過去の記録 ~12/04本日 12/05 | 今後の予定 12/06~


15:30-17:00   数理科学研究科棟(駒場) 122号室
長岡 大 氏 (東大数理)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
[ 講演概要 ]
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2
$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.



10:30-12:00   数理科学研究科棟(駒場) 128号室
澤井 洋 氏 (沼津工業高等専門学校)
LCK structures on compact solvmanifolds
[ 講演概要 ]
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.


16:45-18:15   数理科学研究科棟(駒場) 118号室
磯野優介 氏 (京大数理研)
On fundamental groups of tensor product II$_1$ factors (English)


16:00-17:30   数理科学研究科棟(駒場) 126号室
中島 秀太 氏 (京都大学 数理解析研究所)
最速浸透問題での原点出発の無限測地線の数について (JAPANESE)
[ 講演概要 ]
本講演ではFirst Passage Percolationのgeodesicsについて、最近得られたcoalescenceと呼ばれる性質について述べる。その性質を用いて、infinite geodesics全体の数と原点出発に制限したときの数が一致すること、その系として原点出発のinfinite geodesicの数が定数であることを示す。



15:30-16:30   数理科学研究科棟(駒場) 002号室
会田茂樹 氏 (東京大学大学院数理科学研究科)
ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)
[ 講演概要 ]



17:00-18:30   数理科学研究科棟(駒場) 大講義室号室
Tea: 大講義室前ホワイエ 16:40-17:00
Richard Hain 氏 (Duke University)
Johnson homomorphisms, stable and unstable (ENGLISH)
[ 講演概要 ]
In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.


15:30-17:00   数理科学研究科棟(駒場) 122号室
小関 直紀 氏 (東大数理)
Perverse coherent sheaves on blow-ups at codimension two loci (English)
[ 講演概要 ]
I would like to talk about my recent work in progress.
Let us consider the blow-up X of Y along a subvariety C.
Then the following natural question arises:
What is the relation between moduli space of sheaves on Y
and that of X?
H.Nakajima and K.Yoshioka answered the above question
in the case when Y is a surface and C is a point. They
showed that the moduli spaces are connected by a sequence
of flip-like diagrams. The key ingredient of the proof is
to use perverse coherent sheaves in the sense of T.Bridgeland
and M.Van den Bergh.
In this talk, I will explain how to generalize their theorem
to the case when Y is a smooth projective variety of arbitrary
dimension and C is its codimension two subvariety.


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.

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