## 過去の記録

### 2019年05月02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 ]
1970年代に誕生した現代暗号は、1980年代にその理論的な基礎づけが確立された．今回は、その中核となる概念として，安全性証明のための標準モデル，証明手法としてのシミュレーションパラダイムおよび識別不可能性などを紹介するとともに，それらの概念に基づく代表的暗号機能として，ゼロ知識証明を紹介する．

### 2019年04月30日(火)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 122号室
Jean-Francois Dat 氏 (Sorbonne University)
Moduli space of l-adic Langlands parameters and the stable Bernstein center (English)
[ 講演概要 ]
Motivated by the description of the integral l-adic cohomology of certain Shimura varieties in middle degree, Emerton and Helm have conjectured the existence of a certain local Langlands correspondence for l-adic families of n-dimensional Galois representations. The proof of this conjecture by Helm and Moss relies on a beautiful isomorphism between the ring of functions of the moduli space of l-adic representations and the integral Bernstein center of GL_n(F). We will present a work in progress with Helm, Korinczuk and Moss towards a generalization of this result for arbitrary (tamely ramified) reductive groups.

### 2019年04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) 056号室

Lie-Poisson代数の「変形」とカイラルな場の理論 (日本語)
[ 講演概要 ]

### 2019年04月25日(木)

#### 応用解析セミナー

16:00-18:00   数理科学研究科棟(駒場) 118号室
この日は２つ講演があります．教室と時間にご注意下さい．
Matteo Muratori 氏 (Polytechnic University of Milan) 16:00-17:00
The porous medium equation on noncompact Riemannian manifolds with initial datum a measure
(English)
[ 講演概要 ]
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds. We show existence of solutions that take a finite Radon measure as initial datum, possibly sign-changing. We then prove uniqueness in the class of nonnegative solutions, upon assuming a quadratic lower bound on the Ricci curvature. Our result is "optimal" in the sense that any weak solution necessarily solves a Cauchy problem with initial datum a finite Radon measure. Moreover, as byproducts of the techniques we employ, we obtain some new results in potential analysis on manifolds, concerning the validity of a modified version of the mean-value inequality for superharmonic functions and related properties of potentials of positive Radon measures. Finally, we briefly discuss some work in progress regarding stability of the porous medium equation with respect to the Wasserstein distance, on Riemannian manifolds with Ricci curvature bounded below.
Maurizia Rossi 氏 (University of Pisa) 17:00-18:00
On sharp large deviations for the bridge of a general diffusion
(English)
[ 講演概要 ]
In this talk we provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided b enjoyes a simple condition that is always satisfied in dimension 1. On the other hand, we show that the drift can be influential if this assumption is not satisfied. This talk is based on a joint work with P. Baldi and L. Caramellino.

#### 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 ]

まず、第１回(4月25日）では、現代暗号が誕生した経緯とそれらが現在どのような形で利用されているかについて紹介する。

### 2019年04月24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
Joseph Ayoub 氏 (University of Zurich)
P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes (English)
[ 講演概要 ]
A^1-localisation is a universal construction which produces "cohomology theories" for which the affine line A^1 is contractible. It plays a central role in the theory of motives à la Morel-Voevodsky. In this talk, I'll discuss the analogous construction where the affine line is replaced by the projective line P^1. This is the P^1-localisation which is arguably an unnatural construction since it produces "cohomology theories" for which the projective line P^1 is contractible. Nevertheless, I'll explain a few positive results and some computations around this construction which naturally lead to a definition of Kodaira-Spencer classes of arithmetic nature. (Unfortunately, it is yet unclear if these classes are really interesting and nontrivial.)

#### 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

Varieties of dense globally F-split type with a non-invertible polarized
endomorphism
[ 講演概要 ]
Broustet and Gongyo conjectured that if a normal projective variety X has a non-invertible polaried endomorphism, then X is of Calabi-Yau type. Furthermore, Schwede and Smith conjectured that a projective variety is of Calabi-Yau type if and only if of dense globally F-split type. Therefore it is a natural question to ask if a normal projective variety X has a non-invertible polaried endomorphism, then X is of dense globally F-split type. In this talk, I will introduce simple points and difficult points of the question. Furthermore I will give the affirmative answer of my question for 2-dimensional case.

