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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
山ノ井 克俊 氏 (大阪大学)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
山ノ井 克俊 氏 (大阪大学)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
[ 講演概要 ]
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
2015年12月17日(木)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
このセミナーは講演者が急病のためキャンセルになりました。This seminer is canceled due to the speaker 's sick.
Dulip Piyaratne 氏 (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
http://db.ipmu.jp/member/personal/3989en.html
このセミナーは講演者が急病のためキャンセルになりました。This seminer is canceled due to the speaker 's sick.
Dulip Piyaratne 氏 (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
[ 講演概要 ]
In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
[ 参考URL ]In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
http://db.ipmu.jp/member/personal/3989en.html
2015年12月16日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Yul Otani 氏 (東大数理)
Nuclearity in AQFT and related results
Yul Otani 氏 (東大数理)
Nuclearity in AQFT and related results
博士論文発表会
10:30-11:45 数理科学研究科棟(駒場) 122号室
山本 光 氏 (東京大学大学院数理科学研究科)
Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)
山本 光 氏 (東京大学大学院数理科学研究科)
Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)
FMSPレクチャーズ
10:30-12:00 数理科学研究科棟(駒場) 128号室
Yuri Luchko 氏 (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf
Yuri Luchko 氏 (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
[ 講演概要 ]
In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
[ 参考URL ]In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf
2015年12月15日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
Constantin Teleman 氏 (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
Tea : Common Room 16:30 -- 17:00
Constantin Teleman 氏 (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
[ 講演概要 ]
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.
2015年12月14日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
中田 文憲 氏 (福島大学)
Twistor correspondence for associative Grassmanniann
中田 文憲 氏 (福島大学)
Twistor correspondence for associative Grassmanniann
[ 講演概要 ]
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
金沢篤 氏 (ハーバード大学)
Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
金沢篤 氏 (ハーバード大学)
Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
[ 講演概要 ]
In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.
In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.
2015年12月09日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
David E. Evans 氏 (Cardiff Univ.)
K-theory in subfactors and conformal field theory
David E. Evans 氏 (Cardiff Univ.)
K-theory in subfactors and conformal field theory
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Ted Chinburg 氏 (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
Ted Chinburg 氏 (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ 講演概要 ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
2015年12月08日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
山田 裕一 氏 (電気通信大学)
レンズ空間手術と４次元多様体の Kirby calculus (JAPANESE)
Tea : Common Room 16:30 -- 17:00
山田 裕一 氏 (電気通信大学)
レンズ空間手術と４次元多様体の Kirby calculus (JAPANESE)
[ 講演概要 ]
「３次元球面内の結び目に沿うデーン手術でレンズ空間が生じるもの
を決定せよ」という問題は「レンズ空間手術」と呼ばれています。Berge のリス
