過去の記録 ~05/21本日 05/22 | 今後の予定 05/23~



16:40-17:40   数理科学研究科棟(駒場) 056号室
Gantsooj Batzaya 氏 (東京大学数理科学研究科)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)


16:30-18:00   数理科学研究科棟(駒場) 122号室
山下真 氏 (お茶の水女子大)
Poisson boundary of monoidal categories (ENGLISH)


14:50-16:20   数理科学研究科棟(駒場) 128号室
江島 啓介 氏 (東京大学大学院医学系研究科国際保健政策学
社会伝播の数理モデリング:肥満流行とその対策の効果について (JAPANESE)
[ 講演概要 ]
:As an obesity epidemic has grown worldwide, a variety of
intervention programs have been considered, but a scientific approach
to comparatively assessing the control programs has still to be
considered. The present study aims to describe an obesity epidemic by
employing a simple mathematical model that accounts for both social
contagion and non-contagious hazards of obesity, thereby comparing the
effectiveness of different types of interventions.
An epidemiological model is devised to describe the time- and
age-dependent risk of obesity, the hazard of which is dealt with as
both dependent on and independent of obesity prevalence, and
parameterizing the model using empirically observed data. The
equilibrium prevalence is investigated as our epidemiological outcome,
assessing its sensitivity to different parameters that regulate the
impact of intervention programs and qualitatively comparing the
effectiveness. We compare the effectiveness of different types of
interventions, including those directed to never-obese individuals
(i.e. primary prevention) and toward obese and ex-obese individuals
(i.e. secondary prevention).
The optimal choice of intervention programs considerably varies with
the transmission coefficient of obesity, and a limited
transmissibility led us to favour preventing weight gain among
never-obese individuals. An abrupt decline in the prevalence is
expected when the hazards of obesity through contagious and
non-contagious routes fall into a particular parameter space, with a
high sensitivity to the transmission potential of obesity from person
to person. When a combination of two control strategies can be
selected, primary and secondary preventions yielded similar population
impacts and the superiority of the effectiveness depends on the
strength of the interventions at an individual level.
The optimality of intervention programs depends on the contagiousness
of obesity. Filling associated data gaps of obesity transmission would
help systematically understand the epidemiological dynamics and
consider required control programs.



16:30-18:00   数理科学研究科棟(駒場) 128号室
宮崎 洋一 氏 (日本大学歯学部)
楕円型方程式の正則性定理と領域の滑らかさ (JAPANESE)
[ 講演概要 ]
We consider the Dirichlet boundary problem for a strongly elliptic operator of order $2m$ with non-smooth coefficients, and prove the regularity theorem for $L_p$-based Sobolev spaces when the domain has a boundary of limited smoothness. Compared to the known results, we can weaken the smoothness assumption on the boundary by $m-1$.


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
藤川 英華 氏 (千葉大学大学院理学研究科)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
[ 講演概要 ]
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.


16:30-18:00   数理科学研究科棟(駒場) 126号室
渡部真樹 氏 (東京大学大学院数理科学研究科)
Schubert加群の構造とSchubert加群によるfiltrationについて (JAPANESE)
[ 講演概要 ]
Schubert多項式を研究する道具の1つとして, KraskiewiczとPragaczによって 導入されたSchubert加群があります.
今回の発表では, Schubert加群の構造に関する新しい結果と, そこから得られる, 与えられた加群がSchubert加群によるfiltrationを持つ条件について話します.
また, この研究のもともとの動機はSchubert多項式に関するある問題を考えていたことなので, それについても話す予定です.



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
Boris Hasselblatt 氏 (Tufts Univ)
Godbillon-Vey invariants for maximal isotropic foliations (ENGLISH)
[ 講演概要 ]
The combination of a contact structure and an orientable maximal isotropic foliation gives rise to m+1 Godbillon-Vey invariants for an m+1-dimensional maximal isotropic foliation that are of interest with respect to geometric rigidity: by studying these jointly, we give new proofs of famous "rigidity'' results from the 1980s that require only a very few simple lines of reasoning rather than the elaborate original proofs.



17:30-18:30   数理科学研究科棟(駒場) 056号室
Shenghao Sun 氏 (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
[ 講演概要 ]
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.

(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.)


