過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~



16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)
Nessim Sibony 氏 (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
[ 講演概要 ]
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\\"ahler manifolds.


13:45-14:45   数理科学研究科棟(駒場) 128号室
Karl Oeljeklaus 氏 (University of Provence)
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)


15:00-16:00   数理科学研究科棟(駒場) 128号室
Andrei Iordan 氏 (Univ. Paris VI)
Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds


16:30-17:30   数理科学研究科棟(駒場) 002号室
Nessim Sibony 氏 (Univ. Paris Sud)
Holomorphic Dynamics In Several
Variables: equidistribution properties and statistical behavior



16:30-18:00   数理科学研究科棟(駒場) 056号室
Ingo Runkel 氏 (King's College London)
Algebraic structures in conformal field theory
[ 講演概要 ]
It turned out to be fruitful to isolate questions in CFT which can be formulated in a purely categorical fashion. The way left and right moving degrees of freedom can be combined to a consistent theory is an example of this, the relevant structure being a commutative symmetric Frobenius algebra. This is true independently of whether CFT is formulated via sewing of surfaces or nets of operator algebras. Another example is modular invariance, which has a surprising alternative formulation as a certain maximality condition.


15:00-16:20   数理科学研究科棟(駒場) 056号室
Odo Diekmann 氏 (Mathematical Institute, Utrecht University)
The delay equation formulation of physiologically structured population models
[ 講演概要 ]
Traditionally, physiologically structured population models are formulated in terms of first order partial differential equations with non-local boundary conditions and/or transformed arguments. The stability and bifurcation theory for such equations is, in the quasi-linear case, still very immature.
The aim of this lecture is to explain that, alternatively, one can formulate such models in terms of delay equations (more precisely : renewal equations coupled to delay differential equations) without losing essential information and that for delay equations there is a well-developed local stability and bifurcation theory. As a motivating example we consider the interaction between a size-structured consumer and an unstructured resource. The lecture is based on joint work with Mats Gyllenberg and Hans Metz.



17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
作間 誠 氏 (広島大学)
The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
[ 講演概要 ]
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.



16:30-18:00   数理科学研究科棟(駒場) 126号室
佐野 太郎 氏 (東大数理)
Seshadri constants on rational surfaces with anticanonical pencils

[ 講演概要 ]
射影多様体上の豊富線束の$k$-jet ample性を測る不変量として
その公式を使うと、対数del Pezzo曲面の特異点の情報をSeshadri定数の値から



16:30-18:00   数理科学研究科棟(駒場) 056号室
Mikael Pichot 氏 (東大数物連携宇宙研究機構)
Examples of groups of intermediate rank



10:30-12:00   数理科学研究科棟(駒場) 126号室
赤堀隆夫 氏 (兵庫県立大学)
On the CR Hamiltonian flows
[ 講演概要 ]
The deformation theory of CR structures was initiated by Kuranishi and the versal family of CR structures were constructed by Garfied, Lee and myself "in the sense of Kuranishi". Miyajima also discussed the versal family by the completely different method. While, our method relies on the contact geometry(this suggest that there is a deep relation between Hamiltonian geometry and CR structures). Today, I report that our family is also versal "in the sense of CR Hamiltonian flows".


16:30-18:00   数理科学研究科棟(駒場) 126号室
柳田 伸太郎 氏 (神戸大学理学研究科)
[ 講演概要 ]
今回の講演は吉岡康太との共同研究に基づくものである. 研究の発端は, 向井茂が1980年前後(フーリエ向井変換の発見前後)に考察し, 当時の講演記録に書き残した主張や予想の解読にある.
本研究は, 大まかに言うと, 半等質層とフーリエ向井変換を用いて, アーベル曲面上の安定層のモジュライ空間の構造を調べるというものである.
アーベル曲面上には半等質層と呼ばれる半安定層があり, その分類, 構成方法やコホモロジーが完全に知られている. アーベル曲面のフーリエ向井対は半等質層のモジュライ空間であることも知られている.
今回の研究はこの半等質層をbulding blockとして一般の安定層を構成することを考える. その際に"semi-homogeneous presentation"という概念が必要になる. これはアーベル曲面上の安定層の半等質層によるある種の分解のことである. 曲面のピカール数が1の時, この種の分解の存在が安定層のチャーン指標のみを用いて判定できる.
また安定層のフーリエ変換における振舞いの記述において, 算術群や整数係数2次形式が重要な役割を果たすことも分かる. この事と先に述べた表示の存在から, 安定層のモジュライとアーベル曲面上の点のヒルベルトスキームとの間の双有理変換が明示的に構成できる.
アーベル曲面のフーリエ向井変換のフォーマリズムはK3曲面の変換と共通する部分も少なくない. 講演ではそうした点にも触れつつ, 今回の結果とその証明の概要を解説したい.



