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過去の記録 ～04/21｜本日 04/22 | 今後の予定 04/23～
2018年07月09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
Casey Kelleher 氏 (Princeton University)
Rigidity results for symplectic curvature flow (ENGLISH)
Casey Kelleher 氏 (Princeton University)
Rigidity results for symplectic curvature flow (ENGLISH)
[ 講演概要 ]
We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.
We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.
2018年07月03日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
吉田 純 氏 (東京大学大学院数理科学研究科)
Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)
Tea: Common Room 16:30-17:00
吉田 純 氏 (東京大学大学院数理科学研究科)
Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)
[ 講演概要 ]
The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.
The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.
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
Xun Yu 氏 (Tianjin University)
Surface automorphisms and Salem numbers (English)
Xun Yu 氏 (Tianjin University)
Surface automorphisms and Salem numbers (English)
[ 講演概要 ]
The entropy of a surface automorphism is either zero or the
logarithm of a Salem number.
In this talk, we will discuss which Salem numbers arise in this way. We
will show that any
supersingular K3 surface in odd characteristic has an automorphism the
entropy of which is
the logarithm of a Salem number of degree 22. In particular, such
automorphisms are
not geometrically liftable to characteristic 0.
The entropy of a surface automorphism is either zero or the
logarithm of a Salem number.
In this talk, we will discuss which Salem numbers arise in this way. We
will show that any
supersingular K3 surface in odd characteristic has an automorphism the
entropy of which is
the logarithm of a Salem number of degree 22. In particular, such
automorphisms are
not geometrically liftable to characteristic 0.
2018年07月02日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
世良 透 氏 (京都大学大学院理学研究科)
間欠力学系に関する種々の分布極限定理 (JAPANESE)
世良 透 氏 (京都大学大学院理学研究科)
間欠力学系に関する種々の分布極限定理 (JAPANESE)
[ 講演概要 ]
間欠力学系とは，中立不動点を持つ一次元写像力学系のことである．この力学系は様々な非平衡系に現れる間欠現象のモデルとして，統計物理学などの観点から広く研究されてきた．間欠現象とは，ほぼ周期的かつ持続的な「安定状態」が，非周期的かつ一時的に生ずる「不安定状態」によって繰り返し中断される，という現象を指す．Lorenz(1963)は熱対流の微分方程式モデルを研究し，解軌道の数値プロットから間欠力学系を抽出した．Pomeau--Manneville(1980)は「熱対流の安定状態」を「間欠力学系の中立不動点」と見なして，間欠力学系を介してLorenzの熱対流モデルが持つ間欠性を考察している．
また，間欠力学系は無限エルゴード理論などの観点からも研究され，Markov過程論のアナロジーから種々の分布極限定理が得られてきた．本講演では間欠力学系に関する分布極限定理として，中立不動点から離れた場所(不安定状態)への滞在に関するAaronson(1981)&(1986)，Owada--Samorodnitsky(2015)の結果，および中立不動点近傍(安定状態)への滞在に関するThaler(2002)，S.--Yano(2017+)の結果を紹介する．そしてこれらを統合・精密化した講演者の最近の結果について述べる．間欠力学系の滞在時間のスケール極限として，マルチレイ上を走る歪みBessel拡散過程の原点局所時間や各レイごとの滞在時間が現れる．証明の鍵は周遊理論およびTyran-Kaminska(2010)による定常増分過程の関数型極限定理である．
間欠力学系とは，中立不動点を持つ一次元写像力学系のことである．この力学系は様々な非平衡系に現れる間欠現象のモデルとして，統計物理学などの観点から広く研究されてきた．間欠現象とは，ほぼ周期的かつ持続的な「安定状態」が，非周期的かつ一時的に生ずる「不安定状態」によって繰り返し中断される，という現象を指す．Lorenz(1963)は熱対流の微分方程式モデルを研究し，解軌道の数値プロットから間欠力学系を抽出した．Pomeau--Manneville(1980)は「熱対流の安定状態」を「間欠力学系の中立不動点」と見なして，間欠力学系を介してLorenzの熱対流モデルが持つ間欠性を考察している．
また，間欠力学系は無限エルゴード理論などの観点からも研究され，Markov過程論のアナロジーから種々の分布極限定理が得られてきた．本講演では間欠力学系に関する分布極限定理として，中立不動点から離れた場所(不安定状態)への滞在に関するAaronson(1981)&(1986)，Owada--Samorodnitsky(2015)の結果，および中立不動点近傍(安定状態)への滞在に関するThaler(2002)，S.--Yano(2017+)の結果を紹介する．そしてこれらを統合・精密化した講演者の最近の結果について述べる．間欠力学系の滞在時間のスケール極限として，マルチレイ上を走る歪みBessel拡散過程の原点局所時間や各レイごとの滞在時間が現れる．証明の鍵は周遊理論およびTyran-Kaminska(2010)による定常増分過程の関数型極限定理である．
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
松崎克彦 氏 (早稲田大学)
Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)
松崎克彦 氏 (早稲田大学)
Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)
[ 講演概要 ]
In this talk, I explain a complex analytic method and its applications for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasi-conformally. In RIMS conference "Open Problems in Complex Geometry'' held in 2010, I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and mentioned several problems on the fixed points of group actions on the universal Teichmueller space and its subspaces, and the rigidity of conjugation of certain groups of circle homeomorphisms. I will report on the development of these problems since then.
