## 過去の記録

#### 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

(日本語)
[ 講演概要 ]

（１）の証明にはHutchings等によるEmbedded Contact Homologyの理論，（２）の証明にはMarques-Neves等によるAlmgren-Pitts理論の最近の進展を用いる．これらは技術的には相当異なる理論であるが，どちらも無限次元空間上のMorse理論（あるいはmin-max理論）といえるもので，結果として定義されるmin-max値はいくつかのよく似た性質を満たす．特に，これらのmin-max値の漸近挙動から多様体の体積が復元されるという性質（Laplacianの固有値に対するWeylの法則の類似）が，いずれの証明においても重要な役割を果たす．

### 2018年05月10日(木)

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

#### 講演会

11:00-12:00   数理科学研究科棟(駒場) 123号室
Alexander Bertoloni Meli 氏 (University of California, Berkeley)
The Cohomology of Rapoport-Zink Spaces of EL-Type

[ 講演概要 ]
I will discuss Rapoport-Zink spaces of EL-type and how to explicitly compute a certain variant of their cohomology in terms of the local Langlands correspondence for general linear groups. I will then show how this computation can be used to resolve certain cases of a conjecture of Harris.

### 2018年05月09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
Sug Woo Shin 氏 (University of California, Berkeley)
Endoscopy and cohomology of U(n-1,1) (ENGLISH)
[ 講演概要 ]
We apply the endoscopic classification of automorphic representations for inner forms of unitary groups to bound the growth of cohomology in congruence towers of locally symmetric spaces associated with U(n-1,1). Our bound is sharper than the bound predicted by Sarnak-Xue for general locally symmetric spaces. This is joint work with Simon Marshall.

（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．）

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

#### 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

Factoriality, Connes' invariants and fullness of amalgamated free products (English)

### 2018年05月08日(火)

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

#### 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
Dan Cristofaro-Gardiner 氏 (University of California, Santa Cruz)
Beyond the Weinstein conjecture (ENGLISH)
[ 講演概要 ]
The Weinstein conjecture states that any Reeb vector field on a closed manifold has at least one closed orbit. The three-dimensional case of this conjecture was proved by Taubes in 2007, and Hutchings and I later showed that in this case there are always at least 2 orbits. While examples exist with exactly two orbits, one expects that this lower bound can be significantly improved with additional assumptions. For example, a theorem of Hofer, Wysocki, and Zehnder states that a generic nondegenerate Reeb vector field associated to the "standard" contact structure on $S^3$ has either 2, or infinitely many, closed orbits. We prove that any nondegenerate Reeb vector field has 2 or infinitely many closed orbits as long as the associated contact structure has torsion first Chern class. This is joint work with Mike Hutchings and Dan Pomerleano.

#### 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

Higher order families of lines and Fano manifolds covered by linear
spaces
(Japanese (writing in English))
[ 講演概要 ]
In this talk, for an embedded Fano manifold $X$, we introduce higher
order families of lines and a new invariant $S_X$. They are line
versions of higher order minimal families of rational curves and the
invariant $N_X$ which were introduced in my previous talk on 4th
November 2016. In addition, $S_X$ is related to the dimension of
covering linear spaces. Our goal is to classify Fano manifolds $X$ which
have large $S_X$.

#### 講演会

13:00-14:00   数理科学研究科棟(駒場) 122号室
Sander Mack-Crane 氏 (University of California, Berkeley)
Langlands-Rapoport for the Modular Curve

[ 講演概要 ]
We discuss a concrete version of the Langlands-Rapoport conjecture in the case of the modular curve, and use this case to illuminate some of the more abstract features of the Langlands-Rapoport conjecture for general (abelian type) Shimura varieties.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 052号室

LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter 1/4 < H < 1/2
[ 講演概要 ]
We consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than 1/2 under complete observation. We derive a formula for the likelihood ratio and prove local asymptotic normality when 1/4 < H < 1/2. Our result shows that the convergence rate is $T^{-1/2}$ for the parameters satisfying a certain equation and $T^{-(1-H)}$ for the others.
In this talk, we outline the proof of local asymptotic normality and explain how the different rates of convergence occur and where we use the assumption H > 1/4. We also mention some remaining problems and future directions. This talk is based on arXiv:1804.04108.

### 2018年05月07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

Proper holomorphic mappings and generalized pseudoellipsoids (JAPANESE)
[ 講演概要 ]
We study the classification of proper holomorphic mappings between generalized pseudoellipsoids of different dimensions.

Huang proved some classification theorems of proper holomorphic mappings between balls of different dimensions, which are called gap theorems. Our present theorems are their weakly pseudoconvex versions.

In the theorem, classified mapping is so-called a variables splitting mapping and each component is derived from a homogeneous proper polynomial mapping between balls.

The essential methods are the ''good'' decompositions of CR vector bundle and reduction the mapping under consideration to the mapping of balls. By this reduction, we can apply Huang's gap theorem.

#### 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

(JAPANESE)
[ 講演概要 ]

[1] Eiki Iyoda, Kazuya Kaneko, and Takahiro Sagawa, Phys. Rev. Lett. 119, 100601 (2017).
[2] Toru Yoshizawa, Eiki Iyoda, Takahiro Sagawa, arXiv:1712.07289, accepted by Phys. Rev. Lett. (2018).
[ 参考URL ]
http://www.taksagawa.com

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

### 2018年05月02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
Gabor Szabo 氏 (Copenhagen Univ.)
Classification of Rokhlin flows (English)

### 2018年04月24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

BIRATIONAL BOUNDEDNESS OF RATIONALLY CONNECTED CALABI–YAU 3-FOLDS
(English)
[ 講演概要 ]
Firstly, we show that rationally connected Calabi–Yau 3- folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected 3-folds of ε-CY type form a birationally bounded family for ε > 0. Then we focus on ε-lc log Calabi–Yau pairs (X, B) such that coefficients of B are bounded from below away from zero. We show that such pairs are log bounded modulo flops. As a consequence, we show that rationally connected klt Calabi–Yau 3-folds with mld bounding away from 1 are bounded modulo flops.