ト(1990) が完全なリストと信じられており Heegaard Floer 理論によって進展
はしたものの、解決には至っていません。手法が４次元多様体論に近づいていま
す。その一方 Minimally twisted 5 chain link の例外的デーン手術が再確認さ
れて、レンズ空間からのレンズ空間手術や２成分絡み目に視野が広がったりして
います。
講演では、Berge のリストの多様さと規則性を紹介しつつ、異なる結び目から
同じレンズ空間が生じる組で構成する４次元多様体（丹下基生氏（筑波大）との
共同研究）についてお話しします。
「３次元球面内の結び目に沿うデーン手術でレンズ空間が生じるもの
を決定せよ」という問題は「レンズ空間手術」と呼ばれています。Berge のリス
ト(1990) が完全なリストと信じられており Heegaard Floer 理論によって進展
はしたものの、解決には至っていません。手法が４次元多様体論に近づいていま
す。その一方 Minimally twisted 5 chain link の例外的デーン手術が再確認さ
れて、レンズ空間からのレンズ空間手術や２成分絡み目に視野が広がったりして
います。
講演では、Berge のリストの多様さと規則性を紹介しつつ、異なる結び目から
同じレンズ空間が生じる組で構成する４次元多様体（丹下基生氏（筑波大）との
共同研究）についてお話しします。
2015年12月07日(月)
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
Jean-Dominique Deuschel 氏 (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
[ 講演概要 ]
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
巴山 竜来 氏 (専修大学)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
巴山 竜来 氏 (専修大学)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ 講演概要 ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
Alexey Bondal 氏 (IPMU)
Flops and spherical functors (English)
Alexey Bondal 氏 (IPMU)
Flops and spherical functors (English)
[ 講演概要 ]
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
2015年12月04日(金)
談話会・数理科学講演会
16:50-17:50 数理科学研究科棟(駒場) 123号室
佐々田槙子 氏 (東京大学大学院数理科学研究科)
確率論の問題に現れる無限直積空間上の完全形式と閉形式について (JAPANESE)
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
佐々田槙子 氏 (東京大学大学院数理科学研究科)
確率論の問題に現れる無限直積空間上の完全形式と閉形式について (JAPANESE)
[ 講演概要 ]
ミクロな系の時間発展を表す確率過程からマクロな系の時間発展を表す偏微分方程式を導出する流体力学極限は統計力学を基礎付ける重要なスケール極限の一種である。その証明において、無限直積空間上の微分１形式（もしくはそれに対応するもの）を考え、閉形式の空間を完全形式の空間とその直交空間に分解するという定理が重要な役割を果たしている。この定理は確率過程に対応する（微分）作用素ごとに証明されてきたが、既存の手法は代数的な内容と解析的な内容が混在した複雑なものであった。しかし、講演者らは最近、この問題を代数的な問題と解析的な問題に分け、代数的な部分については、モデルの詳細によらずに非常に一般的に成立することを明らかにした。また、解析的な問題についても、$L^2$空間が作用素とよい関係を持つ基底を持つ場合には、直感的でシンプルな証明が得られることを示した。しかし、この周辺の話題については問題の定式化も含めて未解明な部分が多く、代数や幾何、関数解析等の専門家からの助言が大きな進展をもたらす可能性があると考えている。そこで、講演では問題の背景にはあまり触れずに、無限直積空間上のある種の１形式に関する話題に絞って紹介したい。特に、{0,1}の無限直積に対する具体的な問題を中心に紹介する。
[ 参考URL ]ミクロな系の時間発展を表す確率過程からマクロな系の時間発展を表す偏微分方程式を導出する流体力学極限は統計力学を基礎付ける重要なスケール極限の一種である。その証明において、無限直積空間上の微分１形式（もしくはそれに対応するもの）を考え、閉形式の空間を完全形式の空間とその直交空間に分解するという定理が重要な役割を果たしている。この定理は確率過程に対応する（微分）作用素ごとに証明されてきたが、既存の手法は代数的な内容と解析的な内容が混在した複雑なものであった。しかし、講演者らは最近、この問題を代数的な問題と解析的な問題に分け、代数的な部分については、モデルの詳細によらずに非常に一般的に成立することを明らかにした。また、解析的な問題についても、$L^2$空間が作用素とよい関係を持つ基底を持つ場合には、直感的でシンプルな証明が得られることを示した。しかし、この周辺の話題については問題の定式化も含めて未解明な部分が多く、代数や幾何、関数解析等の専門家からの助言が大きな進展をもたらす可能性があると考えている。そこで、講演では問題の背景にはあまり触れずに、無限直積空間上のある種の１形式に関する話題に絞って紹介したい。特に、{0,1}の無限直積に対する具体的な問題を中心に紹介する。
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 126号室
竹山 美宏 氏 (筑波大学)
q-ボゾン系とアフィンヘッケ代数の変形 (Japanese)
竹山 美宏 氏 (筑波大学)
q-ボゾン系とアフィンヘッケ代数の変形 (Japanese)
[ 講演概要 ]
q-ボゾン系は笹本-和達によって定義された一次元可積分確率過程である. その Q行列は量子逆散乱法により構成できて, 代数的ベーテ仮設法を適用することで固有ベクトルが得られる. 最近の研究で, q-ボゾン系はアフィンヘッケ代数のある変形の表現からも得られることがわかった. この枠組みでは, Q行列の転置に対する固有ベクトルが自然に得られ, 座標的ベーテ仮設法で構成されたものと一致する. この講演では, 以上の結果について概説し, これら二つの方法の関係について議論する.
q-ボゾン系は笹本-和達によって定義された一次元可積分確率過程である. その Q行列は量子逆散乱法により構成できて, 代数的ベーテ仮設法を適用することで固有ベクトルが得られる. 最近の研究で, q-ボゾン系はアフィンヘッケ代数のある変形の表現からも得られることがわかった. この枠組みでは, Q行列の転置に対する固有ベクトルが自然に得られ, 座標的ベーテ仮設法で構成されたものと一致する. この講演では, 以上の結果について概説し, これら二つの方法の関係について議論する.
