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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
戸松玲治 (東大数理)
商型右余イデアルの特徴づけとポワソン境界の分類
戸松玲治 (東大数理)
商型右余イデアルの特徴づけとポワソン境界の分類
2006/11/15
Lectures
16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Mathematical Finance
17:30-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)
塚原 英敦 (成城大)
歪みリスク尺度の1-パラメータ族とその応用
塚原 英敦 (成城大)
歪みリスク尺度の1-パラメータ族とその応用
2006/11/14
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
高瀬将道 (信州大学理学部)
High-codimensional knots spun about manifolds
高瀬将道 (信州大学理学部)
High-codimensional knots spun about manifolds
[ Abstract ]
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.
2006/11/13
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
小野 肇 (東京工業大学)
Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds
小野 肇 (東京工業大学)
Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
青木昌雄 (京大数理研)
Hom stacks and Picard stacks
青木昌雄 (京大数理研)
Hom stacks and Picard stacks
2006/11/10
Geometry Seminar
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
中島啓 (京都大学大学院理学研究科)
箙多様体のベッチ数の計算
中島啓 (京都大学大学院理学研究科)
箙多様体のベッチ数の計算
[ Abstract ]
箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.
箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.
Tuesday Seminar on Topology
17:40-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)
樋上和弘 (東京大学大学院理学系研究科 物理)
WRT invariant for Seifert manifolds and modular forms
樋上和弘 (東京大学大学院理学系研究科 物理)
WRT invariant for Seifert manifolds and modular forms
[ Abstract ]
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.
2006/11/09
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
2006/11/08
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Fredric Flin (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Fredric Flin (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
[ Abstract ]
Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
[ Reference URL ]Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
Geometry Seminar
14:40-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
梶原 健 (横浜国立大学大学院工学研究院応用数学) 14:40-16:10
代数多様体の退化とトロピカル幾何
Counting problem in tropical geometry
梶原 健 (横浜国立大学大学院工学研究院応用数学) 14:40-16:10
代数多様体の退化とトロピカル幾何
[ Abstract ]
トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.
西納 武男 (京都大学理学研究科数学教室) 16:30-18:00トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.
Counting problem in tropical geometry
[ Abstract ]
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
蛭川 潤一 (早稲田大学)
LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
蛭川 潤一 (早稲田大学)
LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses
[ Abstract ]
This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
[ Reference URL ]This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
2006/11/07
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
2006/11/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Mihai Paun (Université Henri Poincaré Nancy)
On the extension of twisted pluricanonical forms
Mihai Paun (Université Henri Poincaré Nancy)
On the extension of twisted pluricanonical forms
2006/11/02
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)
Applied Analysis
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
[ Abstract ]
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
2006/11/01
Number Theory Seminar
16:30-18:45 Room #117 (Graduate School of Math. Sci. Bldg.)
G.Bayarmagnai (東大数理) 16:30-17:30
Essential dimension of some finite group schemes
Jacques Tilouine (パリ北大学) 17:45-18:45
Overconvergent Siegel modular forms
G.Bayarmagnai (東大数理) 16:30-17:30
Essential dimension of some finite group schemes
Jacques Tilouine (パリ北大学) 17:45-18:45
Overconvergent Siegel modular forms
[ Abstract ]
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Ilia NEGRI (Department of Management and Information Technology, University of Bergamo, Italy)
Some problems related to the estimation of the invariant measure of an ergodic diffusion.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html
Ilia NEGRI (Department of Management and Information Technology, University of Bergamo, Italy)
Some problems related to the estimation of the invariant measure of an ergodic diffusion.
[ Abstract ]
We consider a one dimensional ergodic diffusion process solution of a stochastic differential equation. We suppose that the diffusion coefficient is known whereas the drift coefficient $S$ is unknown. Our interest is the invariant measure of the process denoted as $\\mu $. We denote by $f_S$ and $F_S$ the invariant density and the invariant distribution function of $\\mu$ respectively. We present the problems of finding efficient estimators when we observe the trajectory of the diffusion in continuos time over $[0,T]$ and we study asymptotic properties of the estimators when $T$ goes to infinity.
[ Reference URL ]We consider a one dimensional ergodic diffusion process solution of a stochastic differential equation. We suppose that the diffusion coefficient is known whereas the drift coefficient $S$ is unknown. Our interest is the invariant measure of the process denoted as $\\mu $. We denote by $f_S$ and $F_S$ the invariant density and the invariant distribution function of $\\mu$ respectively. We present the problems of finding efficient estimators when we observe the trajectory of the diffusion in continuos time over $[0,T]$ and we study asymptotic properties of the estimators when $T$ goes to infinity.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Tan Yongji (School of Mathematical Science, Fudan University )
A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Tan Yongji (School of Mathematical Science, Fudan University )
A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging
[ Abstract ]
Spontaneous well-logging is an important technique in petroleum exploitation. The potential field is of strong discontinuity on the interface since the spontaneous potential differences. It causes difficulty in mathematical analysis and numerical computing.
