過去の記録 ~09/23本日 09/24 | 今後の予定 09/25~

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
A.P. Veselov 氏 (Loughborough, UK and Tokyo)
Universal formulae for Lie groups and Chern-Simons theory (ENGLISH)
[ 講演概要 ]
In 1990s Vogel introduced an interesting parametrization of simple
Lie algebras by 3 parameters defined up to a common multiple and
permutations. Numerical characteristic is called universal if it can be
expressed in terms of Vogel's parameters (example - the dimension of Lie
algebra). I will discuss some universal formulae for Lie groups
and Chern-Simons theory on 3D sphere.
The talk is based on joint work with R.L. Mkrtchyan and A.N. Sergeev.



16:30-18:00   数理科学研究科棟(駒場) 118号室
窪田陽介 氏 (東大数理)
Finiteness of K-area and the dual of the Baum-Connes conjecture (ENGLISH)


14:50-16:20   数理科学研究科棟(駒場) 128号室
小林 徹也 氏 (東京大学生産技術研究所 統合バイオメディカル国際研究センター)
個体群ダイナミクスの経路積分表現と変分構造 (JAPANESE)
[ 講演概要 ]
本研究は、杉山 友規氏との共同研究である。



14:40-16:10   数理科学研究科棟(駒場) 056号室
Sergei Duzhin 氏 (Steklov Institute of Mathematics)
Bipartite knots (ENGLISH)
[ 講演概要 ]
We give a solution to a part of Problem 1.60 in Kirby's list of open
problems in topology thus proving a conjecture raised in 1987 by
J.Przytycki. A knot is said to be bipartite if it has a "matched" diagram,
that is, a plane diagram that has an even number of crossings which can be
split into pairs that look like a simple braid on two strands with two
crossings. The conjecture was that there exist knots that do not have such
diagrams. I will prove this fact using higher Alexander ideals.
This talk is based on a joint work with my student M.Shkolnikov


10:30-11:30   数理科学研究科棟(駒場) 056号室
木村 芳文 氏 (名古屋大学多元数理科学研究科)
The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)
[ 講演概要 ]
A system of N point vortices is a Hamiltonian dynamical system with N degrees of freedom,and it is known that under certain parameter and initial conditions, there are self-similar collapse solutions for which N vortices collide at a point while rotating without changing the initial shape of configuration. In this talk, I will introduce such collision solutions and discuss some properties of complex time singularities in relation with those solutions.


16:30-18:00   数理科学研究科棟(駒場) 128号室
阿部 健 氏 (名古屋大学)
On estimates for the Stokes flow in a space of bounded functions (JAPANESE)
[ 講演概要 ]
The Stokes equations are well understood on $L^p$ space for various kinds of domains such as bounded or exterior domains, and fundamental to study the nonlinear Navier-Stokes equations. The situation is different for the case $p=\\infty$ since in this case the Helmholtz projection does not act as a bounded operator anymore. In this talk, we show some a priori estimate for a composition operator of the Stokes semigroup and the Helmholtz projection on a space of bounded functions. 


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
小鳥居 祐香 氏 (東京大学大学院数理科学研究科)
On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
[ 講演概要 ]
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥
bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.



10:30-12:00   数理科学研究科棟(駒場) 126号室
高橋良輔 氏 (名古屋大学)
Modified Kähler-Ricci flow on projective bundles (JAPANESE)


16:30-18:00   数理科学研究科棟(駒場) 056号室
及川一誠 氏 (早稲田大学理工学術院)
弱安定化ハイブリッド型不連続Galerkin法について (JAPANESE)
[ 講演概要 ]
ハイブリッド型不連続Galerkin(HDG)法とは、要素内部の未知量に加え、要素間境界上の未知量を導入して定式化を行うという、新しいタイプの不連続Galerkin法である。本講演では、従来のHDG法の安定化項を弱めることによって得られる新手法(弱安定化HDG法)を紹介する。 弱安定化HDG法の理論誤差解析や、ガウス型数値積分公式による実装法、数値計算結果などについて示す。非適合有限要素法との関連性についても述べる。
[ 参考URL ]



16:30-17:30   数理科学研究科棟(駒場) 056号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。ඁ

Mikhail Kapranov 氏 (Kavli IPMU)
Lie algebras from secondary polytopes (ENGLISH)
[ 講演概要 ]
The secondary polytope of a point configuration
in the Euclidean space was introduced by Gelfand, Zelevinsky
and the speaker long time ago in order to understand discriminants
of multi-variable polynomials. These polytopes have
a remarkable factorization (or operadic) property: each
face of any secondary polytope is isomorphic to the
product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich
and Y. Soibelman, will explain how the factorization property
can be used to construct Lie algebra-type objects:
$L_¥infty$ and $A_¥infty$-algebras. These algebras
turn out to be related to the problem of deformation
of triangulated categories with semiorthogonal decompositions.



16:30-18:00   数理科学研究科棟(駒場) 122号室
Ion Nechita 氏 (Univ. Paul Sabatier)
Positive and completely positive maps via free additive powers of probability measures (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
高倉 樹 氏 (中央大学・理工学部)
Vector partition functions and the topology of multiple weight varieties
[ 講演概要 ]
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.



10:30-12:00   数理科学研究科棟(駒場) 126号室
林本 厚志 氏 (長野工業高等専門学校)
一般化された擬楕円体と固有正則写像 (JAPANESE)


15:30-17:00   数理科学研究科棟(駒場) 122号室
中村勇哉 氏 (東京大学数理科学研究科)
On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)
[ 講演概要 ]
We will discuss about the base point free theorem on three-dimensional
pairs defined over the algebraic closure of a finite field.

We know the base point free theorem on arbitrary-dimensional Kawamata
log terminal pairs in characteristic zero. By Birkar and Xu, the base
point free theorem in positive characteristic is known for big line
bundles on three-dimensional Kawamata log terminal pairs defined over
an algebraically closed field of characteristic larger than 5. Over the
algebraic closure of a finite field, a stronger result was proved by Keel.

The purpose of this talk is to generalize the Keel's result. We will
prove the base point free theorem for big line bundles on
three-dimensional log canonical pairs defined over the algebraic closure
of a finite field. This theorem is not valid for another field.

This is joint work with Diletta Martinelli and Jakub Witaszek.



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.
[ 参考URL ]

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