## 過去の記録

### 2018年01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

Wiener汎関数ベクトルの最大値のGauss型近似とその高頻度データ解析への応用 (JAPANESE)
[ 講演概要 ]

の最大値の分布の間のKolmogorov距離を評価する問題を考える. 特に, 最近数理統計学
の分野におけるChernozhukov, Chetverikov & Katoによる一連の研究で発展した,

Wiener汎関数からなるベクトルへと拡張することを試みる. 本報告では, Chernozhukov,
Chetverikov & Kato (2015, PTRF)の結果のWiener汎関数からなるベクトルへの一般化
が可能であることを示す. さらに, 特別な場合として, (同じ次数をもつ)多重Wiener-伊藤積分
のベクトルの最大値の分布とGauss型ベクトルの最大値の分布の間のKolmogorov距離が0に

phenomenonが起きることを示す. 最後に, 高頻度データ解析への応用例を与え、理論の

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

On classification of prime Q-Fano 3-folds with only 1/2(1,1,1)-singularities and of genus less than 2
[ 講演概要 ]
I classified prime Q-Fano threefolds with only 1/2(1,1,1)-singularities and of genus greater than 1 (2002, Nagoya Math. J.).
In this talk, I will explain how the method in that paper can be extended to the case of genus less than 2. The method is so called two ray game. By this method, I can classify the possibilities of such Q-Fano's. The classification is not yet completed since constructions of examples in certain cases are difficult. I will also explain some pretty examples in this talk.

### 2018年01月25日(木)

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 002号室
Norbert A'Campo 氏 (University of Basel)
NUMERICAL ANALYSIS, COBORDISM OF MANIFOLDS AND MONODROMY. (ENGLISH)
[ 講演概要 ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ACampo_abst.pdf
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ACampo.pdf

### 2018年01月23日(火)

#### トポロジー火曜セミナー

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

An invariant of 3-manifolds via homology cobordisms (JAPANESE)
[ 講演概要 ]
For a closed 3-manifold X, we consider the topological invariant defined as the minimal integer g such that X is obtained as the closure of a homology cobordism over a surface of genus g. We prove that the invariant equals one for every lens space, which is contrast to the fact that some lens spaces do not admit any open book decomposition whose page is a surface of genus one. The proof is based on the Chebotarev density theorem and binary quadratic forms in number theory.

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

Wrapping projections and decompositions of Keinian groups (JAPANESE)
[ 講演概要 ]
Let $S$ be a closed surface of genus $g ¥geq 2$. The deformation space $AH(S)$ consists of (conjugacy classes of) discrete faithful representations $\rho:\pi_{1}(S) \to PSL_{2}(\mathbb{C})$.
McMullen, and Bromberg and Holt showed that $AH(S)$ can self-bump, that is, the interior of $AH(S)$ has the self-intersecting closure.
Both of them demonstrated the existence of self-bumping under the exisetence of a non-trivial wrapping projections from an algebraic limits to a geometric limits which wraps an annulus cusp into a torus cusp.
In this talk, given a representation $\rho$ at the boundary of $AH(S)$, we characterize a wrapping projection to a geometric limit associated to $\rho$, by the information of the actions of decomposed Kleinian groups of the image of $\rho$.

### 2018年01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

Recent topics on the study of the Gauss images of minimal surfaces
[ 講演概要 ]
In this talk, we give a survey of recent advances on the study of the images of the Gauss maps of complete minimal surfaces in Euclidean space.

#### 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

On Cauchy noise loss in a stochastic parameter optimization of random matrices

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 号室

ランダムな初期状態をもつ箱玉系とPitmanの定理 (JAPANESE)
[ 講演概要 ]

### 2018年01月17日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 002号室
Ana Caraiani 氏 (Imperial College)
On the vanishing of cohomology for certain Shimura varieties (ENGLISH)
[ 講演概要 ]
I will prove that the compactly supported cohomology of certain unitary or symplectic Shimura varieties at level Gamma_1(p^\infty) vanishes above the middle degree. The key ingredients come from p-adic Hodge theory and studying the Bruhat decomposition on the Hodge-Tate flag variety. I will describe the steps in the proof using modular curves as a toy model. I will also mention an application to Galois representations for torsion classes in the cohomology of locally symmetric spaces for GL_n. This talk is based on joint work in preparation with D. Gulotta, C.Y. Hsu, C. Johansson, L. Mocz, E. Reineke, and S.C. Shih.

