank 3 (English or Japanese)

**Akihiro Kanemitsu**(The University of Tokyo)Classification of Mukai pairs with corank 3 (English or Japanese)

[ Abstract ]

A Mukai pair $(X,E)$ is a pair of a Fano manifold $X$ and an ample vector bundle $E$ of rank $r$ on $X$ such that $c_1(X)=c_1(E)$. Study of such pairs was proposed by Mukai. It is known that, for a Mukai pair $(X,E)$, the rank $r$ of the bundle $E$ is at most $\dim X +1$, and Mukai conjectured the explicit

classification with $r \geq \dim X$. The above conjecture was solved independently by Fujita, Peternell and Ye-Zhang. Also the classification of Mukai pairs with $r= \dim X -1$ was given by Peternell-Szurek-Wi\'sniewski. In this talk I will give the classification of Mukai pairs with $r= \dim X -2$ and $\dim X \geq 5$.

A Mukai pair $(X,E)$ is a pair of a Fano manifold $X$ and an ample vector bundle $E$ of rank $r$ on $X$ such that $c_1(X)=c_1(E)$. Study of such pairs was proposed by Mukai. It is known that, for a Mukai pair $(X,E)$, the rank $r$ of the bundle $E$ is at most $\dim X +1$, and Mukai conjectured the explicit

classification with $r \geq \dim X$. The above conjecture was solved independently by Fujita, Peternell and Ye-Zhang. Also the classification of Mukai pairs with $r= \dim X -1$ was given by Peternell-Szurek-Wi\'sniewski. In this talk I will give the classification of Mukai pairs with $r= \dim X -2$ and $\dim X \geq 5$.

### 2017/10/06

#### Colloquium

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)

[ Reference URL ]

http://lab.twcu.ac.jp/miyachi/English.html

**Akihiko Miyachi**(Tokyo Woman's Christian University)Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)

[ Reference URL ]

http://lab.twcu.ac.jp/miyachi/English.html

### 2017/10/03

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Transitional geometry (ENGLISH)

**Athanase Papadopoulos**(IRMA, Université de Strasbourg)Transitional geometry (ENGLISH)

[ Abstract ]

I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.

I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.

### 2017/10/02

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to intermediate rank geometry (English)

**Mikael Pichot**(RIMS, Kyoto Univ./McGill Univ.)Introduction to intermediate rank geometry (English)

#### Seminar on Geometric Complex Analysis

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

The extension of holomorphic functions on a non-pluriharmonic locus

**Yusaku Tiba**(Ochanomizu University)The extension of holomorphic functions on a non-pluriharmonic locus

[ Abstract ]

Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. In this talk, we show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function on $\Omega$.

Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. In this talk, we show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function on $\Omega$.

### 2017/09/27

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Height functions for motives, Hodge analogues, and Nevanlinna analogues (ENGLISH)

**Kazuya Kato**(University of Chicago)Height functions for motives, Hodge analogues, and Nevanlinna analogues (ENGLISH)

[ Abstract ]

We compare height functions for (1) points of an algebraic variety over a number field, (2) motives over a number field, (3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field, (4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain. Usual Nevanlinna theory uses height functions for (5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study.

We compare height functions for (1) points of an algebraic variety over a number field, (2) motives over a number field, (3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field, (4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain. Usual Nevanlinna theory uses height functions for (5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study.

### 2017/09/26

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representations of Semisimple Lie Groups and Penrose Transform (JAPANESE)

**Hideko Sekiguchi**(The University of Tokyo)Representations of Semisimple Lie Groups and Penrose Transform (JAPANESE)

[ Abstract ]

The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds,

namely, that of positive $k$-planes and that of negative $k$-planes.

The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds,

namely, that of positive $k$-planes and that of negative $k$-planes.

#### Lie Groups and Representation Theory

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representations of Semisimple Lie Groups and Penrose Transform (Japanese)

**Hideko Sekiguchi**(The University of Tokyo)Representations of Semisimple Lie Groups and Penrose Transform (Japanese)

[ Abstract ]

The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.

The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.

I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.

To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.

Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.

### 2017/09/25

#### Seminar on Geometric Complex Analysis

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

Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties

**Christophe Mourougane**(Université de Rennes 1)Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties

[ Abstract ]

It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.

Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.

It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.

Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.

### 2017/09/11

#### Lectures

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

3D field theories with Chern-Simons term for large N in the Weyl gauge (ENGLISH)

**Jean Zinn-Justin**(CEA Saclay)3D field theories with Chern-Simons term for large N in the Weyl gauge (ENGLISH)

[ Abstract ]

ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.

