## Future seminars

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

### 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.)

### 2018/02/22

#### 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

### 2018/02/23

#### Colloquium

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

(JAPANESE)

**Hiromu Tanaka**(Univ. Tokyo)(JAPANESE)

#### 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

### 2018/03/10

#### Colloquium

13:00-14:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Akito FUTAKI**(Univ. Tokyo)(JAPANESE)

#### Colloquium

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

(JAPANESE)

**Yujiro KAWAMATA**(Univ. Tokyo)(JAPANESE)

#### Colloquium

11:00-12:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hitoshi ARAI**(Univ. Tokyo)(JAPANESE)

#### Colloquium

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

(JAPANESE)

**Hiroshi MATANO**(Univ. Tokyo)(JAPANESE)

### 2018/03/23

#### FMSP Lectures

10:00-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric Recursion (ENGLISH)

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

**Jørgen Ellegaard Andersen**(Aarhus University)Geometric Recursion (ENGLISH)

[ Abstract ]

Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the

Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work presented is joint with G. Borot and N. Orantin.

[ Reference URL ]Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the

Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work presented is joint with G. Borot and N. Orantin.

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

### 2018/03/26

#### FMSP Lectures

10:00-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric Recursion (ENGLISH)

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

**Jørgen Ellegaard Andersen**(Aarhus University)Geometric Recursion (ENGLISH)

[ Abstract ]

Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work

presented is joint with G. Borot and N. Orantin.

[ Reference URL ]Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work

presented is joint with G. Borot and N. Orantin.

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

### 2018/04/06

#### Colloquium

15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

### 2018/05/21

#### Algebraic Geometry Seminar

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

TBA (English)

https://www.math.utah.edu/~hacon/

**Christopher Hacon**(Utah/Kyoto)TBA (English)

[ Abstract ]

TBA

[ Reference URL ]TBA

https://www.math.utah.edu/~hacon/