過去の記録 ~05/28本日 05/29 | 今後の予定 05/30~


17:00-18:00   数理科学研究科棟(駒場) 126号室
Frédéric Jouhet 氏 (Université Claude Bernard Lyon 1 / Institut Camille Jordan)
Enumeration of fully commutative elements in classical Coxeter groups (English)
[ 講演概要 ]
An element of a Coxeter group W is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. They index naturally a basis of the (generalized) Temperley-Lieb algebra associated with W. In this talk, focusing on the (affine) type A, I will describe how to
enumerate these elements according to their Coxeter length, in all classical finite and affine Coxeter groups. The methods, which generalize previous work of Stembridge,
involve many combinatorial objects, such as heaps, walks, or parallelogram
polyominoes. This talk is based on joint works with R. Biagioli, M. Bousquet-Mélou and
P. Nadeau.
[ 参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 128号室
小池 貴之 氏 (京都大学)
Complex K3 surfaces containing Levi-flat hypersurfaces
[ 講演概要 ]
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.


16:45-18:15   数理科学研究科棟(駒場) 118号室
増田俊彦 氏 (九大数理)
[ 講演概要 ]
Classification of Roberts actions of strongly amenable
$C^*$-tensor categories on the injective factor of type III$_1$


16:00-17:30   数理科学研究科棟(駒場) 126号室
田原 喜宏 氏 (長岡工業高等専門学校)
マルコフおよびシュレディンガー半群のコンパクト性について (JAPANESE)
[ 講演概要 ]
Markov過程が既約性, 強Feller性および緊密性を持つという仮定のもと, その半群は$L^{2}$-コンパクトであることが竹田雅好氏の最近の研究で明らかにされた. 本講演では, その結果を応用して得られる幾つかの具体的なMarkov半群及びSchroedinger半群のコンパクト性について述べる. 更にこれらに関連して, Green緊密ではあるが, 非可積分な関数の例を述べる.



15:00-16:10   数理科学研究科棟(駒場) 117号室
Alexander A. Novikov 氏 (University of Technology Sydney)
On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models
[ 講演概要 ]
We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math. October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0<H<1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.



17:30-18:30   数理科学研究科棟(駒場) 056号室
Olivier Fouquet 氏 (Université Paris-Sud)
The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras (ENGLISH)
[ 講演概要 ]
The Equivariant Tamagawa Number Conjecture (ETNC) of Kato is an awe-inspiring web of conjectures predicting the special values of L-functions of motives as well as their behaviors under the action of algebras acting on motives. In this talk, I will explain the statement of the ETNC with coefficients in Hecke algebras for motives attached to modular forms, show some consequences in Iwasawa theory and outline a proof (under mild hypotheses on the residual representation) using a combination of the methods of Euler and Taylor-Wiles systems.



15:30-17:00   数理科学研究科棟(駒場) 122号室
古川 勝久 氏 (東大数理)
On separable higher Gauss maps (English)
[ 講演概要 ]
We study the $m$-th Gauss map in the sense of F. L. Zak of a projective variety $X ¥subset P^N$ over an algebraically closed field in any characteristic, where $m$ is an integer with $n:= ¥dim(X) ¥leq m < N$. It is known that the contact locus on $X$ of a general tangent $m$-plane can be non-linear in positive characteristic, if the $m$-th Gauss map is inseparable.

In this talk, I will explain that for any $m$, the locus is a linear variety if the $m$-th Gauss map is separable. I will also explain that for smooth $X$ with $n < N-2$, the $(n+1)$-th Gauss
map is birational if it is separable, unless $X$ is the Segre embedding $P^1 ¥times P^n ¥subset P^{2n-1}$. This is related to L. Ein's classification of varieties with small dual varieties in characteristic zero.

This talk is based on a joint work with Atsushi Ito.


