## 過去の記録

#### 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。
[ 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.
[ 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.

#### 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

Filtered instanton homology and the homology cobordism group (JAPANESE)
[ 講演概要 ]
We give a new family of real-valued invariants {r_s} of oriented homology 3-spheres. The invariants are defined by using some filtered version of instanton Floer homology. The invariants are closely related to the existence of solutions to ASD equations on Y×R for a given homology sphere Y. We show some properties of {r_s} containing a connected sum formula and a negative definite inequality. As applications of such properties of {r_s}, we obtain several new results on the homology cobordism group and the knot concordance group. As one of such results, we show that if the 1-surgery of a knot has the Froyshov invariant negative, then all positive 1/n-surgeries of the knot are linearly independent in the homology cobordism group. This theorem gives a generalization of the theorem shown by Furuta and Fintushel-Stern in ’90. Moreover, we estimate the values of {r_s} for a hyperbolic manifold Y with an error of at most 10^{-50}. It seems the values are irrational. If the values are irrational, we can conclude that the homology cobordism group is not generated by Seifert homology spheres. This is joint work with Yuta Nozaki and Kouki Sato.

### 2019年06月17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
Andrei Pajitnov 氏 (Universite de Nantes)
Inoue surfaces and their generalizations (English)
[ 講演概要 ]
In 1972 M. Inoue constructed complex non-algebraic surfaces that proved very important for classification of surfaces via the Enriques-Kodaira scheme. Inoue surface is the quotient of H ¥times C by action of a discreet group associated to a given matrix in SL(3, Z). In 2005 K. Oeljeklaus and M. Toma generalized Inoue’s construction to higher dimensions. Oeljeklaus-Toma manifold is the quotient of H^s ¥times C^n by action of a discreet group, associated to the maximal order of a given algebraic number field.
In this talk, I will give a brief overview of these works and related results. Then I will discuss a new generalization of Inoue surfaces to higher dimensions. The manifold in question is the quotient of H ¥times C^n by action of a discreet group associated to a given matrix in SL(2n+1, Z). This is joint work with Hisaaki Endo.

### 2019年06月13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 ]
21世紀に入り、公開鍵暗号が発展した新しい暗号概念として完全準同型暗号と関数型暗号が研究されるようになった．これら暗号では，暗号は単に秘匿性を保証するだけではなく，秘匿性を保証したまま様々な演算や高度なデータ検索を可能とする．いわば，暗号化したままクラウド計算やビックデータ検索を行うといったことが可能となる．

### 2019年06月12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

On extension of overconvergent log isocrystals on log smooth varieties (Japanese)
[ 講演概要 ]
Kを混標数の完備な非アルキメデス付値体とし，kをその剰余体とする．
Kedlayaおよび志甫の研究により，k上の滑らかな代数多様体Xとその上の単純正規交叉因子Zについて，X ¥setminus Z上の過収束アイソクリスタルのうちZの周りである種のモノドロミーを持つものは，XにZから定まる対数的構造を入れた対数的代数多様体上の収束対数的アイソクリスタルに延長できることが知られている．

### 2019年06月11日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
Antonio De Rosa 氏 (クーラン数理科学研究所)
Solutions to two conjectures in branched transport: stability and regularity of optimal paths (English)
[ 講演概要 ]
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. The transportation cost in these models is proportional to a concave power $\alpha \in (0,1)$ of the intensity of the flow. We focus on the stability of the optimal transports, with respect to variations of the source and target measures. The stability was known when $\alpha$ is bigger than a critical threshold, but we prove it for every exponent $\alpha \in (0,1)$ and we provide a counterexample for $\alpha=0$. Thus we completely solve a conjecture of the book Optimal transportation networks by Bernot, Caselles and Morel. Moreover the robustness of our proof allows us to get the stability for more general lower semicontinuous functional. Furthermore, we prove the stability for the mailing problem, which was completely open in the literature, solving another conjecture of the aforementioned book. We use the latter result to show the regularity of the optimal networks. (Joint works with Maria Colombo and Andrea Marchese)

### 2019年06月06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 ]