New mathematical model and numerical method is designed to overcome the difficulty and good results is obtained.
[ Reference URL ]Spontaneous well-logging is an important technique in petroleum exploitation. The potential field is of strong discontinuity on the interface since the spontaneous potential differences. It causes difficulty in mathematical analysis and numerical computing.
New mathematical model and numerical method is designed to overcome the difficulty and good results is obtained.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/10/31
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
大島利雄氏 (東大数理)
ルート系の部分系の分類
http://akagi.ms.u-tokyo.ac.jp/seminar.html
大島利雄氏 (東大数理)
ルート系の部分系の分類
[ Abstract ]
ルート系 Ξ からルート系 Σ へのCartan整数を保つ写像の分類を考える(像は Σ の部分系と見なせる).
Σ のWeyl群(Σ の内部同型)で移りあうものを同値とみたときの分類をまず行い,
同値の条件をさらに Ξ の自己同型(部分系の分類に対応),Ξ の既約成分の自己同型の直積,
Σ の自己同型などを許すものに広げた場合の分類や像が放物型かどうかの判定も与える.
ルート系の dual pair の概念を定義し,同値類への Ξ の自己同型の作用の考察に用いる.
[ Reference URL ]ルート系 Ξ からルート系 Σ へのCartan整数を保つ写像の分類を考える(像は Σ の部分系と見なせる).
Σ のWeyl群(Σ の内部同型)で移りあうものを同値とみたときの分類をまず行い,
同値の条件をさらに Ξ の自己同型(部分系の分類に対応),Ξ の既約成分の自己同型の直積,
Σ の自己同型などを許すものに広げた場合の分類や像が放物型かどうかの判定も与える.
ルート系の dual pair の概念を定義し,同値類への Ξ の自己同型の作用の考察に用いる.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
中村 信裕 (東京大学大学院数理科学研究科)
Unsmoothable group actions on elliptic surfaces
中村 信裕 (東京大学大学院数理科学研究科)
Unsmoothable group actions on elliptic surfaces
[ Abstract ]
Let G be a cyclic group of order 3,5 or 7.
We prove the existence of locally linear G-actions on elliptic surfaces which can not be realized by smooth actions with respect to specific smooth structures.
To prove this, we give constraints on smooth actions by using gauge theory.
In fact, we use a mod p vanishing theorem on Seiberg-Witten invariants, which was originally proved by F.Fang.
We give a geometric alternative proof of this, which enables us to extend the theorem.
Let G be a cyclic group of order 3,5 or 7.
We prove the existence of locally linear G-actions on elliptic surfaces which can not be realized by smooth actions with respect to specific smooth structures.
To prove this, we give constraints on smooth actions by using gauge theory.
In fact, we use a mod p vanishing theorem on Seiberg-Witten invariants, which was originally proved by F.Fang.
We give a geometric alternative proof of this, which enables us to extend the theorem.
2006/10/30
PDE Real Analysis Seminar
16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Matti Lassas (Helsinki University of Technology, Institute of Mathematics)
Inverse Problems and Index Formulae for Dirac Operators
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Matti Lassas (Helsinki University of Technology, Institute of Mathematics)
Inverse Problems and Index Formulae for Dirac Operators
[ Abstract ]
We consider a selfadjoin Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M, g)$ with a nonempty boundary.
The operator $D_P$ is specified by a boundary condition $P(u|_{\\partial M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator.
We assume the existence of a chirality operator which decomposes $L2(M, V)$ into two orthogonal subspaces $X_+ \\oplus X_-$.
In the talk we consider the reconstruction of $(M, g)$, $V$, and $D_P$ from the boundary data on $\\partial M$.
The data used is either the Cauchy data, i.e. the restrictions to $\\partial M \\times R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\\times \\C4$, $M \\subset \\R3$. The presented results have been done in collaboration with Yaroslav Kurylev (Loughborough, UK).
[ Reference URL ]We consider a selfadjoin Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M, g)$ with a nonempty boundary.
The operator $D_P$ is specified by a boundary condition $P(u|_{\\partial M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator.
We assume the existence of a chirality operator which decomposes $L2(M, V)$ into two orthogonal subspaces $X_+ \\oplus X_-$.
In the talk we consider the reconstruction of $(M, g)$, $V$, and $D_P$ from the boundary data on $\\partial M$.
The data used is either the Cauchy data, i.e. the restrictions to $\\partial M \\times R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\\times \\C4$, $M \\subset \\R3$. The presented results have been done in collaboration with Yaroslav Kurylev (Loughborough, UK).
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/10/26
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Remi Leandre (Univ. Bourgogne)
Introduction to Brownian surfaces
Remi Leandre (Univ. Bourgogne)
Introduction to Brownian surfaces
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