In this talk, I explain a complex analytic method and its applications for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasi-conformally. In RIMS conference "Open Problems in Complex Geometry'' held in 2010, I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and mentioned several problems on the fixed points of group actions on the universal Teichmueller space and its subspaces, and the rigidity of conjugation of certain groups of circle homeomorphisms. I will report on the development of these problems since then.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
通常の曜日と異なります。
László Székelyhidi Jr. 氏 (Universität Leipzig)
Convex integration in fluid dynamics (English)
通常の曜日と異なります。
László Székelyhidi Jr. 氏 (Universität Leipzig)
Convex integration in fluid dynamics (English)
[ 講演概要 ]
In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.
We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.
In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.
We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.
2018年06月29日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 056号室
石毛和弘 氏 (東京大学大学院数理科学研究科)
放物型方程式の解の冪凸性 (日本語)
石毛和弘 氏 (東京大学大学院数理科学研究科)
放物型方程式の解の冪凸性 (日本語)
[ 講演概要 ]
放物型方程式の解の凸冪性の研究は、Brascamp-Lieb (1976), Korevaar (1983)らの研究を契機として大きく進展し、例えば、正値な値をもつ初期関数の対数が上に凸であるとき、熱流はその凸性を保つこと等が解明されてきた。
本講演では、これら一連の研究を概観した後、Paolo Salani 氏らとの共同研究に基づき、放物型冪凸という概念の導入とその応用、放物型方程式系の解の冪凸性等について述べ、さらに近年の研究の進展について触れる。
放物型方程式の解の凸冪性の研究は、Brascamp-Lieb (1976), Korevaar (1983)らの研究を契機として大きく進展し、例えば、正値な値をもつ初期関数の対数が上に凸であるとき、熱流はその凸性を保つこと等が解明されてきた。
本講演では、これら一連の研究を概観した後、Paolo Salani 氏らとの共同研究に基づき、放物型冪凸という概念の導入とその応用、放物型方程式系の解の冪凸性等について述べ、さらに近年の研究の進展について触れる。
2018年06月27日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Seung-Hyeok Kye 氏 (Seoul National Univ.)
未定
Seung-Hyeok Kye 氏 (Seoul National Univ.)
未定
2018年06月26日(火)
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
渡辺究 氏 (埼玉)
Varieties with nef diagonal (English)
渡辺究 氏 (埼玉)
Varieties with nef diagonal (English)
[ 講演概要 ]
For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a
cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth
del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for
spherical varieties. This is a joint work with Taku Suzuki.
For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a
cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth
del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for
spherical varieties. This is a joint work with Taku Suzuki.
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
小川卓克 氏 (東北大学)
移流拡散方程式の初期値問題について (日本語)
小川卓克 氏 (東北大学)
移流拡散方程式の初期値問題について (日本語)
[ 講演概要 ]
We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.
We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.
