## 過去の記録

### 2014年06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) 126号室

Primitive automorphisms of positive entropy of rational and Calabi-Yau threefolds (JAPANESE)

#### 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

Invariant subrings of the Cox rings of K3surfaces by automorphism groups (JAPANESE)
[ 講演概要 ]
Cox rings were introduced by D.Cox and are important rings which appeared in algebraic geometry. One of the main topic related with Cox rings is the finite generation of them. In this talk, we consider the Cox rings of K3 surfaces and answer the following question asked by D. Huybrechts; Are the invariant subrings of the Cox rings of K3 surfaces by automorphism groups finitely generated in general?

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Anatol Kirillov 氏 (RIMS, Kyoto University)
On some quadratic algebras with applications to Topology,
Algebra, Combinatorics, Schubert Calculus and Integrable Systems. (ENGLISH)
[ 講演概要 ]
The main purpose of my talk is to draw attention of the
participants of the seminar to a certain family of quadratic algebras
which has a wide range of applications to the subject mentioned in the
title of my talk.

### 2014年06月28日(土)

#### 調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
Neal Bez 氏 (埼玉大学) 13:30-15:00
On the multilinear restriction problem (ENGLISH)
[ 講演概要 ]
I will discuss the multilinear restriction problem for the Fourier transform. This will include an overview of the pioneering work of Bennett, Carbery and Tao on this problem and the very losely connected multilinear Kakeya problem. I will also discuss some of my own work in this area which is connected to nonlinear Brascamp-Lieb inequalities (joint work with Jonathan Bennett).
Hong Yue 氏 (Georgia College and State University) 15:30-17:00
John-Nirenberg lemmas for a doubling measure (ENGLISH)
[ 講演概要 ]
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.

### 2014年06月26日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Entropic curvature-dimension condition and Bochner’s inequality (JAPANESE)
[ 講演概要 ]
As a characterization of "lower Ricci curvature bound and upper dimension bound”, there appear several conditions which make sense even on singular spaces. In this talk we show the equivalence in complete generality between two major conditions: a reduced version of curvature-dimension bounds of Sturm-Lott-Villani via entropy and optimal transport and Bakry–¥'Emery's one via Markov generator or the associated heat semigroup. More precisely, it holds for metric measure spaces where Cheeger's L^2-energy functional is a quadratic form. In particular, we establish the full Bochner inequality, which originally comes from the Bochner-Weitzenb¥"ock formula, on such spaces. This talk is based on a joint work with M. Erbar and K.-T. Sturm (Bonn).

### 2014年06月25日(水)

#### 作用素環セミナー

16:45-18:00   数理科学研究科棟(駒場) 122号室

Supersymmetric C*-dynamical systems (JAPANESE)

#### 数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 128号室

T 細胞による腫瘍免疫の数理モデル (JAPANESE)
[ 講演概要 ]

ならず、癌の除去にも貢献している。T リンパ球の集団は非自己(外来抗原)と自

に認識して除去できる機能を有する。癌は生体組織由来で生じるため、一般に
T 細胞による認識が充分でないと考えられる。また、免疫応答は複数段階の複雑
なプロセスを経て初めて活性化されるため、適切に活性化が誘導される必要があ
る。人為的な介入によって免疫細胞を活性化させ、癌を認識させる治療法が今現

を攻撃する T 細胞の増殖を表す関数型を3タイプ想定し、それぞれに対して解
の漸近挙動を解析した。構築したモデルは癌と免疫細胞の個体群動態を記述した

あれば、細胞レベルでの数理モデルと遺伝子制御ネットワークや癌の
heterogeneity、進化や免疫回避といった研究とどうつなげていくかに焦点を当
てて、マルチスケール数理モデルを用いたアプローチ [2] について話題提供をして

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室

Periods of some two dimensional reducible p-adic representations and non-de Rham B-pairs (JAPANESE)

### 2014年06月24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

Piotr Rybka 氏 (University of Warsaw)
Sudden directional diffusion: counting and watching facets (ENGLISH)
[ 講演概要 ]
We study two examples of singular parabolic equations such that the diffusion is so strong that is leads to creation of facets. By facets we mean flat parts of the graphs of solutions with singular slopes. In one of the equations we study there are two singular slopes. The other equation has just one singular slope and the isotropic diffusion term. For both problems we watch and count facet.

