Text only print
Full screen print
Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
2009/06/29
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
藤木 明 (大阪大学)
VII型曲面上の反自己双対双エルミート構造の存在について
藤木 明 (大阪大学)
VII型曲面上の反自己双対双エルミート構造の存在について
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
大川 領 (東京工業大学)
Moduli on the projective plane and the wall-crossing
大川 領 (東京工業大学)
Moduli on the projective plane and the wall-crossing
[ Abstract ]
射影平面上の半安定層のモジュライ空間を、Bridgeland 安定性条件
を用いることにより、ある有限次元代数の半安定表現のモジュライ空間
として構成する。階数が2以下の場合、表現の安定性条件を変化させること
により、壁越え現象としてのflip の記述を得る。
応用として、flip のBetti 数などが計算できる。
射影平面上の半安定層のモジュライ空間を、Bridgeland 安定性条件
を用いることにより、ある有限次元代数の半安定表現のモジュライ空間
として構成する。階数が2以下の場合、表現の安定性条件を変化させること
により、壁越え現象としてのflip の記述を得る。
応用として、flip のBetti 数などが計算できる。
2009/06/25
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
鈴木章斗 (九州大学数理学研究院)
Infrared divergence of scalar quantum field model on pseudo Riemann manifold
鈴木章斗 (九州大学数理学研究院)
Infrared divergence of scalar quantum field model on pseudo Riemann manifold
2009/06/24
Number Theory Seminar
16:30-18:45 Room #056 (Graduate School of Math. Sci. Bldg.)
Vincent Maillot (Paris第7大学) 16:30-17:30
New algebraicity results for analytic torsion
Richard Hain (Duke大学) 17:45-18:45
On the Section Conjecture for the universal curve over function fields
Vincent Maillot (Paris第7大学) 16:30-17:30
New algebraicity results for analytic torsion
Richard Hain (Duke大学) 17:45-18:45
On the Section Conjecture for the universal curve over function fields
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Winston Ou (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
Winston Ou (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
[ Abstract ]
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.
Lectures
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
柳尾 朋洋 (早大 基幹理工)
原子・分子集合体の集団運動における動的秩序と階層性
柳尾 朋洋 (早大 基幹理工)
原子・分子集合体の集団運動における動的秩序と階層性
[ Abstract ]
小さな気体分子の化学反応から、結晶成長、さらにはDNAやタンパク質のような生体高分子の機能発現に至るまで、原子・分子集合体の集団運動と自己組織化の一般原理を明らかにすることは、現代科学の大変興味深い課題である。近年の実験技術の進歩により、これら原子分子系の集団運動の多くは、平衡状態から大きく離れた非平衡状態において発生し、動的な秩序を内包していることが明らかになってきている。本発表では、一例として原子クラスターの構造変化の集団運動を取り上げ、これらの集団運動が、「遅い自由度」と「速い自由度」の間の動的結合によって系統的に生み出される仕組みについて紹介する。あわせて、このような非平衡過程を記述する新たな反応速度論の試みについても紹介する。続いて、より複雑な分子系の例として、生物のDNAをとりあげ、ランジュバン動力学に基づく粗視化モデルを導入することによって、DNAが細胞中で階層的な秩序構造を形成するメカニズムの一端を明らかにする。
小さな気体分子の化学反応から、結晶成長、さらにはDNAやタンパク質のような生体高分子の機能発現に至るまで、原子・分子集合体の集団運動と自己組織化の一般原理を明らかにすることは、現代科学の大変興味深い課題である。近年の実験技術の進歩により、これら原子分子系の集団運動の多くは、平衡状態から大きく離れた非平衡状態において発生し、動的な秩序を内包していることが明らかになってきている。本発表では、一例として原子クラスターの構造変化の集団運動を取り上げ、これらの集団運動が、「遅い自由度」と「速い自由度」の間の動的結合によって系統的に生み出される仕組みについて紹介する。あわせて、このような非平衡過程を記述する新たな反応速度論の試みについても紹介する。続いて、より複雑な分子系の例として、生物のDNAをとりあげ、ランジュバン動力学に基づく粗視化モデルを導入することによって、DNAが細胞中で階層的な秩序構造を形成するメカニズムの一端を明らかにする。
2009/06/23
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
久野 雄介 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications
久野 雄介 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications
[ Abstract ]
Meyer function is a kind of secondary invariant related to the signature
of surface bundles over surfaces. In this talk I will show there exist uniquely the Meyer function
for each smooth projective variety.