16:30-18:00   数理科学研究科棟(駒場) 122号室
見村万佐人 氏 (東北大学)
Group approximation in Cayley topology and coarse geometry
part I: coarse embeddings of amenable groups (ENGLISH)



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
黒木 慎太郎 氏 (東京大学大学院数理科学研究科)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
[ 講演概要 ]
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya


13:00-14:10   数理科学研究科棟(駒場) 052号室
荻原 哲平 氏 (大阪大学金融・保険教育研究センター)
非同期観測と観測ノイズの存在の下での最尤型推定法 (JAPANESE)
[ 講演概要 ]
高頻度金融時系列データを用いた複数資産の統計解析での問題として, 観測ノイズと観測の非同期性があり, 実現共分散などのシンプルな推定量は 観測ノイズや観測の非同期性の下で深刻なバイアスをもつ. この問題を解決するノンパラメトリック型推定量に関する研究は多くあり, 最尤型推定量に関しても, 観測ノイズと非同期観測をそれぞれ単独で扱っているものとして, Gloter and Jacod (2001), Ogihara and Yoshida (2012)などがある. 本発表では, 先行研究を紹介しながら観測ノイズと非同期観測の両方が存在する時の 最尤型推定量の漸近挙動に関する結果を紹介する.
[ 講演参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 126号室
高山 茂晴 氏 (東京大学)
On degenerations of Ricci-flat Kähler manifolds (JAPANESE)



13:30-17:00   数理科学研究科棟(駒場) 128号室
筒井 容平 氏 (東京大学) 13:30-15:00
拡散性を有しない化学物質に対する走化性方程式の有界な解 (JAPANESE)
[ 講演概要 ]
We consider a chemotaxis system with a logarithmic sensitivity and a non-diffusive chemical substance. For some chemotactic sensitivity constants, Ahn and Kang proved the existence of bounded global solutions to the system. An entropy functional was used in their argument to control the cell density by the density of the chemical substance. Our purpose is to show the existence of bounded global solutions for all the chemotactic sensitivity constants. Assuming the smallness on the initial data in some sense, we can get uniform estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu Univ.) and Juan J.L. Vel\\'azquez (Univ. of Bonn).
香川 智修 氏 (東京都市大学) 15:30-17:00
Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)
[ 講演概要 ]
熱核についてはM. W. Wong氏との共同研究である。



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
只野 誉 氏 (大阪大学)
Gap theorems for compact gradient Sasaki Ricci solitons (JAPANESE)
[ 講演概要 ]
In this talk we give some necessary and sufficient conditions for compact gradient Sasaki-Ricci solitons to be Sasaki-Einstein. Our result may be considered as a Sasaki geometry version of recent works by H. Li, and M. Fern¥'andez-L¥'opez-E. Garc¥'ia-Rio.


16:30-17:30   数理科学研究科棟(駒場) 050号室
Cédric Villani 氏 (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature
― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ 講演概要 ]
Optimal transport theory, non-Euclidean geometry and statistical physics met fifteen years ago with the discovery that Ricci curvature can be studied quantitatively thanks to entropy and
Monge-Kantorovich transport.
This unexpected encounter was very fruitful, leading to progress in each of these fields.
[ 講演参考URL ]


16:30-17:30   数理科学研究科棟(駒場) 050号室
Tea: 16:00-16:30 ホワイエにて
Cédric Villani 氏 (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ 講演参考URL ]



16:30-18:00   数理科学研究科棟(駒場) 122号室
Yul Otani 氏 (Univ. Tokyo)
A Supersymmetric model in AQFT (after Buchholz and Grundling) (ENGLISH)



16:30-18:00   数理科学研究科棟(駒場) 128号室
岡田 靖則 氏 (千葉大学大学院理学研究科)
Ultra-differentiable classes and intersection theorems (JAPANESE)
[ 講演概要 ]
There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).


13:00-14:10   数理科学研究科棟(駒場) 052号室
Selma Chaker 氏 (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
[ 講演概要 ]
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
[ 講演参考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
足助 太郎 氏 (東京大学大学院数理科学研究科)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
[ 講演概要 ]
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.


16:30-18:00   数理科学研究科棟(駒場) 126号室
Ivan Cherednik 氏 (The University of North Carolina at Chapel Hill, RIMS
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
[ 講演概要 ]
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.

The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).

The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due

to Braverman and Finkelberg (algebraic theory of affine flag varieties).



10:30-12:00   数理科学研究科棟(駒場) 126号室
神本 丈 氏 (九州大学)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
[ 講演概要 ]
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Andrés Daniel Duarte 氏 (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
[ 講演概要 ]
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.


16:30-18:00   数理科学研究科棟(駒場) 002号室
Chien-Hong Cho 氏 (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
[ 講演概要 ]
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
[ 講演参考URL ]



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
小野 肇 氏 (埼玉大学)
非ハミルトン体積最小なハミルトン安定ラグランジュトーラスについて (JAPANESE)
[ 講演概要 ]
Y. –G. Oh はケーラー多様体内のラグランジュ部分多様体について、ハミルトン変形のもとでの体積の極小性(ハミルトン安定性)や最小性(ハミルトン体積最小性)について考察した。これは等周問題の1つの一般化と考えられ、例えば、複素ユークリッド空間内の標準的トーラスや複素射影空間たちの直積のトーラス軌道などはハミルトン安定であることが知られていた。本講演では次の2つの結果について紹介する:
1. 3次元以上の複素ベクトル空間のほとんどの標準的トーラスはハミルトン体積最小ではない。
2. 3次元以上の任意のコンパクトトーリックケーラー多様体のトーラス軌道にはハミルトン体積最小ではないものが数多く存在する。

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