過去の記録 ~07/14本日 07/15 | 今後の予定 07/16~


16:30-18:00   数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.
[ 参考URL ]



11:00-12:00   数理科学研究科棟(駒場) 126号室
野口 潤次郎 氏 (東大数理)
Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)
[ 講演概要 ]
The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.
In the talk we will fix an error in an application in [NW02], and we will show
Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.
For the finiteness we obtain
Theorem 2. Let the notation be as above.
(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,
recent due to A. Levin.



13:00-18:00   数理科学研究科棟(駒場) 128号室
Jayson Cunanan 氏 (名古屋大学) 13:30-15:00
Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)
[ 講演概要 ]
We study the boundedness of
unimodular Fourier multipliers on Wiener amalgam spaces.
For a real-valued homogeneous function ¥mu
on ¥mathbb{R}^n of degree ¥alpha¥ge 2,
we show the boundedness of the operator e^{i¥mu(D)}
between the weighted Wiener amalgam space
W_s^{p,q} and W^{p,q}
for all 1¥le p,q¥le¥infty and
This threshold is shown to be optimal for regions
¥max(1/q, 1/2)¥le 1/p
¥min(1/q, 1/2)¥geq 1/p.
we give sufficient conditions
for the boundedness of e^{i¥mu(D)}
on W^{p,q} for ¥alpha¥in(0,2).
眞崎 聡 氏 (広島大学) 15:30-17:00
質量劣臨界非線型シュレディンガー方程式の解析 (JAPANESE)
[ 講演概要 ]



16:40-18:50   数理科学研究科棟(駒場) 056号室
Christopher Davis 氏 (University of Copenhagen) 16:40-17:40
An approach to p-adic Hodge theory over number fields (ENGLISH)
[ 講演概要 ]
As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.
Bryden Cais 氏 (University of Arizona) 17:50-18:50
Canonical lifts of norm fields and applications (ENGLISH)
[ 講演概要 ]
In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.


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)。

Bo Berndtsson 氏 (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
[ 講演概要 ]
The classical Brunn-Minkowski theory deals with the volume of convex sets.
It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.



16:00-17:30   数理科学研究科棟(駒場) 002号室
Thomas Giletti 氏 (Univ. of Lorraine at Nancy)
Inside dynamics of pushed and pulled fronts (ENGLISH)
[ 講演概要 ]
Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.



18:00-19:00   数理科学研究科棟(駒場) 117号室
柏原正樹 氏 (京都大学数理解析研究所)
Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)
[ 講演概要 ]
The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.
(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.)


15:00-16:30   数理科学研究科棟(駒場) 122号室
Thomas Ducat 氏 (University of Warwick)
Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)
[ 講演概要 ]
Consider a singular curve C contained in a smooth 3-fold X.
Assuming the existence of a Du Val general elephant S containing C,
I give a normal form for the equations of C in X and an outline of how to
construct a divisorial extraction from this curve. If the general S is
Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit
conditions for the existence of a terminal extraction. A treatment of
the D_{2k+1} case should be possible by similar means.



16:30-18:00   数理科学研究科棟(駒場) 128号室
浜向 直 氏 (東大数理)
符号付き距離関数との比較に基づく改良された等高面法 (JAPANESE)
[ 講演概要 ]
その補助関数に対する偏微分方程式を解くことで曲面の動きを求める。 しかし
時間が経つにつれて解の傾きが小さくなることがあり、 計算機では等高面を取
り出すことが困難となる。 そこで本講演では、方程式を適当に修正すること
で、 ゼロ等高面付近で傾きが小さくならない解が得られることを、 符号付き距


16:30-17:30   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
[ 講演概要 ]
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact


17:30-18:30   数理科学研究科棟(駒場) 056号室
李 暁龍 氏 (東京大学大学院数理科学研究科)
ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
[ 講演概要 ]
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.