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
合田 洋 氏 (東京農工大学)
Twisted Alexander invariants and Hyperbolic volume of knots (JAPANESE)
[ 講演概要 ]
In [1], Müller investigated the asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, and then Menal-Ferrer and Porti [2] have obtained a formula on the volume of a hyperbolic 3-manifold using the Higher-dimensional Reidemeister torsion.

On the other hand, Yoshikazu Yamaguchi has shown that a relationship between the twisted Alexander polynomial and the Reidemeister torsion associated with the adjoint representation of the holonomy representation of a hyperbolic 3-manifold in his thesis [3].

In this talk, we observe that Yamaguchi's idea is applicable to the Higher-dimensional Reidemeister torsion, then we give a volume formula of a hyperbolic knot using the twisted Alexander polynomial.


[1] Müller, W., The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, Metric and differential geometry, 317--352, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.

[2] Menal-Ferrer, P. and Porti, J., Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds. J. Topol., 7 (2014), no. 1, 69--119.

[3] Yamaguchi, Y., On the non-acyclic Reidemeister torsion for knots, Dissertation at the University of Tokyo, 2007.



10:30-12:00   数理科学研究科棟(駒場) 128号室
服部 広大 氏 (慶應義塾大学)
On the moduli spaces of the tangent cones at infinity of some hyper-Kähler manifolds
[ 講演概要 ]
For a metric space $(X,d)$, the Gromov-Hausdorff limit of $(X, a_n d)$ as $a_n \rightarrow 0$ is called the tangent cone at infinity of $(X,d)$. Although the tangent cone at infinity always exists if $(X,d)$ comes from a complete Riemannian metric with nonnegative Ricci curvature, the uniqueness does not hold in general. Colding and Minicozzi showed the uniqueness under the assumption that $(X,d)$ is a Ricci-flat manifold satisfying some additional conditions.
In this talk, I will explain a example of noncompact complete hyper-Kähler manifold who has several tangent cones at infinity, and determine the moduli space of them.



16:30-17:30   数理科学研究科棟(駒場) 126号室
大泉嶺 氏 (国立社会保障・人口問題研究所)
環境変動と個体差の構造人口模型~2重のランダムネスにおける最適戦略の進化~ (JAPANESE)
[ 講演概要 ]



17:00-18:00   数理科学研究科棟(駒場) 056号室
加藤大輝 氏 (東京大学数理科学研究科)
Wild ramification and restrictions to curves (JAPANESE)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
諏訪 立雄 氏 (北海道大学)
Local and global coincidence homology classes (JAPANESE)
[ 講演概要 ]
We consider two differentiable maps between two oriented manifolds. In the case the manifolds are compact with the same dimension and the coincidence points are isolated, there is the Lefschetz coincidence point formula, which generalizes his fixed point formula. In this talk we discuss the case where the dimensions of the manifolds may possible be different so that the coincidence points are not isolated in general. In fact it seems that Lefschetz himself already considered this case (cf. [4]).

We introduce the local and global coincidence homology classes and state a general coincidence point theorem.
We then give some explicit expressions for the local class. We also take up the case of several maps as considered in [1] and perform similar tasks. These all together lead to a generalization of the aforementioned Lefschetz formula. The key ingredients are the Alexander duality in combinatorial topology, intersection theory with maps and the Thom class in Čech-de Rham cohomology. The contents of the talk are in [2] and [3].

[1] C. Biasi, A.K.M. Libardi and T.F.M. Monis, The Lefschetz coincidence class of p maps, Forum Math. 27 (2015), 1717-1728.
[2] C. Bisi, F. Bracci, T. Izawa and T. Suwa, Localized intersection of currents and the Lefschetz coincidence point theorem, Annali di Mat. Pura ed Applicata 195 (2016), 601-621.
[3] J.-P. Brasselet and T. Suwa, Local and global coincidence homology classes, arXiv:1612.02105.
[4] N.E. Steenrod, The work and influence of Professor Lefschetz in algebraic topology, Algebraic Geometry and Topology: A Symposium in Honor of Solomon Lefschetz, Princeton Univ. Press 1957, 24-43.