Our function is a class function on the fundamental group of some open algebraic variety.
I will also talk about its application to local signature for fibered 4-manifolds
Meyer function is a kind of secondary invariant related to the signature
of surface bundles over surfaces. In this talk I will show there exist uniquely the Meyer function
for each smooth projective variety.
Our function is a class function on the fundamental group of some open algebraic variety.
I will also talk about its application to local signature for fibered 4-manifolds
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
岸本崇氏 (埼玉大学理工学研究科)
Group actions on affine cones
岸本崇氏 (埼玉大学理工学研究科)
Group actions on affine cones
[ Abstract ]
The action of the additive group scheme C_+ on normal affine varieties is one of main subjects in affine algebraic geometry for a long time. In this talk, we shall mainly consider the problem about the existence of C_+-actions on affine cones, more precisely, the question:
"Determine the affine cones over smooth projective varieties admitting a (non-trivial) C_+-action ".
This question has an interest from a point of view of singularities. Indeed, a normal Cohen-Macaulay affine variety admitting an action by C_+ has at most rational singularities due to the result of H. Flenner and M. Zaidenberg. In the case of dimension 2, any affine cone over the projective line P^1 has a cyclic quotient singularity, and we can see that it admits, in fact, a C_+-action. Meanwhile, in case of dimension 3, i.e., affine cones over rational surfaces, the situation becomes more subtle.
One of the main results is concerned with a criterion for the existence of a C_+-action on affine cones (of any dimension) in terms of a cylinderlike open subset on the base variety. By making use of it, it is shown that, for any rational surface Y, we can take a suitable embedding of Y in such a way that the associated affine cone admits an action of C_+. Furthermore we are able to confirm that an affine cone over an anticanonically embedded del Pezzo surface of degree greater than or equal to 4 also admits such an action.
Nevertheless, our final purpose to decide whether or not there does exist a C_+-action on the fermat cubic: x^3+y^3+z^3+u^3 =0 in C^4, which is the affine cone over an anticanonically embedded cubic surface, say Y_3, is not yet accomplished. But, we can obtain certain informations about a linear pencil of rational curves on Y_3 arising from a C_+-action which seem to be useful in order to deny an existence of an action of C_+.
The action of the additive group scheme C_+ on normal affine varieties is one of main subjects in affine algebraic geometry for a long time. In this talk, we shall mainly consider the problem about the existence of C_+-actions on affine cones, more precisely, the question:
"Determine the affine cones over smooth projective varieties admitting a (non-trivial) C_+-action ".
This question has an interest from a point of view of singularities. Indeed, a normal Cohen-Macaulay affine variety admitting an action by C_+ has at most rational singularities due to the result of H. Flenner and M. Zaidenberg. In the case of dimension 2, any affine cone over the projective line P^1 has a cyclic quotient singularity, and we can see that it admits, in fact, a C_+-action. Meanwhile, in case of dimension 3, i.e., affine cones over rational surfaces, the situation becomes more subtle.
One of the main results is concerned with a criterion for the existence of a C_+-action on affine cones (of any dimension) in terms of a cylinderlike open subset on the base variety. By making use of it, it is shown that, for any rational surface Y, we can take a suitable embedding of Y in such a way that the associated affine cone admits an action of C_+. Furthermore we are able to confirm that an affine cone over an anticanonically embedded del Pezzo surface of degree greater than or equal to 4 also admits such an action.
Nevertheless, our final purpose to decide whether or not there does exist a C_+-action on the fermat cubic: x^3+y^3+z^3+u^3 =0 in C^4, which is the affine cone over an anticanonically embedded cubic surface, say Y_3, is not yet accomplished. But, we can obtain certain informations about a linear pencil of rational curves on Y_3 arising from a C_+-action which seem to be useful in order to deny an existence of an action of C_+.
