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過去の記録 ～12/04｜本日 12/05 | 今後の予定 12/06～
2016年01月12日(火)
トポロジー火曜セミナー
16:30-18:30 数理科学研究科棟(駒場) 056号室
川崎 盛通 氏 (東京大学大学院数理科学研究科) 16:30-17:30
重い部分集合と非可縮周期軌道 (JAPANESE)
On codimension two contact embeddings in the standard spheres (JAPANESE)
川崎 盛通 氏 (東京大学大学院数理科学研究科) 16:30-17:30
重い部分集合と非可縮周期軌道 (JAPANESE)
[ 講演概要 ]
ビランとポルテロヴィッチ、サラモンによる研究では、開シンプレクティック多
様体Mとその部分集合$X$, $M$内の自由ホモトピー類αに対する相対的なシンプレクテ
ィック容量$C_{BPS}(M,X,α)$を定義した。
$C_{BPS}(M,X,α)$はM上のハミルトン函数がXで十分大きい値を取る場合にαを代表
する周期軌道が存在するかという問題に関わって定義される。
一方で、エントフとポルテロヴィッチは非交叉配置性の文脈でシンプレクティッ
ク多様体の「重い」部分集合というものを定義している。
本講演ではビラン・ポルテロヴィッチ・サラモン容量$C_{BPS}(M,X,α)$の有限性
(適当な設定下での周期軌道の存在)を重い部分集合を用いて示す方法について解
説する。
これまでの研究では(自由ループの)ホモトピー類αを代表する周期軌道の検出に
は、αを代表する軌道のハミルトン・フレアー理論を用いるのが一般的であった。
重い部分集合は(可縮軌道のハミルトン・フレアー理論の)スペクトル不変量を用
いて定義される概念であるので、今回の手法では可縮軌道のハミルトン・フレア
ー理論を用いて非可縮軌道を検出することになる。
古川 遼 氏 (東京大学大学院数理科学研究科) 17:30-18:30ビランとポルテロヴィッチ、サラモンによる研究では、開シンプレクティック多
様体Mとその部分集合$X$, $M$内の自由ホモトピー類αに対する相対的なシンプレクテ
ィック容量$C_{BPS}(M,X,α)$を定義した。
$C_{BPS}(M,X,α)$はM上のハミルトン函数がXで十分大きい値を取る場合にαを代表
する周期軌道が存在するかという問題に関わって定義される。
一方で、エントフとポルテロヴィッチは非交叉配置性の文脈でシンプレクティッ
ク多様体の「重い」部分集合というものを定義している。
本講演ではビラン・ポルテロヴィッチ・サラモン容量$C_{BPS}(M,X,α)$の有限性
(適当な設定下での周期軌道の存在)を重い部分集合を用いて示す方法について解
説する。
これまでの研究では(自由ループの)ホモトピー類αを代表する周期軌道の検出に
は、αを代表する軌道のハミルトン・フレアー理論を用いるのが一般的であった。
重い部分集合は(可縮軌道のハミルトン・フレアー理論の)スペクトル不変量を用
いて定義される概念であるので、今回の手法では可縮軌道のハミルトン・フレア
ー理論を用いて非可縮軌道を検出することになる。
On codimension two contact embeddings in the standard spheres (JAPANESE)
[ 講演概要 ]
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.
2016年01月09日(土)
調和解析駒場セミナー
13:00-18:00 数理科学研究科棟(駒場) 128号室
田中 仁 氏 (東京大学) 13:30-15:00
The n linear embedding theorem
(日本語)
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain
(日本語)
田中 仁 氏 (東京大学) 13:30-15:00
The n linear embedding theorem
(日本語)
[ 講演概要 ]
実関数論の方法による調和解析の分野において，2進立方体を用いた解析は長い歴史を持ち，豊かな内容を持っています．
しかし，それは単純なモデルを与え，それゆえ実験的な考察のための，もしくは最良の定数を決定するための，補助的なものとしての位置づけのみをこれまで与えられてきたように思われます．
ところが，この分野で基本的かつ重要な作用素の一つである特異積分作用素が，この2進立方体が作る正作用素の族によって，各点において支配されることが発見され，2進立方体を用いた解析はその重要性が再認識されるようになりました．
本講演では，この2進立方体が作る加重付多重正作用素の有界性を保証する「n重線形埋蔵定理」について紹介します．
平田賢太郎 氏 (広島大学) 15:30-17:00実関数論の方法による調和解析の分野において，2進立方体を用いた解析は長い歴史を持ち，豊かな内容を持っています．
しかし，それは単純なモデルを与え，それゆえ実験的な考察のための，もしくは最良の定数を決定するための，補助的なものとしての位置づけのみをこれまで与えられてきたように思われます．
ところが，この分野で基本的かつ重要な作用素の一つである特異積分作用素が，この2進立方体が作る正作用素の族によって，各点において支配されることが発見され，2進立方体を用いた解析はその重要性が再認識されるようになりました．
本講演では，この2進立方体が作る加重付多重正作用素の有界性を保証する「n重線形埋蔵定理」について紹介します．
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain
(日本語)
[ 講演概要 ]
2007年にPolacik-Quittner-Soupletは，任意の領域において半線形熱方程式$u_t-\Delta u=u^p$の正値解に対して初期時刻，爆発時刻，領域の境界付近の増大度に関する先験的評価を与えた．
爆発時刻における増大度は最良であるが，初期時刻および領域の境界付近での増大度は最良ではない．
本講演では，調和関数の評価，放物型ポテンシャル論の結果や熱核評価を上手く用いると，$p$が$1$に近い時にはLipschitz領域上の正値解に対してもっと良い評価が得られることを報告する．
2007年にPolacik-Quittner-Soupletは，任意の領域において半線形熱方程式$u_t-\Delta u=u^p$の正値解に対して初期時刻，爆発時刻，領域の境界付近の増大度に関する先験的評価を与えた．
爆発時刻における増大度は最良であるが，初期時刻および領域の境界付近での増大度は最良ではない．
本講演では，調和関数の評価，放物型ポテンシャル論の結果や熱核評価を上手く用いると，$p$が$1$に近い時にはLipschitz領域上の正値解に対してもっと良い評価が得られることを報告する．
2016年01月08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
小木曽啓示 氏 (東京大学大学院数理科学研究科)
Birational geometry through complex dymanics (ENGLISH)
小木曽啓示 氏 (東京大学大学院数理科学研究科)
Birational geometry through complex dymanics (ENGLISH)
[ 講演概要 ]
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so
mpressed.
The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be
observed.
In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:
(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;
(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;
(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus
quotient.
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so
mpressed.
The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be
observed.
In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:
(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;
(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;
(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus
quotient.
2016年01月06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
Benoit Collins 氏 (京大理)
Quantum channels from the free orthogonal quantum group (English)
Benoit Collins 氏 (京大理)
Quantum channels from the free orthogonal quantum group (English)
2016年01月05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
Eric Skibsted 氏 (Aarhus University, Denmark)
Stationary scattering theory on manifolds (English)
Eric Skibsted 氏 (Aarhus University, Denmark)
Stationary scattering theory on manifolds (English)
[ 講演概要 ]
We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).
We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).
2015年12月21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
David Croydon 氏 (University of Warwick)
Scaling limits of random walks on trees (English)
David Croydon 氏 (University of Warwick)
Scaling limits of random walks on trees (English)
[ 講演概要 ]
I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.
I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.
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
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