#### 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

Singular Fibers of smooth maps and Cobordism groups (JAPANESE)
[ 講演概要 ]
Following the pioneering work of R.Thom, cobordism groups of smooth maps have been studied by some mathematicians. Especially, cobordism groups of Morse functions on closed manifolds was studied by O.Saeki and K.Ikegami, B.Kalmar. In this talk, we will introduce cobordism groups among Morse functions on compact manifolds with boundary and study the cobordism groups are trivial or not by using the theory of the universal complex of singular fibers of smooth maps.

### 2018年04月23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

Degeneration and bifurcation of quadratic endomorphisms of $\mathbb{P}^2$ towards a Hénon map (JAPANESE)
[ 講演概要 ]
The space of quadratic holomorphic endomorphisms of $\mathbb{P}^2$ (over $\mathbb{C}$) is canonically identified with the complement of the zero locus of the resultant form on $\mathbb{P}^{17}$, and all Hénon maps, which are (the only) interesting ones among all the quadratic polynomial automorphisms of $\mathbb{C}^2$, live in this zero locus.

We will talk about our joint work with Fabrizio Bianchi (Imperial College, London) on the (algebraic) degeneration of quadratic endomorphisms of $\mathbb{C}^2$ towards Hénon maps in terms of Berteloot-Bianchi-Dupont's bifurcation/unstability theory of holomorphic families of endomorphisms of $\mathbb{P}^k$, which mostly generalizes Mañé-Sad-Sullivan, Lyubich, and DeMarco's seminal and similar theory on $\mathbb{P}^1$.

Some preliminary knowledge on ergodic theory and pluripotential theory would be desirable, but not be assumed.

#### 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

Functional central limit theorems for non-symmetric random walks on nilpotent covering graphs (JAPANESE)
[ 講演概要 ]
ベキ零群を被覆変換群とするような有限グラフの被覆グラフのことをベキ零被覆グラフと呼ぶ。結晶格子(被覆変換群がアーベル群の場合)上のランダムウォークに関してはすでに多くの極限定理が, 離散幾何解析の枠組みで得られている。我々は以前にこれらの研究の延長としてベキ零被覆グラフ上の非対称ランダムウォークの汎関数中心極限定理を考察し,スケール極限として捉えたベキ零Lie群値拡散過程に, ランダムウォークの非対称性からくるドリフト項が現れることをいくつかの技術的な仮定の下で示した。この結果は難波氏が, 2016年7月の本セミナーで報告したが,その後, このドリフト項が実現写像のambiguityによらずに定まる事が分かっただけでなく, 従来の技術的な仮定の多くをはずすことにも成功した。時間があればラフパス理論との関連および証明の概略についても話したい。

### 2018年04月18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

#### 代数学コロキウム

16:00-17:00   数理科学研究科棟(駒場) 002号室
Ildar Gaisin 氏 (東京大学数理科学研究科)
Fargues' conjecture in the GL_2-case (ENGLISH)
[ 講演概要 ]
Recently Fargues announced a conjecture which attempts to geometrize the (classical) local Langlands correspondence. Just as in the geometric Langlands story, there is a stack of G-bundles and a Hecke stack which one can define. The conjecture is based on some conjectural objects, however for a cuspidal Langlands parameter and a minuscule cocharacter, we can define every object in the conjecture, assuming only the local Langlands correspondence. We study the geometry of the non-semi-stable locus in the Hecke stack and as an application we will show the Hecke eigensheaf property of Fargues conjecture holds in the GL_2-case and a cuspidal Langlands parameter. This is joint work with Naoki Imai.

#### 代数学コロキウム

17:10-18:10   数理科学研究科棟(駒場) 002号室

p進代数群の法p表現とHecke環 (JAPANESE)
[ 講演概要 ]
p進代数群の，標数pの体上における表現（法p表現）について，付随するHecke環の表現論の関わりとともにお話をします．これは，G. Henniart，F. HerzigおよびM.-F. Vignérasとの共同研究に基づきます．

### 2018年04月17日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Global existence of a strong solution to the Navier-Stokes equations in a curved thin domain (Japanese)
[ 講演概要 ]
In this talk, we consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a closed surface.
We establish the global-in-time existence of a strong solution for large data when the width of the thin domain is very small.
A key idea is to decompose a three-dimensional vector field into the average part which is almost two-dimensional and the residual part to which we can apply Poincaré type inequalities.
Such decomposition enables us to derive a good estimate for the inner product of the inertia term and the viscous term, which is essential for our arguments.

#### 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

SNC log symplectic structures on Fano products (English/Japanese)
[ 講演概要 ]
In 2014, Lima and Pereira gave a characterization of the even-dimensional projective space in terms of log symplectic Poisson structures. After that Pym gave an another more algebraic proof. In this talk, we will extend the result of Lima and Pereira to the case that the variety is a product of Fano varieties with the cyclic Picard group. This will be proved by extending Pym's proof. As a corollary, we will obtain a characterization of the projective space of all dimensions.