## 過去の記録

### 2017年05月31日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

Stark Systems over Gorenstein Rings (JAPANESE)
[ 講演概要 ]
Gorenstein環上の代数体のGalois表現とSelmer構造に対するStark系の定義について紹介する．
これは佐野昂迪氏とBarry Mazur氏，Karl Rubin氏によって独立に定義された単項イデアル環上のStark系の一般化になっている．
さらに，Stark系の成す加群が階数1の自由加群である事，stark系を用いてSelmer群のFittingイデアル全てを記述できる事を示す．

### 2017年05月30日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
[ 講演概要 ]
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.

#### 東京無限可積分系セミナー

17:30-18:30   数理科学研究科棟(駒場) 002号室

$C$ 型ルート系に付随した $Q$ 関数 (JAPANESE)
[ 講演概要 ]
Schur の $Q$ 関数は，対称群の射影表現の研究の中で Schur によ
って導入された対称関数であり，$A$ 型のルート系に付随した
Hall-Littlewood 対称関数において $t=-1$ としたものでもある．
（$t=0$ としたものが Schur 関数である．）この講演では，$C$

とおいたもの（斜交 $Q$ 関数）を考える．斜交 $Q$ 関数に対する
Pfaffian 公式を紹介し，組合せ論的表示を与えるとともに，いく
つかの正値性予想を提示する．

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

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.

### 2017年05月29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

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.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室

On fundamental groups of tensor product II$_1$ factors (English)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

### 2017年05月26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) 002号室

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 ]
リーマン多様体上にはブラウン運動などの

ループ空間上のディリクレ形式で定まる作用素の

が予想できることになる。
この講演では、この問題について、どのような点が難しいか、

### 2017年05月23日(火)

#### トポロジー火曜セミナー

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.

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

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.

#### 講演会

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
[ 講演参考URL ]
http://math.univ-lyon1.fr/homes-www/jouhet/

### 2017年05月22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

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.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室

(English)
[ 講演概要 ]
Classification of Roberts actions of strongly amenable
$C^*$-tensor categories on the injective factor of type III$_1$

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

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.

### 2017年05月18日(木)

#### 統計数学セミナー

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.

### 2017年05月17日(水)

#### 代数学コロキウム

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.

### 2017年05月16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) 122号室

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.

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

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.

References

[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.

### 2017年05月15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

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.

### 2017年05月11日(木)

#### 数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

一方，個体の多様性には遺伝子疾患や性的優位などの異質性は環境変動とは別
の（内的）不確実性がある，この中で最適生活史スケジュールを考えるには確率

ルを見つける必要がある．本研究ではまず著者が研究してきた個体の多様性を表

を統一した研究を紹介する．さらに、前述の摂動展開理論の連続バージョンへの

を議論したい．

### 2017年05月10日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

Wild ramification and restrictions to curves (JAPANESE)
[ 講演概要 ]
スキーム上のエタール層の暴分岐がすべての曲線への制限のArtin導手で決まるかどうかを調べ、特異点解消を仮定するとそれが正しいこと、特に、スキームが2次元の場合には正しいことを示した。
またその帰結として、(次元に関する仮定なしに)体上の多様体のエタール層のEuler－Poincare標数や、局所体上の多様体のエタール層から定まるGalois表現のSwan導手の交代和もすべての"曲線"への制限のArtin導手で決まるという結果を得た。

### 2017年05月09日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

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].

References
[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.

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

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.

### 2017年05月08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

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.

#### 幾何コロキウム

16:00-17:00   数理科学研究科棟(駒場) 056号室

Parameter rigidity of the action of AN on G/Γ for higher rank semisimple Lie groups
[ 講演概要 ]
Sを連結単連結可解Lie群とし、閉多様体Mへの滑らかな局所自由作用ρを考える。ρがパラメータ剛性をもつとはSのMへの滑らかな局所自由作用でρと同じ軌道分解をもつものがすべて滑らかな写像によってρと共役になることをいう。

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。