2009/06/22
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
早乙女飛成 (筑波大学)
強疑凸多様体間の擬正則写像の楕円型作用素に関する性質について
早乙女飛成 (筑波大学)
強疑凸多様体間の擬正則写像の楕円型作用素に関する性質について
2009/06/20
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
小池 健二 (山梨大学教育人間科学部) 13:30-14:30
射影直線上の6点とI型領域上のテータ関数
射影直線上の6点とI型領域上のテータ関数
成田宏秋 (熊本大学理学部) 15:00-16:00
Fourier coefficients of Arakawa lifting and some degree eight L-function
小池 健二 (山梨大学教育人間科学部) 13:30-14:30
射影直線上の6点とI型領域上のテータ関数
射影直線上の6点とI型領域上のテータ関数
成田宏秋 (熊本大学理学部) 15:00-16:00
Fourier coefficients of Arakawa lifting and some degree eight L-function
[ Abstract ]
次数2のシンプレクティック群ないしはその非コンパクトな内部形式上のヘッケ同時固有的保型形式のフーリエ係数は、保型L関数の中心値と密接に関係すると考えられている。
この講演では「荒川リフト」という内部形式上のカスプ形式に対し、そのフーリエ係数とある次数8の保型L関数の中心値との明示的な関係について最近得られた結果を紹介する。(村瀬篤氏との共同研究)
次数2のシンプレクティック群ないしはその非コンパクトな内部形式上のヘッケ同時固有的保型形式のフーリエ係数は、保型L関数の中心値と密接に関係すると考えられている。
この講演では「荒川リフト」という内部形式上のカスプ形式に対し、そのフーリエ係数とある次数8の保型L関数の中心値との明示的な関係について最近得られた結果を紹介する。(村瀬篤氏との共同研究)
Infinite Analysis Seminar Tokyo
11:00-12:00 Room #117 (Graduate School of Math. Sci. Bldg.)
有田親史 (九大数理)
多成分排他過程の固有値が満たす双対性
有田親史 (九大数理)
多成分排他過程の固有値が満たす双対性
[ Abstract ]
非対称単純排他過程(asymmetric simple exclusion process, ASEP)と呼ばれ
る1次元格子上の確率過程がある。今回はその多成分の場合を考える。系の時間
発展を特徴付けるジェネレータ行列(マルコフ行列)は,Heisenberg模型を含む
Perk-Schultz模型のハミルトニアンの特殊な場合と等価である。講演者らは各粒
子セクターを超立方体の頂点と対応させ固有値の構造を調べた。超立方体上で双
対点を成す2つのセクターの固有値が満たす関係を示した。国場敦夫氏,堺和光
氏,沢辺剛氏との共同研究。
非対称単純排他過程(asymmetric simple exclusion process, ASEP)と呼ばれ
る1次元格子上の確率過程がある。今回はその多成分の場合を考える。系の時間
発展を特徴付けるジェネレータ行列(マルコフ行列)は,Heisenberg模型を含む
Perk-Schultz模型のハミルトニアンの特殊な場合と等価である。講演者らは各粒
子セクターを超立方体の頂点と対応させ固有値の構造を調べた。超立方体上で双
対点を成す2つのセクターの固有値が満たす関係を示した。国場敦夫氏,堺和光
氏,沢辺剛氏との共同研究。
2009/06/18
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
河東泰之 (東大数理)
The super Virasoro algebra and noncommutative geometry
河東泰之 (東大数理)
The super Virasoro algebra and noncommutative geometry
2009/06/17
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
小磯深幸 (奈良女子大学理学部/JSTさきがけ)
Variational problems for anisotropic surface energies
小磯深幸 (奈良女子大学理学部/JSTさきがけ)
Variational problems for anisotropic surface energies
[ Abstract ]
A surface energy is anisotropic if it depends on the direction of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing a fixed volume is called the Wulff shape. We will discuss the characterization of the Wulff shape, the uniqueness and stability of solutions to variational problems for anisotropic surface energy with several boundary conditions.