15:30-17:00   数理科学研究科棟(駒場) 122号室
柴田 康介 氏 (東大数理)
Upper bound of the multiplicity of locally complete intersection singularities (English)
[ 講演概要 ]
The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this talk, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe’s conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.



10:30-12:00   数理科学研究科棟(駒場) 128号室
藤澤 太郎 氏 (東京電機大学)
Semipositivity theorems for a variation of Hodge structure
[ 講演概要 ]
I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.


16:00-17:00   数理科学研究科棟(駒場) 056号室
丸橋広和 氏 (東京大学大学院数理科学研究科(学振PD))
Parameter rigidity of the action of AN on G/Γ for higher rank semisimple Lie groups
[ 講演概要 ]

1990年頃KatokとSpatzierは次の定理を示した。Gを中心有限連結実半単純Lie群で、コンパクトな単純因子、SO(n,1), SU(n,1)と局所同型な単純因子をもたないもの、ΓをGの既約一様格子、G=KANをGの岩澤分解とする。このときGの実階数が2以上ならば可換群AのG/Γへの掛け算による作用はパラメータ剛性をもつ。
一方私は去年、同じ仮定のもと可解Lie群ANのG/Γへの掛け算による作用もパラメータ剛性をもつことを示した。証明には上記Katok-Spatzierの定理の他に、以前私が証明した可解Lie群の作用のパラメータ剛性の十分条件、Pansu、Kleiner-Leeb、Farb-Mosher、Reiter Ahlinによる対称空間の擬等長写像の剛性定理を使う。



15:30-16:30   数理科学研究科棟(駒場) 002号室
松井千尋 氏 (東京大学大学院数理科学研究科)
可積分量子スピン鎖における隠れた超対称性 (JAPANESE)
[ 講演概要 ]
[ 参考URL ]



15:30-17:00   数理科学研究科棟(駒場) 056号室
土谷 洋平 氏 (神奈川工科大学)
nonlocalな古典可積分系に関する最近の話題 (JAPANESE)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
久野 雄介 氏 (津田塾大学)
Formality of the Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem in positive genus (JAPANESE)
[ 講演概要 ]
This talk is based on a joint work with A. Alekseev, N. Kawazumi and F. Naef. Given a compact oriented surface with non-empty boundary and a framing of the surface, one can define the Lie bracket (Goldman bracket) and the Lie cobracket (Turaev bracket) on the vector space spanned by free homotopy classes of loops on the surface. These maps are of degree minus two with respect to a certain filtration. Then one can ask the formality of this Lie bialgebra: is the Goldman-Turaev Lie bialgebra isomorphic to its associated graded?

For surfaces of genus zero, we showed that this question is closely related to the Kashiwara-Vergne (KV) problem in Lie theory (arXiv:1703.05813). A similar result was obtained by G. Massuyeau by using the Kontsevich integral.

Our new topological interpretation of the classical KV problem leads us to introduce a generalization of the KV problem in connection with the formality of the Goldman-Turaev Lie bialgebra for surfaces of positive genus. We will discuss the existence and uniqueness of solutions to the generalized KV problem.


15:30-17:00   数理科学研究科棟(駒場) 122号室
鈴木 拓 氏 (早稲田大学)
On the Picard number of Fano 6-folds with a non-small contraction (English)
[ 講演概要 ]
A generalization of S. Mukai's conjecture says that $\rho(i-1) \leq n$ holds for any Fano $n$-fold with Picard number $\rho$ and pseudo-index $i$, with equality if and only if it is isomorphic to $(\mathbb{P}^{i-1})^{\rho}$. In this talk, we consider this conjecture for $n=6$, which is an open problem, and give a proof of some special cases.


