過去の記録 ~03/27本日 03/28 | 今後の予定 03/29~



10:30-11:30   数理科学研究科棟(駒場) 056号室
Walter Strauss 氏 (Brown University)
Steady Water Waves with Vorticity
[ 講演概要 ]
Consider a classical 2D water wave under the influence of gravity with an arbitrary vorticity function. Assume such a wave is traveling at a constant speed over a flat bed. Then there exist many families of such waves of large amplitude. The proof is based on elliptic PDEs, bifurcation and degree theory. I will also exhibit some recent numerical computations. If the vorticity is sufficiently large, the first stagnation point occurs not at the crest (as with irrotational flows) but on the bed directly below the crest. For variable vorticity the first stagnation point can occur in the interior of the fluid.
[ 参考URL ]


14:40-15:40   数理科学研究科棟(駒場) 123号室
Alex Cook 氏 (Actuarial Mathematics and Statistics,
School of Mathematical and Computer Sciences,
Heriot-Watt University)
Return of the Giant Hogweed: modelling the invasion of Britain by a dangerous alien plant
[ 講演概要 ]
As a result of changing climate and land use, as well as due to human intervention, increasingly species are moving to new abitats. We wish to understand the risk of invasive species entering new areas, and as an example consider the spread of Giant Hogweed (Heracleum mantegazzianum) from SW Asia in Great Britain, a species that has been damaging Britain's biodiversity since it was introduced in the 19th C and which is dangerous to human health. We construct a spatio-temporal stochastic model for its spread (both local and at distance) that takes account of covariates such as the heterogeneous land-cover and climate of the island. We then fit the model directly to observed data. Fitting the model was non-trivial and involved the use of Markov chain Monte Carlo techniques. The approach taken allows spatio-temporal predictions of the future spread of the weed can be made, consistent with the invasion history; it also allows the effect of varying habitats and climate to be understood. The approach we have taken can be generalised to other biological systems exhibiting stochastic variability, and there are clear parallels to epidemic models for the spread of disease within heterogeneous host populations.
[ 参考URL ]



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
Tian-Jun Li 氏 (University of Minnesota)
The Kodaira dimension of symplectic 4-manifolds
[ 講演概要 ]
Various results and questions about symplectic4-manifolds can be
formulated in terms of the notion of the Kodaira dimension. In particular,
we will discuss the classification and the geography problems. It is interesting
to understand how it behaves undersome basic constructions.Time permitting
we will discuss the symplectic birational aspect of this notion and speculate
how to extend it to higher dimensional manifolds.



16:30-18:00   数理科学研究科棟(駒場) 128号室
山下真 氏 (東大数理)
Affine holonomy foliations



16:20-17:30   数理科学研究科棟(駒場) 122号室
小池 健一 氏 (筑波大学大学院数理物質科学研究科)
[ 講演概要 ]
有界な台をもつ非正則な位置尺度母数分布族に対して,その位置母数の逐次点推定を考える.ここでは,平均二乗誤差に費用も加えてリスクを考える.レンジに基づく停止則を提案し,これが漸近有効であることを示す.また,良く知られているRobbinsの逐次推定方式との比較を行い,密度関数の台の端点で密度関数が急激に変化する場合には,提案する逐次推定方式が標本数やリスクの意味で優れていることを示す.この結果は,逐次区間推定に関するKoike (2007)のものと同様であることが分かる
[ 参考URL ]



17:00-18:30   数理科学研究科棟(駒場) 117号室
Tea: 16:40 - 17:00 コモンルーム
Emmanuel Giroux 氏 (ENS Lyon)
Symplectic mapping classes and fillings
[ 講演概要 ]
We will describe a joint work in progress with Paul Biran in
which contact geometry is combined with properties of Lagrangian manifolds
in subcritical Stein domains to obtain nontrivaility results for symplectic
mapping classes.



10:45-12:15   数理科学研究科棟(駒場) 128号室
坂井秀隆 氏 (東京大学)



17:30-19:00   数理科学研究科棟(駒場) 128号室
楠岡 成雄 氏 (東京大)
分布が Fat tail を持つ i.i.d. 確率変数の和に関して



17:30-19:00   数理科学研究科棟(駒場) 118号室
新井 拓児 氏 (慶応大)



15:00-16:30   数理科学研究科棟(駒場) 002号室
Marta Asaeda 氏 (UC Riverside)
Galois groups and an obstruction to principal graphs of subfactors


16:30-18:00   数理科学研究科棟(駒場) 126号室

Karl-Hermann Neeb 氏 (Technische Universität Darmstadt)
A host algebra for the regular representations of the canonical commutation relations
[ 講演概要 ]
We report on joint work with H. Grundling (Sydney).
The concept of a host algebra generalises that of a group $C^*$-algebra to groups which are not locally compact in the sense that its non-degenerate representations are in one-to-one correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a non-zero central character.
[ 参考URL ]



13:00-16:30   数理科学研究科棟(駒場) 117号室
酒井一博 氏 (慶応大経済) 13:00-14:30
[ 講演概要 ]
加藤晃史 氏 (東大数理) 15:00-16:30
AdS/CFT 対応における $a$-maximization について
[ 講演概要 ]
弦双対性の一つである AdS/CFT 対応において、$a$-maximization
$a$-maximization の基本的な構造を説明するとともに、