### 2019年04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) 056号室
Tea: Common Room 16:30-17:00
Christine Vespa 氏 (Université de Strasbourg)
Higher Hochschild homology as a functor (ENGLISH)
[ 講演概要 ]
Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).

In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).

(This is joint work with Geoffrey Powell.)

### 2019年04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

Optimal destabilizer for a Fano manifold (Japanese)
[ 講演概要 ]
Around 2005, S. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence of the normalized Donaldson-Futaki invariants.
For a Fano manifold we construct a sequence of multiplier ideal sheaves from a new geometric flow and answer to Donaldson's question.

#### 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

HDG法の超収束について (Japanese)
[ 講演概要 ]

#### 離散数理モデリングセミナー

17:15-18:30   数理科学研究科棟(駒場) 118号室
Yuri Suris 氏 (Technische Universität Berlin)
Geometry of the Kahan-Hirota-Kimura discretization
[ 講演概要 ]
We will report on some novel results concerning the bilinear discretization of quadratic vector fields.

### 2019年04月19日(金)

#### 作用素環セミナー

13:00-14:30   数理科学研究科棟(駒場) 128号室
Sorin Popa 氏 (UCLA・京大スーパーグローバルコース特別招聘教授)
Coarse decomposition of II$_1$ factors (English)

### 2019年04月17日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 122号室

On the Shafarevich conjecture for minimal surfaces of Kodaira dimension 0 (Japanese)
[ 講演概要 ]
Fを代数体、Sを有限素点の有限集合とする。
Faltings-Zarhinは、固定した正整数gに対して、
Sの外で良還元を持つようなF上のg次元Abel多様体のF上の同型類の有限性を証明した。
(Abel多様体のShafarevich予想)

また、超楕円曲面の還元に関連する話題として、

#### 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

### 2019年04月16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

Thurston’s bounded image theorem (ENGLISH)
[ 講演概要 ]
The bounded image theorem by Thurston constitutes an important step in the proof of his unifomisation theorem for Haken manifolds. Thurston’s original argument was never published and has been unknown up to now. It has turned out a weaker form of this theorem is enough for the proof, and books by Kappovich and by Otal use this weaker version. In this talk, I will show how to prove Thurston’s original version making use of more recent technology. This is joint work with Cyril Lecuire.

### 2019年04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

ある種の完備ケーラー多様体上のL2評価とその応用 (Japanese)
[ 講演概要 ]
しばらく前にL2拡張定理の応用として西野の剛性定理の別証を得たが, 最近これがL2消滅定理だけからも導けることが判明した. その結果, 剛性定理がシュタイン族に対してだけでなく完備ケーラー族に対しても成立することが わかった. この議論を用いると, ある種の完備ケーラー多様体が二つの多様体の直積に分解するための一つの条件を書くことができる. また, 同様の方法によりRadoの定理を高次元に一般化することが可能になる.

### 2019年04月10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
Zongbin Chen 氏 (丘成桐数学科学中心, 清華大学)
The geometry of the affine Springer fibers and Arthur's weighted orbital integrals (English)
[ 講演概要 ]
The affine Springer fibers are geometric objects conceived for the study of orbital integrals. They have complicated geometric structures. We will explain our work on the geometry of affine Springer fibers, with emphasize on the construction of a fundamental domain, and show how the study of the affine Springer fibers can be reduced to that of its fundamental domain. As an application, we will explain how to calculate Arthur's weighted orbital integrals via counting points on the fundamental domain.

（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東大数理, Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は東京からの中継です．）

### 2019年04月09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
Fabio Punzo 氏 (ミラノ工科大学)
The Poisson equation on Riemannian manifolds (English)
[ 講演概要 ]
The talk is concerned with the existence of solutions to the Poisson equation on complete non-compact Riemannian manifolds. In particular, the interplay between the Ricci curvature and the behaviour at infinity of the source function will be discussed. This is a joint work with G. Catino and D.D. Monticelli.

#### 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

Coulomb branches of 3d SUSY gauge theories (JAPANESE)
[ 講演概要 ]
I will give an introduction to a mathematical definition of Coulomb branches of 3-dimensional SUSY gauge theories, given by my joint work with Braverman and Finkelberg. I will emphasize on the role of hypothetical 3d TQFT associated with gauge theories.

