## Seminar information archive

Seminar information archive ～01/18｜Today's seminar 01/19 | Future seminars 01/20～

#### FMSP Lectures

13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The topology of singular points of real analytic curves (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

**Etienne Ghys**(ENS de Lyon)The topology of singular points of real analytic curves (ENGLISH)

[ Abstract ]

In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

[ Reference URL ]In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

### 2018/02/22

#### FMSP Lectures

15:00-16:30 Room #117 (Graduate School of Math. Sci. Bldg.)

The topology of singular points of real analytic curves (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

**Etienne Ghys**(ENS de Lyon)The topology of singular points of real analytic curves (ENGLISH)

[ Abstract ]

In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

[ Reference URL ]In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

### 2018/02/21

#### FMSP Lectures

15:00-16:30 Room #117 (Graduate School of Math. Sci. Bldg.)

The topology of singular points of real analytic curves (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

**Etienne Ghys**(ENS de Lyon)The topology of singular points of real analytic curves (ENGLISH)

[ Abstract ]

In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

[ Reference URL ]In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

#### Tuesday Seminar on Topology

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

The category of bottom tangles in handlebodies, and the Kontsevich integral (ENGLISH)

**Gwénaël Massuyeau**(Université de Bourgogne)The category of bottom tangles in handlebodies, and the Kontsevich integral (ENGLISH)

[ Abstract ]

Habiro introduced the category B of « bottom tangles in handlebodies », which encapsulates the set of knots in the 3-sphere as well as the mapping class groups of 3-dimensional handlebodies. There is a natural filtration on the category B defined using an appropriate generalization of Vassiliev invariants. In this talk, we will show that the completion of B with respect to the Vassiliev filtration is isomorphic to a certain category A which can be defined either in a combinatorial way using « Jacobi diagrams », or by a universal property via the notion of « Casimir Hopf algebra ». Such an isomorphism will be obtained by extending the Kontsevich integral (originally defined as a knot invariant) to a functor Z from B to A. This functor Z can be regarded as a refinement of the TQFT-like functor derived from the LMO invariant and, if time allows, we will evoke the topological interpretation of the « tree-level » of Z. (This is based on joint works with Kazuo Habiro.)

Habiro introduced the category B of « bottom tangles in handlebodies », which encapsulates the set of knots in the 3-sphere as well as the mapping class groups of 3-dimensional handlebodies. There is a natural filtration on the category B defined using an appropriate generalization of Vassiliev invariants. In this talk, we will show that the completion of B with respect to the Vassiliev filtration is isomorphic to a certain category A which can be defined either in a combinatorial way using « Jacobi diagrams », or by a universal property via the notion of « Casimir Hopf algebra ». Such an isomorphism will be obtained by extending the Kontsevich integral (originally defined as a knot invariant) to a functor Z from B to A. This functor Z can be regarded as a refinement of the TQFT-like functor derived from the LMO invariant and, if time allows, we will evoke the topological interpretation of the « tree-level » of Z. (This is based on joint works with Kazuo Habiro.)

### 2018/02/19

#### Numerical Analysis Seminar

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Existence, multiplicity, and orbital stability for travelling waves in a nonlinearly supported beam (English)

**Michael Plum**(Karlsruhe Insitute of Technology)Existence, multiplicity, and orbital stability for travelling waves in a nonlinearly supported beam (English)

[ Abstract ]

For a nonlinear beam equation with exponential nonlinearity, we prove existence of at least 36 travelling wave solutions for the specific wave speed c=1.3. Our proof makes heavy use of computer assistance: starting from numerical approximations, we use a fixed point argument to prove existence of solutions "close to" the approximate ones. Furthermore we investigate the orbital stability of these solutions by making use of both analytical and computer-assisted techniques.

For a nonlinear beam equation with exponential nonlinearity, we prove existence of at least 36 travelling wave solutions for the specific wave speed c=1.3. Our proof makes heavy use of computer assistance: starting from numerical approximations, we use a fixed point argument to prove existence of solutions "close to" the approximate ones. Furthermore we investigate the orbital stability of these solutions by making use of both analytical and computer-assisted techniques.

#### Numerical Analysis Seminar

16:15-17:15 Room #056 (Graduate School of Math. Sci. Bldg.)

An approach to computer-assisted existence proofs for nonlinear space-time fractional parabolic problems (English)

**Kaori Nagatou**(Karlsruhe Insitute of Technology)An approach to computer-assisted existence proofs for nonlinear space-time fractional parabolic problems (English)

[ Abstract ]

We consider an initial boundary value problem for a space-time fractional parabolic equation, which includes the fractional Laplacian, i.e. a nonlocal operator. We treat a corresponding local problem which is obtained by the Caffarelli-Silvestre extension technique, and show how to enclose a solution of the extended problem by computer-assisted means.