（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる

#### 離散数理モデリングセミナー

17:00-18:45   数理科学研究科棟(駒場) 056号室
Samuel Colin 氏 (CBPF, Rio de Janeiro, Brasil) 17:00-17:50
Quantum matter bounce with a dark energy expanding phase (ENGLISH)
[ 講演概要 ]
The matter bounce'' is an alternative scenario to inflationary cosmology, according to which the universe undergoes a contraction, followed by an expansion, the bounce occurring when the quantum effects become important. In my talk, I will show that such a scenario can be unambiguously analyzed in the de Broglie-Bohm pilot-wave interpretation of quantum mechanics. More specifically, I will apply the pilot-wave theory to a Wheeler-DeWitt equation obtained from the quantization of a simple classical mini-superspace model, and show that there are numerical solutions describing bouncing universes with many desirable physical features. For example, one solution contains a dark energy phase during the expansion, without the need to postulate the existence of a cosmological constant in the classical action.
This work was done in collaboration with Nelson Pinto-Neto (CBPF, Rio de Janeiro, Brasil). Further details available at https://arxiv.org/abs/1706.03037.
Thomas Durt 氏 (Aix Marseille Université, Centrale Marseille, Institut Fresnel) 17:50-18:40
Mass of the vacuum: a Newtonian perspective (ENGLISH)
[ 講演概要 ]
One could believe that special relativity forces us to totally renounce to the idea of an aether, but the aether reappears in general relativity which teaches us that space-time is structured by the local metrics. It also reappears in quantum field theory which teaches us that even at zero temperature space is filled by the quantum vacuum energy. Finally, aether reappears in modern astronomy where it was necessary to introduce ill-defined concepts such as dark matter and dark energy in order to explain apparent deviations from Newtonian dynamics (at the level of galactic rotation curves).
Newton dynamics being the unique limit of general relativistic dynamics in the classical regime, dark matter and dark energy can be seen as an ultimate, last chance strategy, aimed at reconciling the predictions of general relativity with astronomical data.
In our talk we shall describe a simple model, derived in the framework of Newtonian dynamics, aimed at explaining puzzling astronomical observations realized at the level of the solar system (Pioneer anomaly) and at the galactic scale (rotation curves), without adopting ad hoc hypotheses about the existence of dark matter and/or dark energy.
The basic idea is that Newtonian gravity is modified due to the presence of a (negative) density, everywhere in space, of mass-energy.

### 2018年01月16日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
On adequacy and the crossing number of satellite knots (JAPANESE)
[ 講演概要 ]
It has always been difficult to prove results regarding the (minimal) crossing number of knots. In particular, apparently easy problems such as knowing the crossing number of the connected sum of knots, or bounding the crossing number of satellite knots have been conjectured through decades, yet still remain open. Focusing on this latter problem, in this talk I will prove that the crossing number of a satellite knot is bounded from below by the crossing number of its companion, when the companion is adequate.

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory (JAPANESE)
[ 講演概要 ]
A relation between the dilatation of pseudo-Anosov braids and fixed point theory was studied by Ivanov. In this talk we reveal a new relationship between the above two subjects by showing a formula for the dilatation of pseudo-Anosov braids by means of the representations of braid groups due to B. Jiang and H. Zheng.

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 056号室
FMSP Tokyo-Princeton joint student seminar
Federico Pasqualotto 氏 (Princeton) -
Large data global solutions for the shallow water system in one space dimension
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf
Naoto Kaziwara 氏 (U. Tokyo) -
Introduction to the maximal Lp-regularity and its applications to the quasi-linear parabolic equations
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf

### 2018年01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

Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds
[ 講演概要 ]
A Hessian manifold is a Riemannian manifold whose metric is locally given by the Hessian of a function with respect to flat coordinates. In this talk, we discuss vanishing theorems of $L^2$-cohomology groups on complete Hessian Manifolds coupled with flat line bundles. In particular, we obtain stronger vanishing theorems on regular convex cones with the Cheng-Yau metrics. Further we show that the Cheng-Yau metrics on regular convex cones give rise to harmonic maps to the positive symmetric matrices.

### 2017年12月26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

K-stability of log Fano hyperplane arrangements (English)
[ 講演概要 ]
We completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.