16:50-18:20   数理科学研究科棟(駒場) 002号室
榊原航也 氏 (東京大学大学院数理科学研究科)
基本解近似解法の理論と応用 (日本語)
[ 講演概要 ]
基本解近似解法 (Method of Fundamental Solutions, MFS) は,線型同次偏微分方程式に対するメッシュフリー数値解法である.MFSのアイディアは非常に単純であり,特異点が考えている領域の外部にある,偏微分作用素の基本解の線型結合により近似解を与え,線型結合の係数は選点法(collocation method)により決定する.つまり,差分法や有限要素法とは異なって,領域のメッシュ分割が不要であり(点を配置するだけである),プログラミングも容易である.さらに,特筆すべき性質として,ある条件下では,近似誤差が点の数に関して指数的に減衰することが知られている(通常の差分法や有限要素法では,近似誤差は多項式オーダーで減衰する).一方で,"どのような点配置の下で誤差は指数減衰するか",という問いに対する決定的な回答は未だに与えられておらず,MFSの理論研究における最も大きな未解決問題であると言ってよい.このように,MFSに対する数学的理論整備はまだまだ発展途上であるが,数値計算の観点からの研究は非常に豊富に行われており,様々な方程式に対して有効と思われる数値計算アルゴリズムが提案されてきた.





10:30-12:00   数理科学研究科棟(駒場) 128号室
今野 宏 氏 (明治大学)
Lagrangian Mean Curvature Flows and Moment maps
[ 講演概要 ]
In this talk, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclid spaces. We also construct Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.


16:45-18:15   数理科学研究科棟(駒場) 118号室
長谷川慧 氏 (九大数理)
Bass-Serre trees of amalgamated free product $C^*$-algebras (English)


16:00-17:30   数理科学研究科棟(駒場) 126号室
会田 茂樹 氏 (東京大学大学院数理科学研究科)
Rough differential equations containing path-dependent bounded variation terms (JAPANESE)
[ 講演概要 ]
反射壁を持つ確率微分方程式の一般化として、経路依存のrough differential equationを定式化し、解の存在と評価を論ずる。また、この評価を用いて、解の分布のサポートを決定できることを報告する。



15:00-   数理科学研究科棟(駒場) 117号室
David Nualart 氏 (Kansas University) -
Central limit theorem for symmetric integrals
[ 講演概要 ]
The purpose of this talk is to present the convergence in distribution of symmetric integrals of functions of the fractional Brownian motion for critical values of the Hurst parameter. This result includes the cases of symmetric integrals defined as the limit of trapeziodal, midpoint and Simpson Riemann sums, where the corresponding critical values of the Hurst parameter are H=1/4, H=1/6 and H=1/10, respectively. As a consequence, we establish a change-of-variable formula in law, where the correction term involves a stochastic integral with respect to an independent standard Brownian motion. The proof is based on the combination of Malliavin calculus and the classical Bernstein's big blocks/small blocks technique.
David Nualart 氏 (Kansas University) -
Stochastic heat equation with rough multiplicative noise
[ 講演概要 ]
The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.



15:30-17:00   数理科学研究科棟(駒場) 122号室
福岡 尊 氏 (東大数理)
On the existence of almost Fano threefolds with del Pezzo fibrations (English)
[ 講演概要 ]
We say that a smooth projective 3-fold is almost Fano if its anti-canonical divisor is nef and big but not ample. By Jahnke-Peternell-Radloff and Takeuchi, the numerical classification of such 3-folds was given. Among the classification results, there exists precisely 10 cases such that it was yet to be known whether these have an example or not. The main result of this talk shows the existence of examples of each of 10 cases. In 9 cases of the 10 cases, the degree of del Pezzo fibrations are 6. We will discuss one of the reason of difficulty constructing del Pezzo fibrations of degree 6. After that, we will show that every almost Fano del Pezzo fibration of degree 6 with specific anti-canonical volume can be embedded into some higher dimensional del Pezzo fibration as a relative linear section.

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