2015年12月03日(木)
統計数学セミナー
16:40-18:00 数理科学研究科棟(駒場) 123号室
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
[ 講演概要 ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
FMSPレクチャーズ
16:40-18:00 数理科学研究科棟(駒場) 123号室
"Learning theory and sparsity" 全3回講演の(3)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
"Learning theory and sparsity" 全3回講演の(3)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
[ 講演概要 ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
[ 参考URL ]In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
2015年12月02日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
山下真 氏 (お茶の水女子大)
Drinfeld center and representation theory for monoidal categories
山下真 氏 (お茶の水女子大)
Drinfeld center and representation theory for monoidal categories
統計数学セミナー
14:55-18:00 数理科学研究科棟(駒場) 056号室
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．
Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
[ 講演概要 ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
FMSPレクチャーズ
14:55-18:00 数理科学研究科棟(駒場) 056号室
"Learning theory and sparsity" 全3回講演の(2)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
"Learning theory and sparsity" 全3回講演の(2)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
[ 講演概要 ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
[ 参考URL ]In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
数理人口学・数理生物学セミナー
14:55-16:40 数理科学研究科棟(駒場) 128号室
八島健太 氏 (総合研究大学院大学)
基本増殖率の感受性解析を用いたネットワーク中心性指標
http://www.soken.ac.jp/
八島健太 氏 (総合研究大学院大学)
基本増殖率の感受性解析を用いたネットワーク中心性指標
[ 講演概要 ]
ネットワーク上における感染症流行を阻止するために，中心性指標を用いた
危険箇所の同定が行われている．感染症侵入の有無は基本増殖率R0により規定さ
れることから，我々は基本増殖率の感受性解析を用いた新たなネットワーク中心
性指標の提案を行った．これを用いて東京都市圏における感染症流行の解析を行
ったところ，既存の中心性指標では見落とされてきた流行動態を明らかにできた．
利用者数最大の新宿駅は2位の東京駅の1.5倍程度の利用者数規模であるが，隔離
政策を行った際の基本増殖率低減への寄与率が約1,000倍も大きいことが分かった．
また，侵入阻止（基本増殖率低下）のために注力すべき箇所と，侵入が起こった
さいに被害低減（最終規模低下）のために注力すべき箇所が必ずしも一致しない
ことが分かった．本講演では，提案したネットワーク中心性指標の紹介および上
記の結果を紹介したい．
[ 参考URL ]ネットワーク上における感染症流行を阻止するために，中心性指標を用いた
危険箇所の同定が行われている．感染症侵入の有無は基本増殖率R0により規定さ
れることから，我々は基本増殖率の感受性解析を用いた新たなネットワーク中心
性指標の提案を行った．これを用いて東京都市圏における感染症流行の解析を行
ったところ，既存の中心性指標では見落とされてきた流行動態を明らかにできた．
利用者数最大の新宿駅は2位の東京駅の1.5倍程度の利用者数規模であるが，隔離
政策を行った際の基本増殖率低減への寄与率が約1,000倍も大きいことが分かった．
また，侵入阻止（基本増殖率低下）のために注力すべき箇所と，侵入が起こった
さいに被害低減（最終規模低下）のために注力すべき箇所が必ずしも一致しない
ことが分かった．本講演では，提案したネットワーク中心性指標の紹介および上
記の結果を紹介したい．
http://www.soken.ac.jp/
2015年12月01日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
Stéphane Malek 氏 (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
Stéphane Malek 氏 (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
[ 講演概要 ]
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
奥田 喬之 氏 (東京大学大学院数理科学研究科)
Monodromies of splitting families for singular fibers (JAPANESE)
Tea : Common Room 16:30 -- 17:00
奥田 喬之 氏 (東京大学大学院数理科学研究科)
Monodromies of splitting families for singular fibers (JAPANESE)
[ 講演概要 ]
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
2015年11月30日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Jean-Pierre Demailly 氏 (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
Jean-Pierre Demailly 氏 (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
[ 講演概要 ]
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
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