10:30-12:00   数理科学研究科棟(駒場) 126号室
宮地 秀樹 氏 (大阪大学)
タイヒミュラー距離の幾何学とその応用 (JAPANESE)
[ 講演概要 ]
タイヒミュラー空間上にはタイヒミュラー距離と呼ばれるリーマン面の擬等角変形理論に関して自然な距離がある. タイヒミュラー距離はタイヒミュラー空間の複素構造に関する小林距離と一致する. この講演では, タイヒミュラー空間の一つのコンパクト化を用いて, タイヒミュラー距離に関する幾何学と曲面上の単純閉曲線の交点数関数による幾何学との関連を解説する. そして, このコンパクト化の性質を応用して得られる, 単位円板からタイヒミュラー空間への正則写像の剛性についても話す.


16:00-17:00   数理科学研究科棟(駒場) 118号室
Victor Isakov 氏 (The Wichita State University)
Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)
[ 講演概要 ]
We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.


15:30-17:00   数理科学研究科棟(駒場) 126号室
佐野 太郎 氏 (University of Warwick)
Deforming elephants of Q-Fano 3-folds (ENGLISH)
[ 講演概要 ]
Shokurov and Reid proved that a Fano 3-fold with canonical
Gorenstein singularities has a Du Val elephant, that is,
a member of the anticanonical linear system with only Du Val singularities.
The classification of Fano 3-folds is based on this fact.
However, for a Fano 3-fold with non-Gorenstein terminal singularities,
the anticanonical system does not contain such a member in general.
Alt{\\i}nok--Brown--Reid conjectured that, if the anticanonical system is non-empty,
a Q-Fano 3-fold can be deformed to that with a Du Val elephant.
In this talk, I will explain how to deform an elephant with isolated
singularities to a Du Val elephant.



14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory IV (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 118号室
谷本溶 氏 (東大数理)
Wedge-local fields in integrable models with bound states (JAPANESE)


16:00-17:00   数理科学研究科棟(駒場) 370号室
Victor Isakov 氏 (The Wichita State University)
Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)
[ 講演概要 ]
We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.


17:00-18:00   数理科学研究科棟(駒場) 370号室
Jin Cheng 氏 (Fudan University)
A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)
[ 講演概要 ]
In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.


16:40-17:40   数理科学研究科棟(駒場) 056号室
Stephen Lichtenbaum 氏 (Brown University)
Special values of zeta-functions of schemes (ENGLISH)
[ 講演概要 ]
We will give conjectured formulas giving the behavior of the
seta-function of regular schemes projective and flat over Spec Z at
non-positive integers in terms of Weil-etale cohomology. We will also
explain the conjectured relationship of Weil-etale cohomology to etale
cohomology, which makes it possible to express these formulas also in terms
of etale cohomology.



14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory III (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 参考URL ]


17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
Rinat Kashaev 氏 (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
[ 講演概要 ]
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.


16:30-18:00   数理科学研究科棟(駒場) 128号室
伊藤 健一 氏 (筑波大)
Threshold properties for one-dimensional discrete Schr\\"odinger operators (JAPANESE)
[ 講演概要 ]
We study the relation between the generalized eigenspace and the asymptotic expansion of the resolvent around the threshold $0$ for the one-dimensional discrete Schr\\"odinger operator on $\\mathbb Z$. We decompose the generalized eigenspace into the subspaces corresponding to the eigenstates and the resonance states only by their asymptotics at infinity, and classify the coefficient operators of the singlar part of resolvent expansion completely in terms of these eigenspaces. Here the generalized eigenspace we consider is largest possible. For an explicit computation of the resolvent expansion we apply the expansion scheme of Jensen-Nenciu (2001). This talk is based on the recent joint work with Arne Jensen (Aalborg University).


16:30-18:00   数理科学研究科棟(駒場) 126号室
森真樹 氏 (東京大学大学院数理科学研究科)
[ 講演概要 ]
その単純加群の分類は、Brundan, Kleshchevと土岡により


15:00-16:00   数理科学研究科棟(駒場) 118号室
Oleg Emanouilov 氏 (Colorado State University)
Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)
[ 講演概要 ]
We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.



14:00-16:00   数理科学研究科棟(駒場) 123号室
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 14:00-14:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 15:00-15:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

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