## 過去の記録

### 2018年07月11日(水)

#### 作用素環セミナー

17:15-18:45   数理科学研究科棟(駒場) 126号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable C*-algebras (cont'd)

### 2018年07月10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) 002号室
いつもと部屋が違います。The room is different from usual.

The effective bound of anticanonical volume of Fano threefolds (English)
[ 講演概要 ]
According to Mori's program, varieties covered by rational curves are
built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the
dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)
of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical
volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,
where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).
Our aim is to find an effective bound of the anticanonical volume -K^3, which is
not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss
some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.
This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 128号室
Canceled!! (諸事情により,講演は取りやめとなりました.)
Sam Nariman 氏 (Northwestern University)
On the moduli space of flat symplectic surface bundles
[ 講演概要 ]
There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of
Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

#### 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
Emmy Murphy 氏 (Northwestern University)
Loose Legendrians and arboreal singularities (ENGLISH)
[ 講演概要 ]
Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室

(Japanese)
[ 講演概要 ]

### 2018年07月09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
Casey Kelleher 氏 (Princeton University)
Rigidity results for symplectic curvature flow (ENGLISH)
[ 講演概要 ]
We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.

### 2018年07月03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

Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)
[ 講演概要 ]
The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.

#### 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
Xun Yu 氏 (Tianjin University)
Surface automorphisms and Salem numbers (English)
[ 講演概要 ]
The entropy of a surface automorphism is either zero or the
logarithm of a Salem number.
In this talk, we will discuss which Salem numbers arise in this way. We
will show that any
supersingular K3 surface in odd characteristic has an automorphism the
entropy of which is
the logarithm of a Salem number of degree 22. In particular, such
automorphisms are
not geometrically liftable to characteristic 0.

### 2018年07月02日(月)

#### 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

[ 講演概要 ]

#### 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

Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)
[ 講演概要 ]
In this talk, I explain a complex analytic method and its applications for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasi-conformally. In RIMS conference "Open Problems in Complex Geometry'' held in 2010, I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and mentioned several problems on the fixed points of group actions on the universal Teichmueller space and its subspaces, and the rigidity of conjugation of certain groups of circle homeomorphisms. I will report on the development of these problems since then.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

László Székelyhidi Jr. 氏 (Universität Leipzig)
Convex integration in fluid dynamics (English)
[ 講演概要 ]
In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.
We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.

### 2018年06月29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

[ 講演概要 ]

### 2018年06月27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
Seung-Hyeok Kye 氏 (Seoul National Univ.)

### 2018年06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

Varieties with nef diagonal (English)
[ 講演概要 ]
For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a
cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth
del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for
spherical varieties. This is a joint work with Taku Suzuki.

#### 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

[ 講演概要 ]
We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.

### 2018年06月25日(月)

#### 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

BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)
[ 講演概要 ]

#### 離散数理モデリングセミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Anton Dzhamay 氏 (University of Northern Colorado)
Gap Probabilities and discrete Painlevé equations
[ 講演概要 ]
It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).
This is joint work with Alisa Knizel (Columbia University)

#### 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
Stephen McKeown 氏 (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
[ 講演概要 ]
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.

### 2018年06月22日(金)

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 128号室
Michael Harrison 氏 (Lehigh University)
Fibrations of R^3 by oriented lines
[ 講演概要 ]
Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.

### 2018年06月20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

Criteria for good reduction of hyperbolic polycurves (JAPANESE)
[ 講演概要 ]
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.

### 2018年06月19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

Dormant Miura opers and Tango structures (Japanese (writing in English))
[ 講演概要 ]
Tango（丹後）構造とは, 正標数の代数曲線で定義された然るべき直線束であり, （小平消滅定理の反例となるなどの, いわゆる）「病理的な」正標数の代数多様体を構成するうえで基本的な概念です. 本発表では, このTango構造と, 一見すると無関係にも見える幾つかのトピック（dormant Miura oper, 3正則グラフのナンバリング, Gaudin模型の対角化etc.）との結びつきや関連する結果について説明させていただきたく予定です.（各トピックについて発表者はそれほど詳しくありませんので, この機会にぜひ皆さまの知見を伺えればと思っております.）

#### 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
Rowan Killip 氏 (UCLA)
KdV is wellposed in $H^{-1}$ (English)

#### 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

Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)
[ 講演概要 ]
エネルギー法の差分解法への応用を意識し, 準線形の双曲型保存則系のあるモデルシステムを例に挙げて, この問題の時間に関して中点則で離散化した半離散解法の時間大域解の存在について議論したい. オリジナルの問題は, Racke(1992)や松村--西原(2004)のテキストで紹介されたエネルギー法によって, 初期値が小さいという仮定の下でアプリオリ評価が得られ, 時間大域解の存在を証明できる. 本発表では, 上記の半離散解法もオリジナルの連続問題と同様にして時間大域解の存在を示すことが可能であることについて紹介したい. また誤差評価もこのエネルギー構造を利用して示すことができることも時間があれば触れる. 本研究は川島秀一氏(早稲田大学)との共同研究に基づく.

#### 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

Characteristic classes via 4-dimensional gauge theory (JAPANESE)
[ 講演概要 ]
Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.

#### トポロジー火曜セミナー

14:30-16:00   数理科学研究科棟(駒場) 056号室
RIKEN iTHEMS と共催

[ 講演概要 ]
アティヤ-フレアー予想は，ゲージ理論におけるフレアーホモロジーとラグランジアンフレアーホモロジーの間の関係に関するものである．その一つの困難は，ラグランジアンフレアーホモロジーを考えるシンプレクティック多様体が特異点を持つことである．双対かつ同変ラグランジアンフレアーホモロジーを考えることで，この困難が解消し，少なくともアティヤ-フレアー予想を数学的に厳密な予想として定式化できることを説明する．