## FMSP Lectures

Seminar information archive ～04/15｜Next seminar｜Future seminars 04/16～

**Seminar information archive**

### 2018/05/07

15:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Introduction to the Langlands-Rapoport conjecture (ENGLISH)

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

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

[ Abstract ]

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.

[ Reference 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

### 2018/03/26

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

### 2018/03/23

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

### 2018/02/23

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

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

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

### 2018/01/25

15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

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

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

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

[ Abstract ]

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

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

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

### 2018/01/16

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

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

[ Reference 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

[ Reference URL ]

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

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

[ Reference URL ]

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

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

[ Reference URL ]

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

### 2017/12/13

17:00-17:45 Room #470 (Graduate School of Math. Sci. Bldg.)

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

[ Abstract ]

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.

[ Reference 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

### 2017/11/06

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Phaseless inverse problems for Maxwell equations (ENGLISH)

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

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

[ Abstract ]

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

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

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

### 2017/10/31

16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Some Geometric Aspects in Inverse Problems (ENGLISH)

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

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

[ Abstract ]

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.

[ Reference 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

### 2017/03/22

13:00- Room #117 (Graduate School of Math. Sci. Bldg.)

Lecture 1: Derived symplectic varieties and the Darboux theorem.

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

[ Reference URL ]

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

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

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

[ Reference URL ]

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

### 2017/02/23

13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

### 2016/11/25

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry V (ENGLISH)

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

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

[ Abstract ]

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.

[ Reference 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

### 2016/11/21

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry IV (ENGLISH)

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

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

[ Abstract ]

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.

[ Reference 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

### 2016/11/18

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry III (ENGLISH)

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

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

[ Abstract ]

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.

[ Reference 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

### 2016/11/16

10:25-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry II (ENGLISH)

[ Abstract ]

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.
[ Reference URL ]

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

**Arthur Ogus**(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

### 2016/11/14

10:25-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Logarithmic Geometry I (ENGLISH)

[ Abstract ]

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.
[ Reference URL ]

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

**Arthur Ogus**(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

### 2016/11/10

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

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

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

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

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/10

13:15-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

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

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

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

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/09

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (7) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (7) (ENGLISH)

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/09

13:15-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (8) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (8) (ENGLISH)

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/09

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Conditional stability in Gelfand-Levitan problem (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

**Oleg Emanouilov**(Colorado State University)Conditional stability in Gelfand-Levitan problem (ENGLISH)

[ Abstract ]

We consider the Laplace-Beltrami operator in the bounded domain on the plane.

The eigenvalues and the traces of the eigenfunctions on part of the boundary are given.

We obtain the double logarithmic stability for the determination of metric up to the gauge equivalence.

[ Reference URL ]We consider the Laplace-Beltrami operator in the bounded domain on the plane.

The eigenvalues and the traces of the eigenfunctions on part of the boundary are given.

We obtain the double logarithmic stability for the determination of metric up to the gauge equivalence.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

### 2016/11/08

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (5) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (5) (ENGLISH)

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/08

13:15-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (6) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (6) (ENGLISH)

[ Abstract ]

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

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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