We consider an initial boundary value problem for a space-time fractional parabolic equation, which includes the fractional Laplacian, i.e. a nonlocal operator. We treat a corresponding local problem which is obtained by the Caffarelli-Silvestre extension technique, and show how to enclose a solution of the extended problem by computer-assisted means.

### 2018/02/14

#### Operator Algebra Seminars

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

Index theory on the Mishchenko bundle (English)

**Valerio Proietti**(Copenhagen Univ.)Index theory on the Mishchenko bundle (English)

### 2018/02/06

#### Infinite Analysis Seminar Tokyo

15:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Sine-square deformation of one-dimensional critical systems (ENGLISH)

Modular invariant representations of the $N=2$ vertex operator superalgebra (ENGLISH)

**Hosho Katsura**(Department of Physics, Graduate School of Science, The Univeristy of Tokyo ) 15:00-16:00Sine-square deformation of one-dimensional critical systems (ENGLISH)

[ Abstract ]

Sine-square deformation (SSD) is one example of smooth boundary conditions that have significantly smaller finite-size effects than open boundary conditions. In a one-dimensional system with SSD, the interaction strength varies smoothly from the center to the edges according to the sine-square function. This means that the Hamiltonian of the system is inhomogeneous, as it lacks translational symmetry. Nevertheless, previous studies have revealed that the SSD leaves the ground state of the uniform chain with periodic boundary conditions (PBC) almost unchanged for critical systems. In particular, I showed in [1,2,3] that the correspondence is exact for critical XY and quantum Ising chains. The same correspondence between SSD and PBC holds for Dirac fermions in 1+1 dimension and a family of more general conformal field theories. If time permits, I will also introduce more recent results [4,5] and discuss the excited states of the SSD systems.

[1] H. Katsura, J. Phys. A: Math. Theor. 44, 252001 (2011).

[2] H. Katsura, J. Phys. A: Math. Theor. 45, 115003 (2012).

[3] I. Maruyama, H. Katsura, T. Hikihara, Phys. Rev. B 84, 165132 (2011).

[4] K. Okunishi and H. Katsura, J. Phys. A: Math. Theor. 48, 445208 (2015).

[5] S. Tamura and H. Katsura, Prog. Theor. Exp. Phys 2017, 113A01 (2017).

Sine-square deformation (SSD) is one example of smooth boundary conditions that have significantly smaller finite-size effects than open boundary conditions. In a one-dimensional system with SSD, the interaction strength varies smoothly from the center to the edges according to the sine-square function. This means that the Hamiltonian of the system is inhomogeneous, as it lacks translational symmetry. Nevertheless, previous studies have revealed that the SSD leaves the ground state of the uniform chain with periodic boundary conditions (PBC) almost unchanged for critical systems. In particular, I showed in [1,2,3] that the correspondence is exact for critical XY and quantum Ising chains. The same correspondence between SSD and PBC holds for Dirac fermions in 1+1 dimension and a family of more general conformal field theories. If time permits, I will also introduce more recent results [4,5] and discuss the excited states of the SSD systems.

[1] H. Katsura, J. Phys. A: Math. Theor. 44, 252001 (2011).

[2] H. Katsura, J. Phys. A: Math. Theor. 45, 115003 (2012).

[3] I. Maruyama, H. Katsura, T. Hikihara, Phys. Rev. B 84, 165132 (2011).

[4] K. Okunishi and H. Katsura, J. Phys. A: Math. Theor. 48, 445208 (2015).

[5] S. Tamura and H. Katsura, Prog. Theor. Exp. Phys 2017, 113A01 (2017).

**Ryo Sato**(Graduate School of Mathematical Sciences, The University of Tokyo) 16:30-17:30Modular invariant representations of the $N=2$ vertex operator superalgebra (ENGLISH)

[ Abstract ]

One of the most remarkable features in representation theory of a (``good'') vertex operator superalgebra (VOSA) is the modular invariance property of the characters. As an application of the property, M. Wakimoto and D. Adamovic proved that all the fusion rules for the simple $N=2$ VOSA of central charge $c_{p,1}=3(1-2/p)$ are computed from the modular $S$-matrix by the so-called Verlinde formula. In this talk, we present a new ``modular invariant'' family of irreducible highest weight modules over the simple $N=2$ VOSA of central charge $c_{p,p'}:=3(1-2p'/p)$. Here $(p,p')$ is a pair of coprime integers such that $p,p'>1$. In addition, we will discuss some generalization of the Verlinde formula in the spirit of Creutzig--Ridout.