2018年06月25日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
濱口 雄史 氏 (京都大学大学院理学研究科)
BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)
濱口 雄史 氏 (京都大学大学院理学研究科)
BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)
[ 講演概要 ]
金利マーケットや商品先物市場では、フォワードカーブのランダムな時間発展挙動を連続関数空間上の無限次元確率過程として記述する手法が用いられる。このモデルでは形式的に非加算無限個の取引可能財が存在するため、ボンドの満期を表す区間上の符号付測度に値を取るポートフォリオを考えることとなる。本講演では、無限次元マーケットにおけるクレームのヘッジに関連して、無限次元マルチンゲール(連続関数空間上のcylindrical martingale)により駆動するリプシッツ型BSDEの解の存在と一意性を示す。さらに、この解が対応する有限次元BSDEの解によって近似できることを示す。これにより、無限次元マーケットにおけるクレームの形式的なヘッジ戦略が、有限次元部分マーケットにおけるFollmer-Schweizer分解、すなわち局所リスク最少戦略の極限として得られることが従う。
金利マーケットや商品先物市場では、フォワードカーブのランダムな時間発展挙動を連続関数空間上の無限次元確率過程として記述する手法が用いられる。このモデルでは形式的に非加算無限個の取引可能財が存在するため、ボンドの満期を表す区間上の符号付測度に値を取るポートフォリオを考えることとなる。本講演では、無限次元マーケットにおけるクレームのヘッジに関連して、無限次元マルチンゲール(連続関数空間上のcylindrical martingale)により駆動するリプシッツ型BSDEの解の存在と一意性を示す。さらに、この解が対応する有限次元BSDEの解によって近似できることを示す。これにより、無限次元マーケットにおけるクレームの形式的なヘッジ戦略が、有限次元部分マーケットにおけるFollmer-Schweizer分解、すなわち局所リスク最少戦略の極限として得られることが従う。
離散数理モデリングセミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Anton Dzhamay 氏 (University of Northern Colorado)
Gap Probabilities and discrete Painlevé equations
Anton Dzhamay 氏 (University of Northern Colorado)
Gap Probabilities and discrete Painlevé equations
[ 講演概要 ]
It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).
This is joint work with Alisa Knizel (Columbia University)
It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).
This is joint work with Alisa Knizel (Columbia University)
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
Stephen McKeown 氏 (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
Stephen McKeown 氏 (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
[ 講演概要 ]
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.
2018年06月22日(金)
講演会
16:00-17:00 数理科学研究科棟(駒場) 128号室
Michael Harrison 氏 (Lehigh University)
Fibrations of R^3 by oriented lines
Michael Harrison 氏 (Lehigh University)
Fibrations of R^3 by oriented lines
[ 講演概要 ]
Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.
Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.
2018年06月20日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 056号室
長町一平 氏 (東京大学数理科学研究科)
Criteria for good reduction of hyperbolic polycurves (JAPANESE)
長町一平 氏 (東京大学数理科学研究科)
Criteria for good reduction of hyperbolic polycurves (JAPANESE)
[ 講演概要 ]
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.
2018年06月19日(火)
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
若林 泰央 氏 (東工大)
Dormant Miura opers and Tango structures (Japanese (writing in English))
若林 泰央 氏 (東工大)
Dormant Miura opers and Tango structures (Japanese (writing in English))
[ 講演概要 ]
Tango（丹後）構造とは, 正標数の代数曲線で定義された然るべき直線束であり, （小平消滅定理の反例となるなどの, いわゆる）「病理的な」正標数の代数多様体を構成するうえで基本的な概念です. 本発表では, このTango構造と, 一見すると無関係にも見える幾つかのトピック（dormant Miura oper, 3正則グラフのナンバリング, Gaudin模型の対角化etc.）との結びつきや関連する結果について説明させていただきたく予定です.（各トピックについて発表者はそれほど詳しくありませんので, この機会にぜひ皆さまの知見を伺えればと思っております.）
Tango（丹後）構造とは, 正標数の代数曲線で定義された然るべき直線束であり, （小平消滅定理の反例となるなどの, いわゆる）「病理的な」正標数の代数多様体を構成するうえで基本的な概念です. 本発表では, このTango構造と, 一見すると無関係にも見える幾つかのトピック（dormant Miura oper, 3正則グラフのナンバリング, Gaudin模型の対角化etc.）との結びつきや関連する結果について説明させていただきたく予定です.（各トピックについて発表者はそれほど詳しくありませんので, この機会にぜひ皆さまの知見を伺えればと思っております.）
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
Rowan Killip 氏 (UCLA)
KdV is wellposed in $H^{-1}$ (English)
Rowan Killip 氏 (UCLA)
KdV is wellposed in $H^{-1}$ (English)
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
吉川周二 氏 (大分大学理工学部)
Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)
吉川周二 氏 (大分大学理工学部)
Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)
[ 講演概要 ]
エネルギー法の差分解法への応用を意識し, 準線形の双曲型保存則系のあるモデルシステムを例に挙げて, この問題の時間に関して中点則で離散化した半離散解法の時間大域解の存在について議論したい. オリジナルの問題は, Racke(1992)や松村--西原(2004)のテキストで紹介されたエネルギー法によって, 初期値が小さいという仮定の下でアプリオリ評価が得られ, 時間大域解の存在を証明できる. 本発表では, 上記の半離散解法もオリジナルの連続問題と同様にして時間大域解の存在を示すことが可能であることについて紹介したい. また誤差評価もこのエネルギー構造を利用して示すことができることも時間があれば触れる. 本研究は川島秀一氏(早稲田大学)との共同研究に基づく.