A surface energy is anisotropic if it depends on the direction of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing a fixed volume is called the Wulff shape. We will discuss the characterization of the Wulff shape, the uniqueness and stability of solutions to variational problems for anisotropic surface energy with several boundary conditions.
2009/06/16
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
佐藤 正寿 (東京大学大学院数理科学研究科)
The abelianization of the level 2 mapping class group
佐藤 正寿 (東京大学大学院数理科学研究科)
The abelianization of the level 2 mapping class group
[ Abstract ]
The level d mapping class group is a finite index subgroup of the mapping class group of an orientable closed surface. For d greater than or equal to 3, the abelianization of this group is equal to the first homology group of the moduli space of nonsingular curves with level d structure.
In this talk, we determine the abelianization of the level d mapping class group for d=2 and odd d. For even d greater than 2, we also determine it up to a cyclic group of order 2.
The level d mapping class group is a finite index subgroup of the mapping class group of an orientable closed surface. For d greater than or equal to 3, the abelianization of this group is equal to the first homology group of the moduli space of nonsingular curves with level d structure.
In this talk, we determine the abelianization of the level d mapping class group for d=2 and odd d. For even d greater than 2, we also determine it up to a cyclic group of order 2.
2009/06/15
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
野口潤次郎 (東京大学)
A unicity theorem and Erdös' problem for polarized semi-abelian varieties (joint with P. Corvaja)
野口潤次郎 (東京大学)
A unicity theorem and Erdös' problem for polarized semi-abelian varieties (joint with P. Corvaja)
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Vladimir P. Kostov (Nice大学)
On the Schur-Szeg\\"o composition of polynomials
Vladimir P. Kostov (Nice大学)
On the Schur-Szeg\\"o composition of polynomials
[ Abstract ]
The Schur-Szeg\\"o composition of the degree $n$ polynomials $P:=\\sum_{j=0}^na_jx^j$ and $Q:=\\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$) is representable as a Schur-Szeg\\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\\sigma_1$, $\\ldots$, $\\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$
The Schur-Szeg\\"o composition of the degree $n$ polynomials $P:=\\sum_{j=0}^na_jx^j$ and $Q:=\\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$) is representable as a Schur-Szeg\\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\\sigma_1$, $\\ldots$, $\\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$
Algebraic Geometry Seminar
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
馬 昭平氏 (東大数理)
アーベル曲面の分解と2次形式
馬 昭平氏 (東大数理)
アーベル曲面の分解と2次形式
[ Abstract ]
複素Abel曲面が楕円曲線の積に分解可能である時、分解の仕方は一般に何通りも
ありうる。いくつかの場合に分解の個数公式が求められてきた(林田、塩田-三谷
)。本講演では、すべての分解可能な複素Abel曲面に対して、2次形式論の技法
を用いて分解数の公式を与える。関連して次のことも話す:合同モジュラー曲線
上のAtkin-Lehner対合の幾何学的意味;正定値2元2次形式の類数と判別式形式
の等長群の関係。
複素Abel曲面が楕円曲線の積に分解可能である時、分解の仕方は一般に何通りも
ありうる。いくつかの場合に分解の個数公式が求められてきた(林田、塩田-三谷
)。本講演では、すべての分解可能な複素Abel曲面に対して、2次形式論の技法
を用いて分解数の公式を与える。関連して次のことも話す:合同モジュラー曲線
上のAtkin-Lehner対合の幾何学的意味;正定値2元2次形式の類数と判別式形式
の等長群の関係。
2009/06/11
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Chris Heunen (Radboud Universiteit Nijmegen)
A topos for algebraic quantum theory
Chris Heunen (Radboud Universiteit Nijmegen)
A topos for algebraic quantum theory
2009/06/10
Number Theory Seminar
16:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Kahn (Paris第7大学)
On the classifying space of a linear algebraic group
Bruno Kahn (Paris第7大学)
On the classifying space of a linear algebraic group
Lectures
15:30-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)
永幡幸生 (阪大基礎工)
格子気体のスペクトルギャップについて
永幡幸生 (阪大基礎工)
格子気体のスペクトルギャップについて
2009/06/09
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
五味 清紀 (京都大学大学院理学研究科)
A finite-dimensional construction of the Chern character for
twisted K-theory
五味 清紀 (京都大学大学院理学研究科)
A finite-dimensional construction of the Chern character for
twisted K-theory
[ Abstract ]
Twisted K-theory is a variant of topological K-theory, and
is attracting much interest due to applications to physics recently.
