## FMSPレクチャーズ

過去の記録 ～05/25｜次回の予定｜今後の予定 05/26～

担当者 | 河野俊丈 |
---|

**過去の記録**

### 2018年05月16日(水)

14:45-15:45 数理科学研究科棟(駒場) 122号室

Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)

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

**M.M. Lavrentʼev, Jr. 氏**(Novosibirsk State University)Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)

[ 講演概要 ]

We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.

[ 講演参考URL ]We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.

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

### 2018年05月11日(金)

15:00-17:00 数理科学研究科棟(駒場) 123号室

全5回講演の(5)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

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

全5回講演の(5)

**Sug Woo Shin 氏**(University of California, Berkeley)Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ 講演概要 ]

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

[ 講演参考URL ]In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

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

### 2018年05月10日(木)

15:00-17:00 数理科学研究科棟(駒場) 123号室

全5回講演の(4)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

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

全5回講演の(4)

**Sug Woo Shin 氏**(University of California, Berkeley)Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ 講演概要 ]

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

[ 講演参考URL ]In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

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

### 2018年05月09日(水)

15:00-17:00 数理科学研究科棟(駒場) 123号室

全5回講演の(3)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

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

全5回講演の(3)

**Sug Woo Shin 氏**(University of California, Berkeley)Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ 講演概要 ]

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

[ 講演参考URL ]In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

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

### 2018年05月08日(火)

15:00-17:00 数理科学研究科棟(駒場) 123号室

全5回講演の(2)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ 講演概要 ]

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.
[ 講演参考URL ]

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

全5回講演の(2)

**Sug Woo Shin 氏**(University of California, Berkeley)Introduction to the Langlands-Rapoport conjecture (ENGLISH)

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

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

### 2018年05月07日(月)

15:00-17:00 数理科学研究科棟(駒場) 123号室

全5回講演の(1)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

[ 講演概要 ]

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.
[ 講演参考URL ]

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

全5回講演の(1)

**Sug Woo Shin 氏**(University of California, Berkeley)Introduction to the Langlands-Rapoport conjecture (ENGLISH)

In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.

(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.

(ii) Statement of the conjecture: After setting up the language of

Galois gerbs, we state the Langlands-Rapoport conjecture.

(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.

(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of

Hecke-Frobenius correspondences.

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

### 2018年03月26日(月)

10:00-12:00 数理科学研究科棟(駒場) 002号室

全2回講演の(2)

Geometric Recursion (ENGLISH)

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

全2回講演の(2)

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

[ 講演概要 ]

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.

[ 講演参考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年03月23日(金)

10:00-12:00 数理科学研究科棟(駒場) 002号室

全2回講演の(1)

Geometric Recursion (ENGLISH)

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

全2回講演の(1)

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

[ 講演概要 ]

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.

[ 講演参考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年02月23日(金)

13:30-15:00 数理科学研究科棟(駒場) 002号室

全3回講演の(3)

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

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

全3回講演の(3)

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

[ 講演概要 ]

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.

[ 講演参考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年02月22日(木)

15:00-16:30 数理科学研究科棟(駒場) 117号室

全3回講演の(2)

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

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

全3回講演の(2)

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

[ 講演概要 ]

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.

[ 講演参考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年02月21日(水)

15:00-16:30 数理科学研究科棟(駒場) 117号室

全3回講演の(1)

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

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

全3回講演の(1)

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

[ 講演概要 ]

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.

[ 講演参考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年01月25日(木)

15:00-16:30 数理科学研究科棟(駒場) 002号室

NUMERICAL ANALYSIS, COBORDISM OF MANIFOLDS AND MONODROMY. (ENGLISH)

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

**Norbert A'Campo 氏**(University of Basel)NUMERICAL ANALYSIS, COBORDISM OF MANIFOLDS AND MONODROMY. (ENGLISH)

[ 講演概要 ]

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

[ 講演参考URL ]http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ACampo_abst.pdf

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

### 2018年01月16日(火)

10:30-11:30 数理科学研究科棟(駒場) 056号室

FMSP Tokyo-Princeton joint student seminar

Large data global solutions for the shallow water system in one space dimension

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf

Introduction to the maximal Lp-regularity and its applications to the quasi-linear parabolic equations

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf

FMSP Tokyo-Princeton joint student seminar

**Federico Pasqualotto 氏**(Princeton) -Large data global solutions for the shallow water system in one space dimension

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf

**Naoto Kaziwara 氏**(U. Tokyo) -Introduction to the maximal Lp-regularity and its applications to the quasi-linear parabolic equations

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf

### 2017年12月13日(水)

17:00-17:45 数理科学研究科棟(駒場) 470号室

An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)

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

**Anar Rahimov 氏**(The Institute of Control Systems of ANAS and Baku State University)An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)

[ 講演概要 ]

We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.

[ 講演参考URL ]We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.

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

### 2017年11月06日(月)

17:00-18:00 数理科学研究科棟(駒場) 118号室

Phaseless inverse problems for Maxwell equations (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf

**V. G. Romanov 氏**(Sobolev Institute of Mathematics)Phaseless inverse problems for Maxwell equations (ENGLISH)

[ 講演概要 ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf

[ 講演参考URL ]http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf

### 2017年10月31日(火)

16:00-17:00 数理科学研究科棟(駒場) 118号室

Some Geometric Aspects in Inverse Problems (ENGLISH)

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

**V. G. Romanov 氏**(Sobolev Institute of Mathematics)Some Geometric Aspects in Inverse Problems (ENGLISH)

[ 講演概要 ]

We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.

