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Seminar information archive
Seminar information archive ～04/21｜Today's seminar 04/22 | Future seminars 04/23～
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
栗林 勝彦 (信州大学)
On the (co)chain type levels of spaces
栗林 勝彦 (信州大学)
On the (co)chain type levels of spaces
[ Abstract ]
Avramov, Buchweitz, Iyengar and Miller have introduced
the notion of the level for an object of a triangulated category.
The invariant measures the number of steps to build the given object
out of some fixed object with triangles.
Using this notion in the derived category of modules over a (co)chain
algebra,
we define a new topological invariant, which is called
the (co)chain type level of a space.
In this talk, after explaining fundamental properties of the invariant,
I describe the chain type level of the Borel construction
of a homogeneous space as a computational example.
I will also relate the chain type level of a space to algebraic
approximations of the L.-S. category due to Kahl and to
the original L.-S. category of a map.
Avramov, Buchweitz, Iyengar and Miller have introduced
the notion of the level for an object of a triangulated category.
The invariant measures the number of steps to build the given object
out of some fixed object with triangles.
Using this notion in the derived category of modules over a (co)chain
algebra,
we define a new topological invariant, which is called
the (co)chain type level of a space.
In this talk, after explaining fundamental properties of the invariant,
I describe the chain type level of the Borel construction
of a homogeneous space as a computational example.
I will also relate the chain type level of a space to algebraic
approximations of the L.-S. category due to Kahl and to
the original L.-S. category of a map.
Lectures
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 5
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 5
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
2010/01/25
GCOE lecture series
14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Charles Fefferman (Princeton University)
Extension of Functions and Interpolation of Data
Charles Fefferman (Princeton University)
Extension of Functions and Interpolation of Data
[ Abstract ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.
Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?
Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?
What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.
Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?
Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?
What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?
Lectures
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Colin Guillarmou (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds
Colin Guillarmou (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
權業 善範 (東大数理)
On weak Fano varieties with log canonical singularities
權業 善範 (東大数理)
On weak Fano varieties with log canonical singularities
[ Abstract ]
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
2010/01/22
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)
中川淳一 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
中川淳一 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
Lectures
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 3
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 3
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
2010/01/21
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
山下真 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
山下真 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
Applied Analysis
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
Danielle Hilhorst (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
[ Abstract ]
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
2010/01/20
Geometry Seminar
17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Craig Van Coevering (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
Craig Van Coevering (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
[ Abstract ]
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
Lectures
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 2
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 2
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
Mathematical Biology Seminar
14:40-16:10 Room #052 (Graduate School of Math. Sci. Bldg.)
江島啓介 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
江島啓介 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
[ Abstract ]
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
2010/01/19
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
岡田 靖則 (千葉大・理)
超函数の有界性と Massera 型定理について
岡田 靖則 (千葉大・理)
超函数の有界性と Massera 型定理について
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
高井博司 (首都大学東京)
Entire Cyclic Cohomology of Noncommutative Spheres
高井博司 (首都大学東京)
Entire Cyclic Cohomology of Noncommutative Spheres
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
小林 亮一 (名古屋大学)
Localization via group action and its application to
the period condition of algebraic minimal surfaces
小林 亮一 (名古屋大学)
Localization via group action and its application to
the period condition of algebraic minimal surfaces
[ Abstract ]
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The ``collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The ``collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.
Lectures
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 1
伊東一文 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 1
[ Abstract ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions
2010/01/18
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
奥間智弘 (山形大学地域教育文化学部)
スプライス商特異点について
奥間智弘 (山形大学地域教育文化学部)
スプライス商特異点について
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Anne-Sophie Kaloghiros (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
Anne-Sophie Kaloghiros (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
[ Abstract ]
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.
In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are ``topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.
In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are ``topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.
2010/01/15
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)
中川淳一 (新日本製鐵(株)技術開発本部)
製鐵プロセスにおける数学
中川淳一 (新日本製鐵(株)技術開発本部)
製鐵プロセスにおける数学
2010/01/14
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Marius Junge (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory
Marius Junge (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory
2010/01/13
Lectures
16:45-17:45 Room #128 (Graduate School of Math. Sci. Bldg.)
Felix Rubin (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble
Felix Rubin (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble
Lectures
15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Allman (Warwick 大学)
Breaking the chain: slow versus fast pulling
Michael Allman (Warwick 大学)
Breaking the chain: slow versus fast pulling
2010/01/12
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
西岡斉治 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
西岡斉治 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
[ Abstract ]
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
[ Reference URL ]差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
Tuesday Seminar on Topology
16:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
篠原 克寿 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
On a generalized suspension theorem for directed Fukaya categories
篠原 克寿 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
[ Abstract ]
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
二木 昌宏 (東京大学大学院数理科学研究科) 17:30-18:30In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
On a generalized suspension theorem for directed Fukaya categories
[ Abstract ]
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
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