## 過去の記録

#### 代数幾何学セミナー

13:00-14:30   数理科学研究科棟(駒場) 122号室
いつもと曜日・時間・部屋が異なります。

Construction of non-Kähler Calabi-Yau 3-folds by smoothing normal crossing varieties (TBA)
[ 講演概要 ]
It is an open problem whether there are only finitely many diffeomorphism types of projective Calabi-Yau 3-folds. Kawamata--Namikawa developed log deformation theory of normal crossing Calabi-Yau varieties. As an application of their result, one can construct examples of Calabi-Yau manifolds by smoothing SNC varieties. In this talk, I will explain how to construct examples of non-Kähler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. If time permits, I will also explain an example of involutions on a family of K3 surfaces which do not lift biregularly to the total space. This is based on joint work with Kenji Hashimoto.

### 2019年07月08日(月)

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

たとえば、高次元の常微分方程式においては計算量の観点から時間刻みを十分小さくとれないため、離散化誤差を無視できないと考えられる。 そこで本研究では、データに基づいて離散化誤差の大きさを見積もることでパラメータの推定精度を改善する手法を提案する。 数値実験によって、提案手法が離散化誤差を適切に定量化して推定精度を改善することが確認された。 本研究は大阪大学の宮武勇登准教授との共同研究である。

#### 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

[ 講演概要 ]
A Riemann-Roch theorem on a connected finite graph was initiated by M. Baker and S. Norine, where connected graph with finite vertices was investigated and unit weight was given on each edge and vertex of the graph. Since a counterpart of the lowest exponents of the complex variable in the Laurent series was proposed as divisor for the Riemann-Roch theorem on graph, its relationships with tropical geometry were highlighted earlier than other complex analytical observations on graphs. On the other hand, M. Baker and F. Shokrieh revealed tight relationships between chip-firing games and potential theory on graphs, by characterizing reduced divisors on graphs as the solution to an energy minimization problem. The objective of this talk is to establish a Riemann-Roch theorem on an edge-weighted infinite graph. We introduce vertex weight assigned by the given weights of adjacent edges other than the units for expression of divisors and assume finiteness of total mass of graph. This is a joint work with A. Atsuji.

### 2019年07月05日(金)

#### 代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) 123号室
いつもと曜日・時間・部屋が異なります。

Durfee-type inequality for complete intersection surface singularities
[ 講演概要 ]
Durfee's negativity conjecture says that the signature of the Milnor fiber of a 2-dimensional isolated complete intersection singularity is always negative. In this talk, I will explain that this conjecture is true (more precisely, the signature is bounded above by the negative number determined by the geometric genus, the embedding dimension and the number of irreducible components of the exceptional set of the minimal resolution) by using the theory of invariants of fibered surfaces. If time permits, I will explain the higher dimensional analogue of Durfee's conjecture for isolated complete intersection singularities.

### 2019年07月04日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2019年07月03日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室
Amine Marrakchi 氏 (京大数理研)
Tensor product decompositions and rigidity of full factors

#### 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

Explicit calculation of values of the regulator maps on a certain type of Kummer surfaces (Japanese)
[ 講演概要 ]

### 2019年07月02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

Brane coproducts and their applications (JAPANESE)
[ 講演概要 ]
The loop coproduct is a coproduct on the homology of the free loop space of a Poincaré duality space (or more generally a Gorenstein space). In this talk, I will introduce two kinds of brane coproducts which are generalizations of the loop coproduct to the homology of a sphere space (i.e. the mapping space from a sphere). Their constructions are based on the finiteness of the dimensions of mapping spaces in some sense. As an application, I will show the vanishing of some cup products on sphere spaces by comparing these two brane coproducts. This gives a generalization of a result of Menichi for the case of free loop spaces.

### 2019年07月01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
Yeping Zhang 氏 (京都大学)
BCOV invariant and birational equivalence (English)
[ 講演概要 ]
Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.

#### 社会数理コロキウム

17:00-18:30   数理科学研究科棟(駒場) 056号室
18:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。

[ 講演概要 ]
AI や5G、IoT（モノのインターネット）は、近い将来、日本経済に多大な恩恵をもたらしうる。実際、AI やIoT を「武器」に、成長し続ける日本企業は少なくない。そこで本講演では、デジタル産業の創生に関わり続けてきた経験をもとに、「デジタルトランスフォーメーションという大きなうねり」によって、情報通信、流通、農業、金融・保険、医療・福祉がどう変わるかついて述べる。そして、急速に進化するデジタル社会を生き抜くには何が必要か？ 変化の本質を見極め牽引するために不可欠な数学・数理科学の重要性を説く。
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20190701.pdf

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 117号室

セラミックス球によるスケール形成防止効果と人体に及ぼす効用 (Japanese)
[ 講演概要 ]
セラミックス球を電解質溶液に浸したその界面に超強電場が発生することが知られている 。その電場に接触した炭酸カルシウム結晶に電気分極を生じ、それに基づく電気的エネル ギー（分極エネルギー）が化学ポテンシャルの一部として分配される。この分極エネルギ ーは核の生成を極端に妨害すると同時に生成した核の表面自由エネルギーを減少させる。 この現象がスケール形成防止効果を表現している。そのメカニズムが数理的手法を用いて 解明される。　更に、上記超強電場が水の分子集団に上記と同様な変化を生成することが 示される。この事実をもとにセラミックス球を人体に接触させたとき、如何なる現象が生 じるかについて議論する。