### 2017年12月25日(月)

#### 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

Kazhdan's property (T) and semidefinite programming

### 2017年12月21日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

Well-posedness and qualitative behavior of Peskin's problem of an immersed elastic filament in 2D Stokes flow
(Japanese)
[ 講演概要 ]
A prototypical fluid-structure interaction (FSI) problem is that of a closed elastic filament immersed in 2D Stokes flow, where the fluids inside and outside the closed filament have equal viscosity. This problem was introduced in the context of Peskin's immersed boundary method, and is often used to test computational methods for FSI problems. Here, we study the well-posedness and qualitative behavior of this problem.

We show local existence and uniqueness with initial configuration in the Holder space C^{1,\alpha}, 0<\alpha<1, and show furthermore that the solution is smooth for positive time. We show that the circular configurations are the only stationary configurations, and show exponential asymptotic stability with an explicit decay rate. Finally, we identify a scalar quantity that goes to infinity if and only if the solution ceases to exist. If this quantity is bounded for all time, we show that the solution must converge exponentially to a circle.

This is joint work with Analise Rodenberg and Dan Spirn.

#### 数理人口学・数理生物学セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

### 2017年12月19日(火)

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Finite volume scheme for the Hamilton-Jacobi equation on an evolving surface (Japanese)
[ 講演概要 ]
In this talk we consider the first-order Hamilton-Jacobi equation on a given closed evolving surface embedded into the three-dimensional Euclidean space, which describes the motion of a closed curve on the evolving surface. Our aim is to give a numerical scheme and establish its convergence and an error estimate between numerical and viscosity solutions.
Based on a finite volume scheme for the Hamilton-Jacobi equation on a flat domain introduced by Kim and Li (J. Comput. Math., 2015), we construct a numerical scheme on triangulated surfaces and prove its monotonicity and consistency without assuming that the triangulation is acute. Then applying these results we show the convergence of a numerical solution to a viscosity solution and an error estimate of the same order as in the case of a flat stationary domain.
This talk is based on a joint work with Prof. Klaus Deckelnick (Otto von Guericke University Magdeburg) and Prof. Charles M. Elliott (University of Warwick).

#### トポロジー火曜セミナー

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

Deformation of holomorphic quadratic differentials and its applications (JAPANESE)
[ 講演概要 ]
Quadratic differentials are standard and important objects in Teichmuller theory. The deformation space (moduli space) of the quadratic differentials is applied to many fields of mathematics. In this talk, I will develop the deformation of quadratic differentials. Indeed, following pioneer works by A. Douady, J. Hubbard, H. Masur and W. Veech, we describe the infinitesimal deformations in the odd (co)homology groups on the double covering spaces defined from the square roots of the quadratic differentials. We formulate the decomposition theorem for the infinitesimal deformations with keeping in mind of the induced deformation of the moduli of underlying complex structures. As applications, we obtain the Levi form of the Teichmuller distance, and an alternate proof of the Krushkal formula on the pluricomplex Green function on the Teichmuller space.

### 2017年12月18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

Gradient flow of the Ding functional
[ 講演概要 ]
This is a joint work with T. Collins and R. Takahashi. We introduce the flow in the title to study the stability of a Fano manifold. The first result is the long-time existence of the flow. In the stable case it then converges to the Kähler-Einstein metric. In general the flow is expected to produce the optimally destabilizing degeneration of a Fano manifold. We confirm this expectation in the toric case.

#### 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

Isomorphism and Morita equivalence classes for crossed product of irrational rotation algebras by cyclic subgroups of $SL_2({\mathbb Z})$ (English)

### 2017年12月14日(木)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 123号室

Gerard van der Geer 氏 (Universiteit van Amsterdam)
Algebraic curves and modular forms of low degree (English)
[ 講演概要 ]
For genus 2 and 3 modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such modular forms for genus 2 and 3 using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
158から128に変更されました．
I-Kun, Chen 氏 (Kyoto University)
Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain
(English)
[ 講演概要 ]
We consider the diffuse reflection boundary problem for the linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a $C^2$ strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. Velocity averaging effect for stationary solutions as well as observations in geometry are used in this research.

#### 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
Linquan Ma 氏 (University of Utah)
Perfectoid test ideals (English)
[ 講演概要 ]
Inspired by the recent solution of the direct summand conjecture
of Andre and Bhatt, we introduce perfectoid multiplier/test ideals in mixed
characteristic. As an application, we obtain a uniform bound on the growth
of symbolic powers in regular local rings of mixed characteristic analogous
to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal
characteristic. This is joint work with Karl Schwede.