17:00-18:00   数理科学研究科棟(駒場) 056号室
小沢登高 氏 (東大数理)
Dixmier's Similarity Problem ---Littlewood and Forests--- (一般の数学者向け)



15:30-17:00   数理科学研究科棟(駒場) 470号室
金井 政宏 氏 (東大数理)
ASEPおよびzero-range processの分配関数



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
北山 貴裕 氏 (東京大学大学院数理科学研究科)
Torsion volume forms and twisted Alexander functions on
character varieties of knots

[ 講演概要 ]
Using non-acyclic Reidemeister torsion, we can canonically
construct a complex volume form on each component of the
lowest dimension of the $SL_2(\\mathbb{C})$-character
variety of a link group.
This volume form enjoys a certain compatibility with the
following natural transformations on the variety.
Two of them are involutions which come from the algebraic
structure of $SL_2(\\mathbb{C})$ and the other is the
action by the outer automorphism group of the link group.
Moreover, in the case of knots these results deduce a kind
of symmetry of the $SU_2$-twisted Alexander functions
which are globally described via the volume form.


16:30-18:00   数理科学研究科棟(駒場) 128号室
Ivana Alexandrova 氏 (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
[ 講演概要 ]
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.



10:30-12:00   数理科学研究科棟(駒場) 126号室
藤木 明 氏 (大阪大学)


16:30-18:00   数理科学研究科棟(駒場) 126号室
大川 領 氏 (東京工業大学)
Moduli on the projective plane and the wall-crossing
[ 講演概要 ]
射影平面上の半安定層のモジュライ空間を、Bridgeland 安定性条件
により、壁越え現象としてのflip の記述を得る。
応用として、flip のBetti 数などが計算できる。



16:30-18:00   数理科学研究科棟(駒場) 056号室
鈴木章斗 氏 (九州大学数理学研究院)
Infrared divergence of scalar quantum field model on pseudo Riemann manifold



16:30-18:45   数理科学研究科棟(駒場) 056号室
Vincent Maillot 氏 (Paris第7大学) 16:30-17:30
New algebraicity results for analytic torsion
Richard Hain 氏 (Duke大学) 17:45-18:45
On the Section Conjecture for the universal curve over function fields


10:30-11:30   数理科学研究科棟(駒場) 056号室
Winston Ou 氏 (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
[ 講演概要 ]
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.


15:30-17:00   数理科学研究科棟(駒場) 122号室
柳尾 朋洋 氏 (早大 基幹理工)
[ 講演概要 ]



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
久野 雄介 氏 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications
[ 講演概要 ]
Meyer function is a kind of secondary invariant related to the signature
of surface bundles over surfaces. In this talk I will show there exist uniquely the Meyer function
for each smooth projective variety.
Our function is a class function on the fundamental group of some open algebraic variety.
I will also talk about its application to local signature for fibered 4-manifolds


16:30-18:00   数理科学研究科棟(駒場) 126号室
岸本崇氏 氏 (埼玉大学理工学研究科)
Group actions on affine cones
[ 講演概要 ]
The action of the additive group scheme C_+ on normal affine varieties is one of main subjects in affine algebraic geometry for a long time. In this talk, we shall mainly consider the problem about the existence of C_+-actions on affine cones, more precisely, the question:

"Determine the affine cones over smooth projective varieties admitting a (non-trivial) C_+-action ".

This question has an interest from a point of view of singularities. Indeed, a normal Cohen-Macaulay affine variety admitting an action by C_+ has at most rational singularities due to the result of H. Flenner and M. Zaidenberg. In the case of dimension 2, any affine cone over the projective line P^1 has a cyclic quotient singularity, and we can see that it admits, in fact, a C_+-action. Meanwhile, in case of dimension 3, i.e., affine cones over rational surfaces, the situation becomes more subtle.

One of the main results is concerned with a criterion for the existence of a C_+-action on affine cones (of any dimension) in terms of a cylinderlike open subset on the base variety. By making use of it, it is shown that, for any rational surface Y, we can take a suitable embedding of Y in such a way that the associated affine cone admits an action of C_+. Furthermore we are able to confirm that an affine cone over an anticanonically embedded del Pezzo surface of degree greater than or equal to 4 also admits such an action.

Nevertheless, our final purpose to decide whether or not there does exist a C_+-action on the fermat cubic: x^3+y^3+z^3+u^3 =0 in C^4, which is the affine cone over an anticanonically embedded cubic surface, say Y_3, is not yet accomplished. But, we can obtain certain informations about a linear pencil of rational curves on Y_3 arising from a C_+-action which seem to be useful in order to deny an existence of an action of C_+.



10:30-12:00   数理科学研究科棟(駒場) 126号室
早乙女飛成 氏 (筑波大学)



13:30-16:00   数理科学研究科棟(駒場) 123号室
小池 健二 氏 (山梨大学教育人間科学部) 13:30-14:30
成田宏秋 氏 (熊本大学理学部) 15:00-16:00
Fourier coefficients of Arakawa lifting and some degree eight L-function

[ 講演概要 ]

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