14:30-16:00   数理科学研究科棟(駒場) 122号室
坊向伸隆 氏 (大阪市立大学)
The classification of simple irreducible pseudo-Hermitian symmetric spaces: from a view of elliptic orbits
[ 講演概要 ]
In this talk, we call a special elliptic element an Spr-element, we create an equivalence relation on the set of Spr-elements of a real form of a complex simple Lie algebra, and we classify Spr-elements of each real form of all complex simple Lie algebras under our equivalence relation. Besides, we demonstrate that the classification of Spr-elements under our equivalence relation corresponds to that of simple irreducible pseudo-Hermitian symmetric Lie algebras under Berger's equivalence relation. In terms of the correspondence, we achieve the classification of simple irreducible pseudo-Hermitian symmetric Lie algebras without Berger's classification.
[ 参考URL ]


16:00-17:30   数理科学研究科棟(駒場) 122号室
金行壮二 氏 (上智大学名誉教授)
Causalities, G-structures and symmetric spaces
[ 講演概要 ]
Let M be an $n$-dimensional smooth manifold, $F(M)$ the frame bundle of $M$, and let $G$ be a Lie subgroup of $GL(n,\\mathbb R)$. We say that $M$ has a $G$-structure, if there exists a principal subbundle $Q$ of $F(M)$ with structure group $G$. Let $C$ be a causal cone in $\\mathbb R^n$, and let $Aut C$ denote the automorphism group of $C$.

Starting from a causal structure $\\mathcal{C}$ on $M$ with model cone $C$, we construct an $Aut C$-structure $Q(\\mathcal{C})$. Several concepts on causal structures can be interpreted as those on $Aut C$-structures. As an example, the causal automorphism group $Aut(M,\\mathcal{C})$ of $M$ coincides with the automorphism group $Aut(M,Q(\\mathcal{C}))$ of the $Aut C$-structure.

As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space $M$ to the global causal automorphism of the compactification of $M$.
[ 参考URL ]



16:20-17:30   数理科学研究科棟(駒場) 122号室
沖本 竜義 氏 (横浜国立大学経済学部・大学院国際社会科学研究科)
New Evidence of Asymmetric Dependence Structures in International Equity Markets
[ 講演概要 ]
A number of recent studies found two asymmetries in dependence structures in international equity markets; specifically, dependence tends to be high in (1) highly volatile markets and (2) bear markets. In this paper, a further investigation on asymmetric dependence structures in international equity markets is performed under the use of the Markov switching model and copula theory. Combining these two theories enables us to model dependence structures with sufficient flexibility. Using this flexible framework we indeed found that there are two distinct regimes in the US-UK market. We also showed that, for the US-UK market, the bear regime is better described by an asymmetric copula with lower tail dependence with clear rejection of the Markov switching multivariate Normal model. In addition, we showed ignorance of this further asymmetry in bear markets is very costly for risk management. Lastly, we conducted similar analysis for other G7 countries, where we found other c ases where the use of a Markov switching multivariate Normal model would be inappropriate.
[ 参考URL ]



16:30-18:00   数理科学研究科棟(駒場) 126号室
甲斐千舟 氏 (九州大学)
A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps
[ 講演概要 ]
When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order.

In this talk, we investigate this order-reversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *-map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *-map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order.
[ 参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 128号室
厚地淳 氏 (慶応大学)
熱核を用いたNevanlinna理論 --- Gauss mapへの試み



16:30-18:00   数理科学研究科棟(駒場) 128号室
小川朋宏 氏 (東大数理)
On the statistical equivalence for sets of quantum states


15:00-16:30   数理科学研究科棟(駒場) 002号室
真野元 氏 (東京大学数理科学研究科)
The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)
[ 講演概要 ]
The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.
This is a joint work with T. Kobayashi.
[ 参考URL ]



14:30-16:00   数理科学研究科棟(駒場) 122号室
Mikhail Kapranov 氏 (Yale 大学)
Riemann-Roch for determinantal gerbes and smooth manifolds
[ 講演概要 ]
A version of the Riemann-Roch theorem for curves due to Deligne, describes the determinant of the cohomology of a vector bundle E on a curve.
If one realizes E via the Krichever construction, the determinant of the cohomology becomes a Hom-space in the determinantal gerbe for the vector space over the field of power series. So one has a ``local" Riemann-Roch problem of description of this gerbe itself. The talk will present the results of a joint work with E. Vasserot describing the class of such a gerbe in a family which geometrically can be seen as a circle fibration. This can be further generalized to the case of a fibration with fibers being smooth compact manifolds of any dimension d (joint work with P. Bressler, B. Tsygan and E. Vasserot).


16:30-18:00   数理科学研究科棟(駒場) 128号室
宮尾 忠宏 氏 (岡山大自然科学研究科 学振特別研究員 )


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
渡邉 忠之 氏 (京都大学数理解析研究所)
Kontsevich's characteristic classes for higher dimensional homology sphere bundles
[ 講演概要 ]
As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich
constructed universal characteristic classes of smooth fiber bundles with fiber
diffeomorphic to a singularly framed odd dimensional homology sphere.
In this talk, I will give a sketch proof of our result on non-triviality of the
Kontsevich classes for 7-dimensional homology sphere bundles.



10:30-12:00   数理科学研究科棟(駒場) 128号室
Si, Quang Duc 氏 (東大数理)
Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables



16:30-18:00   数理科学研究科棟(駒場) 128号室
戸松玲治 氏 (東大数理)



16:30-17:30   数理科学研究科棟(駒場) 117号室
宮崎 直 氏 (東京大学大学院数理科学研究科)
$(g,K)$-module structures of principal series representations
of $Sp(3,R)$

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