We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.

We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.

Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.

ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.

We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.

We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.

Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.

### 2017/08/30

#### thesis presentations

10:00-11:15 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2017/08/25

#### thesis presentations

11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2017/08/23

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation

**Sebastian Holtz**(Humboldt University of Berlin)Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation

[ Abstract ]

In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.

In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.

### 2017/07/28

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Free orthogonal groups and quantum information

(English)

**Benoit Collins**(Kyoto Univ.)Free orthogonal groups and quantum information

(English)

#### thesis presentations

14:00-15:15 Room #128 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

15:45-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2017/07/25

#### thesis presentations

15:00-16:15 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2017/07/21

#### Colloquium of mathematical sciences and society

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

### 2017/07/18

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)

**Fuetaro Yobuko**(Tohoku University)On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)

[ Abstract ]

In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.

In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

(日本語)

**Tsuyoshi Yoneda**(University of Tokyo)(日本語)

### 2017/07/13

#### Applied Analysis

16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

### 2017/07/11

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Arithmetic and dynamical degrees of self-maps of algebraic varieties (English or Japanese)

**Yohsuke Matsuzawa**(The University of Tokyo)Arithmetic and dynamical degrees of self-maps of algebraic varieties (English or Japanese)

[ Abstract ]

The first dynamical degree is an important birational invariant which measures the geometric complexity of dominant rational self-maps of algebraic varieties. On the other hand, when the variety is defined over a number field, one can associate to an orbit an invariant using Weil height function, called arithmetic degree, which measures the arithmetic complexity of the orbit. It is conjectured that the arithmetic degree of a Zariski dense orbit is equal to the first dynamical degree (Kawaguchi-Silverman). I will explain several results related to this conjecture. I will also explain applications to proofs of purely geometric statements.

The first dynamical degree is an important birational invariant which measures the geometric complexity of dominant rational self-maps of algebraic varieties. On the other hand, when the variety is defined over a number field, one can associate to an orbit an invariant using Weil height function, called arithmetic degree, which measures the arithmetic complexity of the orbit. It is conjectured that the arithmetic degree of a Zariski dense orbit is equal to the first dynamical degree (Kawaguchi-Silverman). I will explain several results related to this conjecture. I will also explain applications to proofs of purely geometric statements.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Some remarkable quotients of virtual braid groups (ENGLISH)

**Celeste Damiani**(JSPS, Osaka City University)Some remarkable quotients of virtual braid groups (ENGLISH)

[ Abstract ]

Virtual braid groups are one of the most famous generalizations of braid groups. We introduce a family of quotients of virtual braid groups, called

Virtual braid groups are one of the most famous generalizations of braid groups. We introduce a family of quotients of virtual braid groups, called

*loop braid groups*. These groups have been an object of interest in different domains of mathematics and mathematical physics, and can be found in the literature also by names such as*groups of permutation-conjugacy automorphisms, braid- permutation groups, welded braid groups, weakly virtual braid groups, untwisted ring groups*, and others. We show that they share with braid groups the property of admitting many different definitions. After that we consider a further family of quotients called*unrestricted virtual braids*, describe their structure and explore their relations with fused links.#### thesis presentations

15:00-16:15 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2017/07/10

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Phase transitions in exponential random graphs (ENGLISH)

**Mei Yin**(University of Denver)Phase transitions in exponential random graphs (ENGLISH)

[ Abstract ]

Large networks have become increasingly popular over the last decades, and their modeling and investigation have led to interesting and new ways to apply statistical and analytical methods. The introduction of exponential random graphs has aided in this pursuit, as they are able to capture a wide variety of common network tendencies by representing a complex global structure through a set of tractable local features. This talk with focus on the phenomenon of phase transitions in large exponential random graphs. The main techniques that we use are variants of statistical physics but the exciting new theory of graph limits, which has rich ties to many parts of mathematics and beyond, also plays an important role in the interdisciplinary inquiry. Some open problems and conjectures will be presented.

Large networks have become increasingly popular over the last decades, and their modeling and investigation have led to interesting and new ways to apply statistical and analytical methods. The introduction of exponential random graphs has aided in this pursuit, as they are able to capture a wide variety of common network tendencies by representing a complex global structure through a set of tractable local features. This talk with focus on the phenomenon of phase transitions in large exponential random graphs. The main techniques that we use are variants of statistical physics but the exciting new theory of graph limits, which has rich ties to many parts of mathematics and beyond, also plays an important role in the interdisciplinary inquiry. Some open problems and conjectures will be presented.

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