過去の記録

過去の記録 ~07/14本日 07/15 | 今後の予定 07/16~

2020年01月28日(火)

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
関野 希望 氏 (東京大学大学院数理科学研究科)
Existence problems for fibered links (JAPANESE)
[ 講演概要 ]
It is known that every connected orientable closed 3-manifold has a fibered knot. However, finding (and classifying) fibered links whose fiber surfaces are fixed homeomorphism type in a given 3-manifold is difficult in general. We give a criterion of a simple closed curve on a genus 2g Heegaard surface being a genus g fibered knot in terms of its Heegaard diagram. As an application, we can prove the non-existence of genus one fibered knots in some Seifert manifolds.
There is one generalization of fibered links, homologically fibered links. This requests that the complement of the "fiber surface" is a homologically product of a surface and an interval. We give a necessary and sufficient condition for a connected sums of lens spaces of having a homologically fibered link whose fiber surfaces are some fixed types as some algebraic equations.

トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室
渡部 淳 氏 (東京大学大学院数理科学研究科)
Fibred cusp b-pseudodifferential operators and its applications (JAPANESE)
[ 講演概要 ]
Melrose's b-calculus and its variants are important tools to study index problems on manifolds with singularities. In this talk, we introduce a new variant "fibred cusp b-calculus", which is a generalization of fibred cusp calculus of Mazzeo-Melrose and b-calculus of Melrose. We discuss the basic property of this calculus and give a relative index formula. As its application, we prove the index theorem for a Z/k manifold with boundary, which is a generalization of the mod k index theorem of Freed-Melrose.

Lie群論・表現論セミナー

10:00-16:40   数理科学研究科棟(駒場) 号室
Kavli IPMU
Taito Tauchi 氏 (The University of Tokyo) 10:00-11:00
Relationship between orbit decomposition on the flag varieties and multiplicities of induced representations (English)
Mikhail Kapranov 氏 (Kavli IPMU) 11:20-12:20
TBA (English)
Michael Pevzner 氏 (University of Reims) 14:00-15:00
From Symmetry breaking toward holographic transform in representation theory (English)
Leticia Barchini 氏 (Oklahoma University) 15:40-16:40
Cells of Harish-Chandra modules
(English)

2020年01月27日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
辻 元 氏 (上智大学)
Canonical measure and it’s applications
[ 講演概要 ]
The canonical measure is a natural generalization of K\”ahler-Einstein metrics to the case of projective manifolds with nonnegative Kodaira dimension. In this talk we consider the variation of canonical measures under projective deformations and give some applications.

Lie群論・表現論セミナー

9:30-16:30   数理科学研究科棟(駒場) 号室
Kavli IPMU, 9:30--10:00 Registration
Joseph Bernstein 氏 (Tel Aviv and The University of Tokyo) 10:00-11:00
TBA (English)
Toshiyuki Kobayashi 氏 (The University of Tokyo) 11:20-12:20
Regular Representations on Homogeneous Spaces (English)
Laura Geatti 氏 (University of Roma) 14:00-15:00
The adapted hyper-K\"ahler structure on the tangent bundle of a Hermitian symmetric space (English)
Simon Gindikin 氏 (Rutgers University) 15:30-16:30
UNIVERSAL NATURE OF THE HOROSPHERICAL TRANSFORM IN SYMMETRIC SPACES (English)

2020年01月22日(水)

FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 128号室
Samuli Siltanen 氏 (University of Helsinki)
Complex principal type operators in inverse conductivity problem (ENGLISH)
[ 講演概要 ]
Stroke is a leading cause of death all around the world. There are two main types of stroke: ischemic (blood clot preventing blood flow to a part of the brain) and hemorrhagic (bleeding in the brain). The symptoms are the same, but treatments very different. A portable "stroke classifier" would be a life-saving equipment to have in ambulances, but so far it does not exist. Electrical Impedance Tomography (EIT) is a promising and harmless imaging method for stroke classification. In EIT one attempts to recover the electric conductivity inside a domain from electric boundary measurements. This is a nonlinear and ill-posed inverse problem. The so-called Complex Geometric Optics (CGO) solutions have proven to be a useful computational tool for reconstruction tasks in EIT. A new property of CGO solutions is presented, showing that a one-dimensional Fourier transform in the spectral variable provides a connection to parallel-beam Xray tomography of the conductivity. One of the consequences of this “nonlinear Fourier slice theorem” is a novel capability to recover inclusions within inclusions in EIT. In practical imaging, measurement noise causes strong blurring in the recovered profile functions. However, machine learning algorithms can be combined with the nonlinear PDE techniques in a fruitful way. As an example, simulated strokes are classified into hemorrhagic and ischemic using EIT measurements.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SamuliSiltanen.pdf