[ 講演参考URL ]We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.

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

### 2017年03月22日(水)

13:00- 数理科学研究科棟(駒場) 117号室

Lecture 1: Derived symplectic varieties and the Darboux theorem.

Lecture 2: The moduli of anti-canonically marked del Pezzo surfaces. (ENGLISH)

[ 講演参考URL ]

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

**Ian Grojnowski 氏**(University of Cambridge)Lecture 1: Derived symplectic varieties and the Darboux theorem.

Lecture 2: The moduli of anti-canonically marked del Pezzo surfaces. (ENGLISH)

[ 講演参考URL ]

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

### 2017年02月23日(木)

13:30-15:00 数理科学研究科棟(駒場) 122号室

結晶学, 量子ビーム科学分野との連携の中で見たこと, 考えたこと (JAPANESE)

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

**富安 亮子 氏**(山形大学理学部)結晶学, 量子ビーム科学分野との連携の中で見たこと, 考えたこと (JAPANESE)

[ 講演概要 ]

結晶学は、結晶を含む固体材料の構造を中心的に扱う学術領域であり、X線・中性子線・電子線等に関わる量子ビーム科学分野から様々な基盤技術が提供されている。

得られた実験データの解析に用いられる様々な手法やソフトウェア、加えて、より一般に結晶構造の記述に関係する議論は、数理結晶学とも呼ばれ、数学者にとっては比較的入りやすい。

話者がこの分野に参入した直接のきっかけは、応用代数分野とよく類似した様々な問題が残っていたことであるので、その辺の数学の話を主に紹介する。得られた定理は、観測誤差を伴うデータ処理において、数学の厳密さをどのように解析アルゴリズムの成功率に反映させるかという問題に直結するもので、話者や高エネ研が配布している結晶学ソフトウェアの基盤となっている。

[ 講演参考URL ]結晶学は、結晶を含む固体材料の構造を中心的に扱う学術領域であり、X線・中性子線・電子線等に関わる量子ビーム科学分野から様々な基盤技術が提供されている。

得られた実験データの解析に用いられる様々な手法やソフトウェア、加えて、より一般に結晶構造の記述に関係する議論は、数理結晶学とも呼ばれ、数学者にとっては比較的入りやすい。

話者がこの分野に参入した直接のきっかけは、応用代数分野とよく類似した様々な問題が残っていたことであるので、その辺の数学の話を主に紹介する。得られた定理は、観測誤差を伴うデータ処理において、数学の厳密さをどのように解析アルゴリズムの成功率に反映させるかという問題に直結するもので、話者や高エネ研が配布している結晶学ソフトウェアの基盤となっている。

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

### 2016年11月25日(金)

10:25-12:10 数理科学研究科棟(駒場) 126号室

Introduction to Logarithmic Geometry V (ENGLISH)

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

**Arthur Ogus 氏**(University of California, Berkeley)Introduction to Logarithmic Geometry V (ENGLISH)

[ 講演概要 ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

[ 講演参考URL ]Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

### 2016年11月21日(月)

10:25-12:10 数理科学研究科棟(駒場) 126号室

Introduction to Logarithmic Geometry IV (ENGLISH)

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

**Arthur Ogus 氏**(University of California, Berkeley)Introduction to Logarithmic Geometry IV (ENGLISH)

[ 講演概要 ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

[ 講演参考URL ]Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

### 2016年11月18日(金)

10:25-12:10 数理科学研究科棟(駒場) 126号室

Introduction to Logarithmic Geometry III (ENGLISH)

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

**Arthur Ogus 氏**(University of California, Berkeley)Introduction to Logarithmic Geometry III (ENGLISH)

[ 講演概要 ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

[ 講演参考URL ]Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

### 2016年11月16日(水)

10:25-12:10 数理科学研究科棟(駒場) 128号室

Introduction to Logarithmic Geometry II (ENGLISH)

[ 講演概要 ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.
[ 講演参考URL ]

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

**Arthur Ogus 氏**(University of California, Berkeley)Introduction to Logarithmic Geometry II (ENGLISH)

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

### 2016年11月14日(月)

10:25-12:10 数理科学研究科棟(駒場) 126号室

Introduction to Logarithmic Geometry I (ENGLISH)

[ 講演概要 ]

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.
[ 講演参考URL ]

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

**Arthur Ogus 氏**(University of California, Berkeley)Introduction to Logarithmic Geometry I (ENGLISH)

Logarithmic Geometry was invented (or discovered) in the 1980's, with crucial ideas contributed by Deligne, Faltings, Fontaine, Illusie, and especially K. Kato. It provides a systematic framework for the study of the related phenomena of compactification and degeneration in algebraic and arithmetic geometry, with applications to number theory. I will attempt to explain the main ideas and foundations of Kato's version of log geometry, with an emphasis on its geometric and topological aspects.

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

### 2016年11月10日(木)

10:30-11:30 数理科学研究科棟(駒場) 128号室

The BV space in variational and evolution problems (9) (ENGLISH)

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

**Piotr Rybka 氏**(the University of Warsaw)The BV space in variational and evolution problems (9) (ENGLISH)

[ 講演概要 ]

http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ 講演参考URL ]http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016年11月10日(木)

13:15-14:15 数理科学研究科棟(駒場) 128号室

The BV space in variational and evolution problems (10) (ENGLISH)

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

**Piotr Rybka 氏**(the University of Warsaw)The BV space in variational and evolution problems (10) (ENGLISH)

[ 講演概要 ]

http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ 講演参考URL ]http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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