## 今後の予定

### 2015年11月30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
Jean-Pierre Demailly 氏 (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
[ 講演概要 ]
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.

#### 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
Fabrizio Catanese 氏 (Universität Bayreuth)
Interesting surfaces which are coverings of a rational surface branched over few lines (English)
[ 講演概要 ]
Surfaces which are covers of the plane branched over 5 or 6 lines have provided answers to long standing questions, for instance the BCD surfaces for Fujita's question on semiampleness of VHS (Dettweiler-Cat); and examples of ball quotients (Hirzebruch), automorphisms acting trivially on integral cohomology (Cat-Gromadtzki), canonical maps with high degree or image-degree (Pardini, Bauer-Cat). I shall speak especially about the above Abelian coverings of the plane, the geometry of the del Pezzo surface of degree 5, the rigidity of BCD surfaces, and a criterion for a fibred surface to be a projective classifying space.

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
Raoul Normand 氏 (中央研究院 數學研究所)
Self-organized criticality in a discrete model of limited aggregation
[ 講演概要 ]
We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.

### 2015年12月01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) 126号室
Stéphane Malek 氏 (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
[ 講演概要 ]
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).

#### 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

Monodromies of splitting families for singular fibers (JAPANESE)
[ 講演概要 ]
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.

### 2015年12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) 118号室

Drinfeld center and representation theory for monoidal categories

#### 統計数学セミナー

14:55-18:00   数理科学研究科棟(駒場) 056号室

Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
[ 講演概要 ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.

#### FMSPレクチャーズ

14:55-18:00   数理科学研究科棟(駒場) 056号室
"Learning theory and sparsity" 全3回講演の(2)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
[ 講演概要 ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

#### 数理人口学・数理生物学セミナー

14:55-16:40   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]
ネットワーク上における感染症流行を阻止するために，中心性指標を用いた

れることから，我々は基本増殖率の感受性解析を用いた新たなネットワーク中心

ったところ，既存の中心性指標では見落とされてきた流行動態を明らかにできた．

また，侵入阻止（基本増殖率低下）のために注力すべき箇所と，侵入が起こった
さいに被害低減（最終規模低下）のために注力すべき箇所が必ずしも一致しない
ことが分かった．本講演では，提案したネットワーク中心性指標の紹介および上

[ 講演参考URL ]
http://www.soken.ac.jp/

### 2015年12月03日(木)

#### 統計数学セミナー

16:40-18:00   数理科学研究科棟(駒場) 123号室

Arnak Dalalyan 氏 (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
[ 講演概要 ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.

#### FMSPレクチャーズ

16:40-18:00   数理科学研究科棟(駒場) 123号室
"Learning theory and sparsity" 全3回講演の(3)
Arnak Dalalyan 氏 (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
[ 講演概要 ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

### 2015年12月04日(金)

#### 談話会・数理科学講演会

16:50-17:50   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]
ミクロな系の時間発展を表す確率過程からマクロな系の時間発展を表す偏微分方程式を導出する流体力学極限は統計力学を基礎付ける重要なスケール極限の一種である。その証明において、無限直積空間上の微分１形式（もしくはそれに対応するもの）を考え、閉形式の空間を完全形式の空間とその直交空間に分解するという定理が重要な役割を果たしている。この定理は確率過程に対応する（微分）作用素ごとに証明されてきたが、既存の手法は代数的な内容と解析的な内容が混在した複雑なものであった。しかし、講演者らは最近、この問題を代数的な問題と解析的な問題に分け、代数的な部分については、モデルの詳細によらずに非常に一般的に成立することを明らかにした。また、解析的な問題についても、$L^2$空間が作用素とよい関係を持つ基底を持つ場合には、直感的でシンプルな証明が得られることを示した。しかし、この周辺の話題については問題の定式化も含めて未解明な部分が多く、代数や幾何、関数解析等の専門家からの助言が大きな進展をもたらす可能性があると考えている。そこで、講演では問題の背景にはあまり触れずに、無限直積空間上のある種の１形式に関する話題に絞って紹介したい。特に、{0,1}の無限直積に対する具体的な問題を中心に紹介する。
[ 講演参考URL ]

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

q-ボゾン系とアフィンヘッケ代数の変形 (Japanese)
[ 講演概要 ]
q-ボゾン系は笹本-和達によって定義された一次元可積分確率過程である. その Q行列は量子逆散乱法により構成できて, 代数的ベーテ仮設法を適用することで固有ベクトルが得られる. 最近の研究で, q-ボゾン系はアフィンヘッケ代数のある変形の表現からも得られることがわかった. この枠組みでは, Q行列の転置に対する固有ベクトルが自然に得られ, 座標的ベーテ仮設法で構成されたものと一致する. この講演では, 以上の結果について概説し, これら二つの方法の関係について議論する.

### 2015年12月07日(月)

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
[ 講演概要 ]
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.

#### 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

Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ 講演概要 ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.

#### 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
Alexey Bondal 氏 (IPMU)
TBA (English)
[ 講演概要 ]
TBA

### 2015年12月08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

レンズ空間手術と４次元多様体の Kirby calculus (JAPANESE)
[ 講演概要 ]
「３次元球面内の結び目に沿うデーン手術でレンズ空間が生じるもの
を決定せよ」という問題は「レンズ空間手術」と呼ばれています。Berge のリス
ト(1990) が完全なリストと信じられており Heegaard Floer 理論によって進展
はしたものの、解決には至っていません。手法が４次元多様体論に近づいていま
す。その一方 Minimally twisted 5 chain link の例外的デーン手術が再確認さ
れて、レンズ空間からのレンズ空間手術や２成分絡み目に視野が広がったりして
います。
講演では、Berge のリストの多様さと規則性を紹介しつつ、異なる結び目から

### 2015年12月09日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
David E. Evans 氏 (Cardiff Univ.)
K-theory in subfactors and conformal field theory

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Ted Chinburg 氏 (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ 講演概要 ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.

(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.)

### 2015年12月14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

Twistor correspondence for associative Grassmanniann
[ 講演概要 ]
It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.

#### 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

Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)
[ 講演概要 ]
In this talk, I will introduce partial compactification of a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.

### 2015年12月15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
Constantin Teleman 氏 (University of California, Berkeley)
The Curved Cartan Complex (ENGLISH)
[ 講演概要 ]
The Cartan model computes the equivariant cohomology of a smooth manifold X with
differentiable action of a compact Lie group G, from the invariant polynomial
functions on the Lie algebra with values in differential forms and a deformation
of the de Rham differential. Before extracting invariants, the Cartan differential
does not square to zero and is apparently meaningless. Unrecognised was the fact
that the full complex is a curved algebra, computing the quotient by G of the
algebra of differential forms on X. This generates, for example, a gauged version of
string topology. Another instance of the construction, applied to deformation
quantisation of symplectic manifolds, gives the BRST construction of the symplectic
quotient. Finally, the theory for a X point with an additional quadratic curving
computes the representation category of the compact group G, and this generalises
to the loop group of G and even to real semi-simple groups.

### 2015年12月16日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
Yul Otani 氏 (東大数理)
Nuclearity in AQFT and related results

#### 博士論文発表会

10:30-11:45   数理科学研究科棟(駒場) 122号室

Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)

### 2015年12月17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) 122号室

Dulip Piyaratne 氏 (IPMU)
TBA (English)
[ 講演概要 ]
TBA
[ 講演参考URL ]
http://db.ipmu.jp/member/personal/3989en.html