2020年01月21日(火)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室
普段と部屋が異なりますのでご注意ください。The room is different from our usual.
Matthias Schütt 氏 (Universität Hannover)
(Few) rational curves on K3 surfaces (English)
[ 講演概要 ]
Rational curves play a fundamental role for the structure of a K3 surface. I will first review the general theory before focussing on the case of low degree curves where joint work with S. Rams (Krakow) extends bounds of Miyaoka and Degtyarev. Time permitting, I will also discuss the special case of smooth rational curves as well as applications to Enriques surfaces.

Lie群論・表現論セミナー

14:00-16:00   数理科学研究科棟(駒場) 126号室
Joseph Bernstein 氏 (Tel Aviv University)
On Plancherel measure (English)

2020年01月20日(月)

数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 056号室
Yves A. B. C. Barbosa 氏 (Politecnico di Milano)
Isogeometric Hierarchical Model Reduction: from analysis to patient-specific simulations (English)
[ 講演概要 ]
In the field of hemodynamics, numerical models have evolved to account for the demands in speed and accuracy of modern diagnostic medicine. In this context, we studied in detail Hierarchical Model Reduction technique combined with Isogeometric Analysis (HigaMOD), a technique recently developed in [Perotto, Reali, Rusconi and Veneziani (2017)]. HigaMod is a reduction procedure used to downscale models when the phenomenon at hand presents a preferential direction of flow, e.g., when modelling the blood flow in arteries or the water flow in a channel network. The method showed a significant improvement in reducing the computational power and simulation time, while giving enough information to analyze the problem at hand.

Recently, we focused our work in solving the ADR problem and the Stokes problem in a patient-specific framework. Specifically, we evaluate the computational efficiency of HigaMod in simulating the blood flow in coronary arteries and cerebral arteries. The main goal is to assess the
mprovement that 1D enriched models can provide, with respect to traditional full models, when dealing with demanding 3D CFD simulations. The results obtained, even though preliminary, are promising [Brandes, Barbosa and Perotto (2019); Brandes, Barbosa, Perotto and Suito (2020)].

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
足立 真訓 氏 (静岡大学)
Diederich-Fornaess and Steinness indices for abstract CR manifolds
[ 講演概要 ]
The Diederich-Fornaes and Steinness indices are estimated for weakly pseudoconvex domains in complex manifolds in terms of the D'Angelo 1-form of the boundary CR manifolds. In particular, CR invariance of these indices is shown when the domain is Takeuchi 1-convex. This is a joint work with Jihun Yum (Pusan National University).

2020年01月16日(木)

情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室
入江 広隆 氏 (株式会社デンソー/理化学研究所)
アニーリング型量子計算の基礎 (Japanese)
[ 講演概要 ]
量子アニーリングとは、量子情報の連続操作によって行う量子計算手法の一種であり、現在2000量子ビットを持つ量子アニーリングマシンがD-Wave Systems社によって提供されている。本講演では量子アニーリングの基本概念を概観したのち、実際の実機での構成及び量子アニーリングによる計算手法を幅広く解説する。その中で現状の課題及び未来への期待について議論したい。

2020年01月14日(火)

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry (JAPANESE)
[ 講演概要 ]
Berger's classification of holonomy groups of Riemannian manifolds includes exceptional cases of the Lie groups G2 and Spin(7). Many authors have studied G2- and Spin(7)-manifolds with torus symmetry. In this talk, we generalize the celebrated examples due to Bryant and Salamon and study G2-manifolds with SO(3)-symmetry. Such torsion-free G2-structures are described as a dynamical system of SU(3)-structures on an SO(3)-fibration over a 3-manifold. As a main result, we reduce this system into a constrained Hamiltonian dynamical system on the cotangent bundle over the space of all Riemannian metrics on the 3-manifold. The Hamiltonian function is very similar to that of the Hamiltonian formulation of general relativity.

トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室
石橋 典 氏 (東京大学大学院数理科学研究科)
Algebraic entropy of sign-stable mutation loops (JAPANESE)
[ 講演概要 ]
Since its discovery, the cluster algebra has been developed with friutful connections with other branches of mathematics, unifying several combinatorial operations as well as their positivity notions. A mutation loop induces several dynamical systems via cluster transformations, and they form a group which can be seen as a combinatorial generalization of the mapping class groups of marked surfaces.
We introduce a new property of mutation loops called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropicalized cluster X-transformation. A sign-stable mutation loop has a numerical invariant which we call the "cluster stretch factor", in analogy with the stretch factor of a pseudo-Anosov mapping class on a marked surface. We compute the algebraic entropies of the cluster A- and X-transformations induced by a sign-stable mutation loop, and conclude that these two coincide with the logarithm of the cluster stretch factor. This talk is based on a joint work with Shunsuke Kano.

解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
Erik Skibsted 氏 (オーフス大学)
Scattering near a two-cluster threshold (English)
[ 講演概要 ]
For a one-body Schr\"odinger operator with an attractive slowly decaying potential the scattering matrix is well-defined at the energy zero, and the structure of its singularities is well-studied. The usual (non-relativistic) model for the Hydrogen atom is a particular example of such Schr\"odinger operator.
Less is known on scattering at a two-cluster threshold of an $N$-body Schr\"odinger operator for which the effective interaction between the two bound clusters is attractive Coulombic. An example of interest is scattering at a two-cluster threshold of a neutral atom/molecule. We present results of an ongoing joint work with X.P. Wang on the subject, including a version of the Sommerfeld uniqueness result and its applications.
We shall also present general results on spectral theory at a two-cluster threshold (not requiring the effective interaction to be attractive Coulombic). This includes a general structure theorem on the bound and resonance states at the threshold as well as a resolvent expansion in weighted spaces above the threshold (under more restrictive conditions). Applications to scattering theory will be indicated.

2020年01月10日(金)

講演会

10:00-11:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

2020年01月09日(木)

情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室
藤原 洋 氏 (株式会社ブロードバンドタワー)
AI/IoTによる製造業の革新と経営学 (Japanese)
[ 講演概要 ]
製造業は、大きな変革期を迎えている。かつての製造業は、物理的なプロセスのみでメカニカル製品のみ存在していたが、IT(情報技術)の導入により、第1次製造業IT革命(1960~1970年代)、第2次製造業IT革命(1980~2000年代)を経て、今日は、AI/IoTによる第3次革命製造業革命の時代を迎えている。現在の製造業現場、製品に組み込まれたセンサー、プロセッサー、ソフトウェアによって、クラウド上に製品データを収集し分析可能になっている。本講義では、このような製造業IT革命の歴史をふまえ「スマートコネクテッドプロダクト」の概念について述べる。

講演会

14:00-17:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

講演会

16:00-17:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

2020年01月07日(火)

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
浅尾 泰彦 氏 (東京大学大学院数理科学研究科)
Magnitude homology of crushable spaces (JAPANESE)
[ 講演概要 ]
The magnitude homology and the blurred magnitude homology are novel notions of homology theory for general metric spaces coined by Leinster et al. They are expected to be dealt with in the context of Topological Data Analysis since its original idea is based on a kind of "persistence of points clouds". However, little property of them has been revealed. In this talk, we see that the blurred magnitude homology is trivial when a metric space is contractible by a distance decreasing homotopy. We use techniques from singular homology theory.

トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室
浅野 知紘 氏 (東京大学大学院数理科学研究科)
Intersection number estimate of rational Lagrangian immersions in cotangent bundles via microlocal sheaf theory (JAPANESE)
[ 講演概要 ]
Guillermou associated sheaves to exact Lagrangian submanifolds in cotangent bundles and proved topological properties of the Lagrangian submanifolds. In this talk, I will give an estimate on the displacement energy of rational Lagrangian immersions in cotangent bundles with intersection number estimates via microlocal sheaf theory. This result overlaps with results by Chekanov, Liu, and Akaho via Floer theory. This is joint work with Yuichi Ike.

2019年12月27日(金)

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 126号室
Xiao Fang 氏 (Chinese University of Hong Kong)
High order distributional approximations by Stein's method
[ 講演概要 ]
Stein's method is a powerful tool to proving distributional approximations with error bounds. In this talk, we present two recent developments of Stein's method for high order approximations. (1) Together with Li Luo and Qi-Man Shao, we consider skewness correction in normal approximation. We prove a refined Cram\'er-type moderate deviation result for a class of statistics possessing a local structure. We discuss applications to $k$-runs, U-statistics and subgraph counts. (2) Together with Anton Braverman and Jim Dai, we derive and justify new diffusion approximations with state-dependent diffusion coefficients for stationary distributions of Markov chains. We discuss applications to the Erlang-C system, a hospital inpatient flow model and the auto-regressive model.

