過去の記録 ~08/21本日 08/22 | 今後の予定 08/23~


15:25-16:05   数理科学研究科棟(駒場) 126号室
Matti Lassas 氏 (University of Helsinki)
Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)
[ 講演概要 ]
We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.

We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.

Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.

The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.
The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.

[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674
[ 講演参考URL ]



13:00-17:00   数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.



16:45-18:15   数理科学研究科棟(駒場) 118号室
Alexander Kumjian 氏 (Univ. Nevada, Reno)
A Stabilization Theorem for Fell Bundles over Groupoids


16:00-17:30   数理科学研究科棟(駒場) 122号室
Yves Dermenjian 氏 (Aix-Marseille Universite)
A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)
[ 講演参考URL ]



16:30-18:30   数理科学研究科棟(駒場) 056号室
川崎 盛通 氏 (東京大学大学院数理科学研究科) 16:30-17:30
重い部分集合と非可縮周期軌道 (JAPANESE)
[ 講演概要 ]
様体Mとその部分集合$X$, $M$内の自由ホモトピー類αに対する相対的なシンプレクテ



古川 遼 氏 (東京大学大学院数理科学研究科) 17:30-18:30
On codimension two contact embeddings in the standard spheres (JAPANESE)
[ 講演概要 ]
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.



13:00-18:00   数理科学研究科棟(駒場) 128号室
田中 仁 氏 (東京大学) 13:30-15:00
The n linear embedding theorem
[ 講演概要 ]
平田賢太郎 氏 (広島大学) 15:30-17:00
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain
[ 講演概要 ]
2007年にPolacik-Quittner-Soupletは,任意の領域において半線形熱方程式$u_t-\Delta u=u^p$の正値解に対して初期時刻,爆発時刻,領域の境界付近の増大度に関する先験的評価を与えた.



16:50-17:50   数理科学研究科棟(駒場) 123号室
小木曽啓示 氏 (東京大学大学院数理科学研究科)
Birational geometry through complex dymanics (ENGLISH)
[ 講演概要 ]
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so

The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be

In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:

(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;

(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;

(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus



16:45-18:15   数理科学研究科棟(駒場) 118号室
Benoit Collins 氏 (京大理)
Quantum channels from the free orthogonal quantum group (English)



16:50-18:20   数理科学研究科棟(駒場) 126号室
Eric Skibsted 氏 (Aarhus University, Denmark)
Stationary scattering theory on manifolds (English)
[ 講演概要 ]
We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).



16:50-18:20   数理科学研究科棟(駒場) 128号室
David Croydon 氏 (University of Warwick)
Scaling limits of random walks on trees (English)
[ 講演概要 ]
I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.


10:30-12:00   数理科学研究科棟(駒場) 128号室
山ノ井 克俊 氏 (大阪大学)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
[ 講演概要 ]
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.



15:30-17:00   数理科学研究科棟(駒場) 122号室
このセミナーは講演者が急病のためキャンセルになりました。This seminer is canceled due to the speaker 's sick.
Dulip Piyaratne 氏 (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
[ 講演概要 ]
In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
[ 講演参考URL ]



16:45-18:15   数理科学研究科棟(駒場) 118号室
Yul Otani 氏 (東大数理)
Nuclearity in AQFT and related results


10:30-11:45   数理科学研究科棟(駒場) 122号室
山本 光 氏 (東京大学大学院数理科学研究科)
Special Lagrangian submanifolds and mean curvature flows(特殊ラグランジュ部分多様体と平均曲率流について) (JAPANESE)


10:30-12:00   数理科学研究科棟(駒場) 128号室
Yuri Luchko 氏 (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
[ 講演概要 ]
In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
[ 講演参考URL ]



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
Constantin Teleman 氏 (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
[ 講演概要 ]
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.



10:30-12:00   数理科学研究科棟(駒場) 128号室
中田 文憲 氏 (福島大学)
Twistor correspondence for associative Grassmanniann
[ 講演概要 ]
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.


15:30-17:00   数理科学研究科棟(駒場) 122号室
金沢篤 氏 (ハーバード大学)
Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
[ 講演概要 ]
In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.



16:45-18:15   数理科学研究科棟(駒場) 118号室
David E. Evans 氏 (Cardiff Univ.)
K-theory in subfactors and conformal field theory


18:00-19:00   数理科学研究科棟(駒場) 056号室
Ted Chinburg 氏 (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ 講演概要 ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.

(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.)



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
山田 裕一 氏 (電気通信大学)
レンズ空間手術と4次元多様体の Kirby calculus (JAPANESE)
[ 講演概要 ]
を決定せよ」という問題は「レンズ空間手術」と呼ばれています。Berge のリス
ト(1990) が完全なリストと信じられており Heegaard Floer 理論によって進展
す。その一方 Minimally twisted 5 chain link の例外的デーン手術が再確認さ
 講演では、Berge のリストの多様さと規則性を紹介しつつ、異なる結び目から



16:50-18:20   数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
[ 講演概要 ]
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.


10:30-12:00   数理科学研究科棟(駒場) 128号室
巴山 竜来 氏 (専修大学)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ 講演概要 ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Alexey Bondal 氏 (IPMU)
Flops and spherical functors (English)
[ 講演概要 ]
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be



16:50-17:50   数理科学研究科棟(駒場) 123号室
佐々田槙子 氏 (東京大学大学院数理科学研究科)
確率論の問題に現れる無限直積空間上の完全形式と閉形式について (JAPANESE)
[ 講演概要 ]
[ 講演参考URL ]

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