#### 数理人口学・数理生物学セミナー

11:00-12:00   数理科学研究科棟(駒場) 123号室
Joel E. Cohen 氏 (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
[ 講演概要 ]
A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
[ 講演参考URL ]

### 2019年06月28日(金)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室
いつもと曜日が異なります。

Rational curves on prime Fano 3-folds (TBA)
[ 講演概要 ]
One of important topics in algebraic geometry is the space of rational curves, e.g., the dimension and the number of components of the moduli spaces of rational curves on an algebraic variety X. One of interesting situations where this question is extensively studied is when X is a Fano variety since in this case X is rationally connected so that it does contain a lots of rational curves. In this talk I will talk about my joint work with Brian Lehmann which settles this problem for most Fano 3-folds of Picard rank 1, e.g., a general quartic 3-fold in P^4, and our approach is inspired by Manin’s conjecture which predicts the asymptotic formula for the counting function of rational points on a Fano variety. In particular we systematically use geometric invariants in Manin’s conjecture which have been studied by many mathematicians including Brian and me.

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

### 2019年06月27日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2019年06月26日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

KMS states on operator algebras associated with self-similar group actions

### 2019年06月25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
Tian-Jun Li 氏 (University of Minnesota)
Geometry of symplectic log Calabi-Yau surfaces (ENGLISH)
[ 講演概要 ]
This is a survey on the geometry of symplectic log Calabi-Yau surfaces, which are the symplectic analogues of Looijenga pairs. We address the classification up to symplectic deformation, the relations between symplectic circular sequences and anti-canonical sequences, contact trichotomy, and symplectic fillings. This is a joint work with Cheuk Yu Mak.

### 2019年06月24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

A certain holomorphic invariant and its applications (Japanese)
[ 講演概要 ]
In this talk, we first explain a Bergman geometric proof of inequivalence of the unit ball and the bidisk. In this proof, the homogeneity of the domains plays a substantial role. We next explain a recent attempt to extend our method for non-homogeneous cases.

### 2019年06月21日(金)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2019年06月20日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 118号室

[ 講演概要 ]

#### 数理人口学・数理生物学セミナー

16:00-17:00   数理科学研究科棟(駒場) 056号室
Eric Foxall 氏 (University of Alberta)
Diffusion limit for the partner model at the critical value (ENGLISH)
[ 講演概要 ]
The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the
threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.

### 2019年06月19日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

Type classification of extreme quantized characters

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室

A pencil of Enriques surfaces with non-algebraic integral Hodge classes (TBA)
[ 講演概要 ]
The integral Hodge conjecture is the statement that the integral Hodge classes are algebraic on smooth complex projective varieties. It is known that the conjecture can fail in general. There are two types of counterexamples, ones with non-algebraic integral Hodge classes of torsion-type and of non-torsion type, the first of which were given by Atiyah-Hirzebruch and Kollar, respectively.

In this talk, we exhibit a pencil of Enriques surfaces defined over Q with non-algebraic integral Hodge classes of non-torsion type. This construction relates to certain questions concerning rational points of algebraic varieties.

This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question on the universality of the Abel-Jacobi maps.

This is a joint work with John Christian Ottem.

### 2019年06月18日(火)

#### 統計数学セミナー

11:00-12:10   数理科学研究科棟(駒場) 052号室
Xiaohui Chen 氏 (University of Illinois at Urbana–Champaign)
Gaussian and bootstrap approximations of high-dimensional U-statistics with applications and extensions　※変更の可能性あり

[ 講演概要 ]
We shall first discuss the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. A two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed. Subject to mild moment conditions on the kernel, we establish the explicit rate of convergence that decays polynomially in sample size for a high-dimensional scaling limit, where the dimension can be much larger than the sample size. We also provide computable approximation methods for the quantiles of the maxima of centered U-statistics. Specifically, we provide a unified perspective for the empirical, the randomly reweighted, and the multiplier bootstraps as randomly reweighted quadratic forms, all asymptotically valid and inferentially first-order equivalent in high-dimensions.

The bootstrap methods are applied on statistical applications for high-dimensional non-Gaussian data including: (i) principled and data-dependent tuning parameter selection for regularized estimation of the covariance matrix and its related functionals; (ii) simultaneous inference for the covariance and rank correlation matrices. In particular, for the thresholded covariance matrix estimator with the bootstrap selected tuning parameter, we show that the Gaussian-like convergence rates can be achieved for heavy-tailed data, which are less conservative than those obtained by the Bonferroni technique that
ignores the dependency in the underlying data distribution. In addition, we also show that even for subgaussian distributions, error bounds of the bootstrapped thresholded covariance matrix estimator can be much tighter than those of the minimax estimator with a universal threshold.

Time permitting, we will discuss some extensions to the infinite-dimensional version (i.e., U-processes of increasing complexity) and to the randomized inference via the incomplete U-statistics whose computational cost can be made independent of the order.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Piotr Rybka 氏 (University of Warsaw)
Ways to treat a diffusion problem with the fractional Caputo derivative
[ 講演概要 ]
The problem
$u_t = (D^\alpha u)_x + f$
augmented with initial and boundary data appear in model of subsurface flows. Here, $D^\alpha u$ denotes the fractional Caputo derivative of order $\alpha \in (0,1)$.

We offer three approaches:
1) from the point of view of semigroups;
2) from the point of view of the theory of viscosity solutions;
3) from the point of view of numerical simulations.

This is a joint work with T. Namba, K. Ryszewska, V. Voller.