統計数学セミナー

16:30-17:40   数理科学研究科棟(駒場) 126号室
Nikolai Leonenko 氏 (Cardiff University)
Heavy-Tailed Fractional Pearson Diffusions
[ 講演概要 ]
We define fractional Pearson diffusions [5,7,8] by non-Markovian time change in the corresponding Pearson diffusions [1,2,3,4]. They are governed by the time-fractional diffusion equations with polynomial coefficients depending on the parameters of the corresponding Pearson distribution. We present the spectral representation of transition densities of fractional Pearson diffusions, which depend heavily on the structure of the spectrum of the infinitesimal generator of the corresponding non-fractional Pearson diffusion. Also, we present the strong solutions of the Cauchy problems associated with heavy-tailed fractional Pearson diffusions and the correlation structure of these diffusions [6] .
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs) [9,10,11]. The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model, Wright-Fisher model and Ehrenfest-Brillouin-type models. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with non-independent increments.

This is a joint work with M. Meerschaert (Michigan State University, USA), I. Papic (University of Osijek, Croatia), N.Suvak (University of Osijek, Croatia) and A. Sikorskii (Michigan State University and Arizona University, USA).

References:
[1] Avram, F., Leonenko, N.N and Suvak, N. (2013), On spectral analysis of heavy-tailed Kolmogorov-Pearson diffusion, Markov Processes and Related Fields, Volume 19, N 2 , 249-298
[2] Avram, F., Leonenko, N.N and Suvak, N., (2013), Spectral representation of transition density of Fisher-Snedecor diffusion, Stochastics, 85 (2013), no. 2, 346—369
[3] Bourguin, S., Campese, S., Leonenko, N. and Taqqu,M.S. (2019) Four moments theorems on Markov chaos, Annals of Probability, 47, N3, 1417–1446
[4] Kulik, A.M. and Leonenko, N.N. (2013) Ergodicity and mixing bounds for the Fisher-Snendecor diffusion, Bernoulli, Vol. 19, No. 5B, 2294-2329
[5] Leonenko, N.N., Meerschaert, M.M and Sikorskii, A. (2013) Fractional Pearson diffusions, Journal of Mathematical Analysis and Applications, vol. 403, 532-546
[6] Leonenko, N.N., Meerschaert, M.M and Sikorskii, A. (2013) Correlation Structure of Fractional Pearson diffusion, Computers and Mathematics with Applications, 66, 737-745
[7] Leonenko,N.N., Meerschaert,M.M., Schilling,R.L. and Sikorskii, A. (2014) Correlation Structure of Time-Changed Lévy Processes, Communications in Applied and Industrial Mathematics, Vol. 6 , No. 1, p. e-483 (22 pp.)
[8] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2017) Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications, 127, N11, 3512-3535
[9] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2018) Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli, Vol. 24, No. 4B, 3603-3627
[10] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2019) Ehrenfest-Brillouin-type correlated continuous time random walks and fractional Jacoby diffusion, Theory Probablity and Mathematical Statistics, Vol. 99,123-133.
[11] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2019) Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology, submitted

2019年12月26日(木)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
山下真 氏 (Oslo Univ.)
Categorical quantization of symmetric spaces and reflection equation

2019年12月25日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室
Bin Gui 氏 (Rutgers Univ.)
Connes fusion on the unit circle
(English)

2019年12月20日(金)

談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 056号室
楠岡成雄 氏 (東京大学・明治大学)
機械学習に関する一考察 (日本語)
[ 講演概要 ]
機械学習が現在流行しているが、その手法にはさまざまなものがある。
本講演では、機械学習のある典型的な場合について、
その理論根拠となるはずの統計的学習理論の考え方を紹介する。
特に、深層学習(neural network)に関して、
その表現力とStone-Weierstrassの定理との関係、
一様大数の法則に関するいくつかの計算結果を紹介する。

講演者は機械学習の研究を始めたばかりの初心者であるが、機械学習の理論的研究に
は様々な数学の視点が有用ではないかと感じている。
機械学習への興味を持っていただければと思っている。

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