### 2019年04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 ]
フェーズフィールドを用いたき裂進展に関する近似エネルギー変分モデルは，弾性体に対する脆性破壊のモデルとしてBourdin-Francfort-Marigo によって導入されたが，近年多様な応用研究が行われている．講演者と木村はエネルギー勾配流の方程式としてより数値計算しやすいき裂進展方程式を得たが，さらに田中のアイデアにより粘弾性体に対応した方程式系を導出した．この粘弾性モデルから得られたき裂進展における粘性の影響と，さらにどのような応用が可能となるかについて述べる．

### 2019年04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
Jongil Park 氏 (Seoul National University)
A topological interpretation of symplectic fillings of a normal surface singularity (ENGLISH)
[ 講演概要 ]
One of active research areas in symplectic 4-manifolds is to classify symplectic fillings of certain 3-manifolds equipped with a contact structure.
Among them, people have long studied symplectic fillings of the link of a normal surface singularity. Note that the link of a normal surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure.

In this talk, I’d like to investigate a topological surgery description for minimal symplectic fillings of the link of quotient surface singularities and weighted homogeneous surface singularities with a canonical contact structure. Explicitly, I’ll show that every minimal symplectic filling of the link of quotient surface singularities and weighted homogeneous surface singularities satisfying certain conditions can be obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding surface singularity. This is joint work with Hakho Choi.

### 2019年03月27日(水)

#### 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) 123号室

Florian Naef 氏 (Université de Genève)
On a moduli space interpretation of the Turaev cobracket (ENGLISH)
[ 講演概要 ]
Given an oriented surface, Goldman defines a Lie bracket on the vector space spanned by free homotopy classes of loops in terms of intersections. This Lie bracket is the universal version of the Atiyah-Bott Poisson structure on the moduli space of flat connections. Using self-intersections Turaev defines a Lie cobracket on loops. We give a possible interpretation of this structure on moduli spaces of flat connections in the form of a natural BV operator on the moduli space of flat connection with values in a super Lie algebra equipped with an odd pairing. This is joint work with A. Alekseev, J. Pulmann and P. Ševera.

### 2019年03月26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
Michael Hutchings 氏 (University of California, Berkeley)
Cube capacities (ENGLISH)
[ 講演概要 ]
We define a new series of symplectic capacities using equivariant symplectic homology. These capacities are conjecturally equal to the Ekeland-Hofer capacities, but can be computed in many more examples. In particular, we use these capacities to find many examples of symplectic embeddings of cubes where the cube is as large as possible. This is joint work with Jean Gutt.

### 2019年03月22日(金)

#### 談話会・数理科学講演会

13:00-17:00   数理科学研究科棟(駒場) 大講義室号室

[ 講演概要 ]

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~shu/

[ 講演概要 ]

「新しい発見は… 思い切り手を伸ばした 1ミリ先にある！」
[ 参考URL ]
http://gauss.ms.u-tokyo.ac.jp/index-j.html

[ 講演概要 ]

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~tsuboi/

### 2019年03月13日(水)

#### 統計数学セミナー

14:00-15:10   数理科学研究科棟(駒場) 052号室
Yury A. Kutoyants 氏 (Laboratoire Manceau de Mathématiques, Le Mans University)
On parameter estimation of hidden Markov processes
[ 講演概要 ]
We present a survey of several results devoted to parameter estimation of partially observed models. The hidden processes are Ornstein-Uhlenbeck process and Telegraph process. We describe the asymptotic behavior of the MLE and BE of the unknown parameters of hidden processes and special attention is paid to a new class of estimators called Multi-step MLE-processes, which have the same asymptotic properties as the MLE but can be calculated much easier than MLE.

The corresponding articles are

1.Kutoyants Yu. A., " On the multi-step MLE-process for ergodic
diffusion", (arXiv 1504.01869) Stochastic Processes and their
Applications, 2017, 127, 2243-2261.

2.Khasminskii, R. Z. and Kutoyants, Yu. A. "On parameter estimation of
hidden telegraph process". (arXiv:1509.02704 ) Bernoulli, 2018, 24, 3,
2064-2090.

3.Kutoyants, Yu. A. "On parameter estimation of hidden
Ornstein-Uhlenbeck process", Journal of Multivariate Analysis. 2019,
169, 1, 248-263.

4.Kutoyants, Yu. A. "On parameter estimation of hidden ergodic
Ornstein-Uhlenbeck process", 2019, submitted (arXiv:1902.08500)