Usually, twisted K-theory is formulated infinite-dimensionally, and
hence known constructions of its Chern character are more or less
abstract. The aim of my talk is to explain a purely finite-dimensional
construction of the Chern character for twisted K-theory, which allows
us to compute examples concretely. The construction is based on
twisted version of Furuta's generalized vector bundle, and Quillen's
superconnection.
This is a joint work with Yuji Terashima.
Twisted K-theory is a variant of topological K-theory, and
is attracting much interest due to applications to physics recently.
Usually, twisted K-theory is formulated infinite-dimensionally, and
hence known constructions of its Chern character are more or less
abstract. The aim of my talk is to explain a purely finite-dimensional
construction of the Chern character for twisted K-theory, which allows
us to compute examples concretely. The construction is based on
twisted version of Furuta's generalized vector bundle, and Quillen's
superconnection.
This is a joint work with Yuji Terashima.
2009/06/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
大沢健夫 (名古屋大学)
正因子の正値性について
大沢健夫 (名古屋大学)
正因子の正値性について
Kavli IPMU Komaba Seminar
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Kiyonori Gomi (Kyoto University)
Multiplication in differential cohomology and cohomology operation
Kiyonori Gomi (Kyoto University)
Multiplication in differential cohomology and cohomology operation
[ Abstract ]
The notion of differential cohomology refines generalized
cohomology theory so as to incorporate information of differential
forms. The differential version of the ordinary cohomology has been
known as the Cheeger-Simons cohomology or the smooth Deligne
cohomology, while the general case was introduced by Hopkins and
Singer around 2002.
The theme of my talk is the cohomology operation induced from the
squaring map in the differential ordinary cohomology and the
differential K-cohomology: I will relate these operations to the
Steenrod operation and the Adams operation. I will also explain the
roles that the squaring maps play in 5-dimensional Chern-Simons theory
for pairs of B-fields and Hamiltonian quantization of generalized
abelian gauge fields.
The notion of differential cohomology refines generalized
cohomology theory so as to incorporate information of differential
forms. The differential version of the ordinary cohomology has been
known as the Cheeger-Simons cohomology or the smooth Deligne
cohomology, while the general case was introduced by Hopkins and
Singer around 2002.
The theme of my talk is the cohomology operation induced from the
squaring map in the differential ordinary cohomology and the
differential K-cohomology: I will relate these operations to the
Steenrod operation and the Adams operation. I will also explain the
roles that the squaring maps play in 5-dimensional Chern-Simons theory
for pairs of B-fields and Hamiltonian quantization of generalized
abelian gauge fields.
2009/06/04
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
中神祥臣 (日本女子大)
Determinant for rectangular martices
中神祥臣 (日本女子大)
Determinant for rectangular martices
2009/06/03
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
須藤孝一 (大阪大学)
Evolution of microstructures on crystal surfaces by surface diffusion
須藤孝一 (大阪大学)
Evolution of microstructures on crystal surfaces by surface diffusion
[ Abstract ]
We have studied the shape evolution of microstructures fabricated on silicon surfaces by surface diffusion during annealing. Various interesting phenomena, such as corner rounding, facet growth, and void formation, have been experimentally observed. We discuss these observations both from macroscopic and mesoscopic viewpoints. The evolution of macroscopic surface profiles is discussed using evolution equations based on the continuum surface picture. We analyze the mesoscopic scale aspects of the shape evolution using a step-flow model.
We have studied the shape evolution of microstructures fabricated on silicon surfaces by surface diffusion during annealing. Various interesting phenomena, such as corner rounding, facet growth, and void formation, have been experimentally observed. We discuss these observations both from macroscopic and mesoscopic viewpoints. The evolution of macroscopic surface profiles is discussed using evolution equations based on the continuum surface picture. We analyze the mesoscopic scale aspects of the shape evolution using a step-flow model.
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194 Next >