One of the most remarkable features in representation theory of a (``good'') vertex operator superalgebra (VOSA) is the modular invariance property of the characters. As an application of the property, M. Wakimoto and D. Adamovic proved that all the fusion rules for the simple $N=2$ VOSA of central charge $c_{p,1}=3(1-2/p)$ are computed from the modular $S$-matrix by the so-called Verlinde formula. In this talk, we present a new ``modular invariant'' family of irreducible highest weight modules over the simple $N=2$ VOSA of central charge $c_{p,p'}:=3(1-2p'/p)$. Here $(p,p')$ is a pair of coprime integers such that $p,p'>1$. In addition, we will discuss some generalization of the Verlinde formula in the spirit of Creutzig--Ridout.

### 2018/02/04

#### Seminar on Probability and Statistics

12:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Nonlinear Economic Time Series Models

Analytic, representation and statistical aspects related to fractional Gaussian processes.

**Yukai Yang**(Uppsala University) 12:30-15:00Nonlinear Economic Time Series Models

[ Abstract ]

The lecture goes through several chapters in the book “Modelling Nonlinear Economic Time Series” by Teräsvirta, Tjøstheim and Granger in 2010. The lecture serves as an introduction for the students and researchers who are interested in this area. It introduces a number of examples of families of nonlinear time series parametric models in economic theory. It also talks about testing linearity against parametric alternatives with the presence of a characterization of the identification problem in many situations. Different ways of solving the identification problem are presented and their merits and disadvantages are discussed.

The lecture goes through several chapters in the book “Modelling Nonlinear Economic Time Series” by Teräsvirta, Tjøstheim and Granger in 2010. The lecture serves as an introduction for the students and researchers who are interested in this area. It introduces a number of examples of families of nonlinear time series parametric models in economic theory. It also talks about testing linearity against parametric alternatives with the presence of a characterization of the identification problem in many situations. Different ways of solving the identification problem are presented and their merits and disadvantages are discussed.

**Yuliia Mishura**(The Taras Shevchenko National University of Kiev ) 15:30-18:00Analytic, representation and statistical aspects related to fractional Gaussian processes.

[ Abstract ]

We consider the properties of fractional Gaussian processes whose covariance function is situated between two self-similarities, or, in other words, these processes belong to the generalized quasi-helix, according to geometric terminology of Kahane. For such processes we consider the two-sided bounds for maximal functionals and the representation results. We consider stochastic differential equations involving fractional Brownian motion and present also several results on statistical estimations for them.

We consider the properties of fractional Gaussian processes whose covariance function is situated between two self-similarities, or, in other words, these processes belong to the generalized quasi-helix, according to geometric terminology of Kahane. For such processes we consider the two-sided bounds for maximal functionals and the representation results. We consider stochastic differential equations involving fractional Brownian motion and present also several results on statistical estimations for them.

### 2018/02/02

#### Seminar on Probability and Statistics

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

Estimation of ratios of intensities in a Cox-type model of limit order books

**Ioane Muni Toke**(Centrale Supelec Paris)Estimation of ratios of intensities in a Cox-type model of limit order books

[ Abstract ]

We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The Cox-like intensities of the counting processes of events are assumed to share an unobserved and unspecified baseline intensity, which in finance can be identified to a global market activity affecting all events. The model is formulated in terms of relative responses of the intensities to covariates, and relative parameters can be estimated by quasi likelihood maximization. Consistency and asymptotic normality of the estimators are proven. Computationally intensive inferences are run on large samples of tick-by-tick data (35+ stocks and 220+ trading days, adding to more than one billion events). Penalization methods are also investigated. Results of the model are interpreted in terms of probability of occurrence of events. Excellent agreement with empirical data is found. Estimated model reproduces known empirical facts on imbalance, spread and queue sizes, and helps identifying trading signals of interests on a given stock.

Joint work with N.Yoshida.

We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The Cox-like intensities of the counting processes of events are assumed to share an unobserved and unspecified baseline intensity, which in finance can be identified to a global market activity affecting all events. The model is formulated in terms of relative responses of the intensities to covariates, and relative parameters can be estimated by quasi likelihood maximization. Consistency and asymptotic normality of the estimators are proven. Computationally intensive inferences are run on large samples of tick-by-tick data (35+ stocks and 220+ trading days, adding to more than one billion events). Penalization methods are also investigated. Results of the model are interpreted in terms of probability of occurrence of events. Excellent agreement with empirical data is found. Estimated model reproduces known empirical facts on imbalance, spread and queue sizes, and helps identifying trading signals of interests on a given stock.

Joint work with N.Yoshida.

#### thesis presentations

9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)

### 2018/02/01

#### thesis presentations

9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

10:45-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)

#### thesis presentations

15:45-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

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