エネルギー法の差分解法への応用を意識し, 準線形の双曲型保存則系のあるモデルシステムを例に挙げて, この問題の時間に関して中点則で離散化した半離散解法の時間大域解の存在について議論したい. オリジナルの問題は, Racke(1992)や松村--西原(2004)のテキストで紹介されたエネルギー法によって, 初期値が小さいという仮定の下でアプリオリ評価が得られ, 時間大域解の存在を証明できる. 本発表では, 上記の半離散解法もオリジナルの連続問題と同様にして時間大域解の存在を示すことが可能であることについて紹介したい. また誤差評価もこのエネルギー構造を利用して示すことができることも時間があれば触れる. 本研究は川島秀一氏(早稲田大学)との共同研究に基づく.
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
今野 北斗 氏 (東京大学大学院数理科学研究科)
Characteristic classes via 4-dimensional gauge theory (JAPANESE)
Tea: Common Room 16:30-17:00
今野 北斗 氏 (東京大学大学院数理科学研究科)
Characteristic classes via 4-dimensional gauge theory (JAPANESE)
[ 講演概要 ]
Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.
Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.
トポロジー火曜セミナー
14:30-16:00 数理科学研究科棟(駒場) 056号室
RIKEN iTHEMS と共催
深谷 賢治 氏 (サイモンズセンター, SUNY)
相対かつ同変ラグランジアンフレアーホモロジーとアティヤ-フレアー予想 (JAPANESE)
RIKEN iTHEMS と共催
深谷 賢治 氏 (サイモンズセンター, SUNY)
相対かつ同変ラグランジアンフレアーホモロジーとアティヤ-フレアー予想 (JAPANESE)
[ 講演概要 ]
アティヤ-フレアー予想は，ゲージ理論におけるフレアーホモロジーとラグランジアンフレアーホモロジーの間の関係に関するものである．その一つの困難は，ラグランジアンフレアーホモロジーを考えるシンプレクティック多様体が特異点を持つことである．双対かつ同変ラグランジアンフレアーホモロジーを考えることで，この困難が解消し，少なくともアティヤ-フレアー予想を数学的に厳密な予想として定式化できることを説明する．
アティヤ-フレアー予想は，ゲージ理論におけるフレアーホモロジーとラグランジアンフレアーホモロジーの間の関係に関するものである．その一つの困難は，ラグランジアンフレアーホモロジーを考えるシンプレクティック多様体が特異点を持つことである．双対かつ同変ラグランジアンフレアーホモロジーを考えることで，この困難が解消し，少なくともアティヤ-フレアー予想を数学的に厳密な予想として定式化できることを説明する．
2018年06月18日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
種村 秀紀 氏 (慶應義塾大学理工学部数理科学科)
相互作用をもつ無限個の剛体球の系 (JAPANESE)
種村 秀紀 氏 (慶應義塾大学理工学部数理科学科)
相互作用をもつ無限個の剛体球の系 (JAPANESE)
[ 講演概要 ]
粒子間にハードコア相互作用があるとき、その粒子系は剛体球の系と見なすことができ、さらに各々の粒子が独立なブラウン運動により駆動されている場合は、Skorohod 型方程式の解として表すことができる。本講演では、粒子数が無限個であり、剛体球間に長距離相互作用がある場合に、対応する無限次元Skorohod 型方程式を導入し、その解の存在と一意性について議論する。
粒子間にハードコア相互作用があるとき、その粒子系は剛体球の系と見なすことができ、さらに各々の粒子が独立なブラウン運動により駆動されている場合は、Skorohod 型方程式の解として表すことができる。本講演では、粒子数が無限個であり、剛体球間に長距離相互作用がある場合に、対応する無限次元Skorohod 型方程式を導入し、その解の存在と一意性について議論する。
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 122号室
Ryszard Nest 氏 (Copenhagen Univ.)
Equivariant index theorem (English)
Ryszard Nest 氏 (Copenhagen Univ.)
Equivariant index theorem (English)
2018年06月13日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
田中亮吉 氏 (東北大学)
Poisson boundary for the discrete affine group (English)
田中亮吉 氏 (東北大学)
Poisson boundary for the discrete affine group (English)
2018年06月12日(火)
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
柴田 崇広 氏 (京都大学)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
柴田 崇広 氏 (京都大学)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
[ 講演概要 ]
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
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
三松 佳彦 氏 (中央大学)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
Tea: Common Room 16:30-17:00
三松 佳彦 氏 (中央大学)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
[ 講演概要 ]
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
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