For the system with two singular slopes a natural question arises if any solution may have an infinite number of oscillations. We also show that the solutions we constructed are viscosity solutions. This in turn gives estimates on the extinction time based on the comparison principle.

#### トポロジー火曜セミナー

17:10-18:10   数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム

On third homologies of quandles and of groups via Inoue-Kabaya map (JAPANESE)
[ 講演概要 ]
In this talk, we demonstrate certain quandles, which are defined from a
group $G$ and an isomorphism $¥rho:G - G$, and introduce the following
results: First, "Inoue-Kabaya chain map" is formulated as a map from
quandle homology to group homology. For example, with respect to every
Alexander quandle over F_q, the all of Mochizuki 3-cocycle is derived
from some group 3-cocycle, and mostly interpreted by a Massey products.
In addition, for universal centrally extended quandles, the chain map
induces an isomorphism between the 3-rd homologies (up to certain
torsion parts).

#### 古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 122号室

D7型離散パンルヴェ方程式の既約性
(JAPANESE)
[ 講演概要 ]

### 2014年06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) 126号室

[ 講演概要 ]
The problem is the local finite generation of a relation sheaf $R(f_1, \ldots, f_q)$ in $\mathcal{O}_n=\mathcal{O}_{C^n}$. After $f_j$ reduced to Weierstrass' polynomials in $z_n$, it is the key to apply the induction in $n$ to show that elements of $R(f_1, \ldots, q)$ are expressed by $z_n$-polynomial-like elements of degree at most $p=\max_j\deg f_j$ over $\mathcal{O}_n$. In that proof one is used to use a divison by $f_j$ of $\deg f_j=p$ (Oka '48, Cartan '50, Hörmander, Demailly, . . .). In this talk we shall confirm that the division abve works by making use of $f_k$ of the minimum degree $\min_j \deg f_j$. This proof is natrually compatible with the simple case when some $f_j$ is a unit, and gives some improvement in the degree estimate of generators.

### 2014年06月19日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Antipodal structure of the intersection of real forms and its applications (JAPANESE)
[ 講演概要 ]
A subset A of a Riemannian symmetric space is called an antipodal set if the geodesic symmetry s_x fixes all points of A for each x in A. This notion was first introduced by Chen and Nagano. Tanaka and Tasaki proved that the intersection of two real forms L_1 and L_2 in a Hermitian symmetric space of compact type is an antipodal set of L_1 and L_2. As an application, we calculate the Lagrangian Floer homology of a pair of real forms in a monotone Hermitian symmetric space. Then we obtain a generalization of the Arnold-Givental inequality. We expect to generalize the above results to the case of complex flag manifolds. In fact, using the k-symmetric structure, we can describe an antipodal set of a complex flag manifold. Moreover we can observe the antipodal structure of the intersection of certain real forms in a complex flag manifold.

This talk is based on a joint work with Hiroshi Iriyeh and Hiroyuki Tasaki.

### 2014年06月18日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Toward the classification of irreducible unitary spherical representations of the Drinfeld double of $SU_q(3)$ (ENGLISH)

### 2014年06月17日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム

2次元軌道体群の円周への作用の有界オイラー数 (JAPANESE)
[ 講演概要 ]
Burger,Iozzi,Wienhardは連結かつ向き付けられた有限型の穴あき曲面の基本群
の円周への作用に対して有界オイラー数を定義した.有界オイラー数を含むMilnor-Wood型
の不等式が成立しその最大性はフックス作用を準共役を除いて特徴付ける.被覆を考えること
により有界オイラー数の定義は2次元軌道体群の作用に対して拡張される.Milnor-Wood型の

などのいくつかの2次元軌道体群のフックス作用の持ち上げがいつ有界オイラー数により特徴
づけられるかについて記述する.

#### 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
Bao Châu Ngô 氏 (University of Chicago, VIASM)
Vinberg's monoid and automorphic L-functions (ENGLISH)
[ 講演概要 ]
We will explain a generalisation of the construction of the local factors of Godement-Jacquet's L-functions, based on Vinberg's monoid.

(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.)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Pablo Ramacher 氏 (Marburg University)
SINGULAR EQUIVARIANT ASYMPTOTICS AND THE MOMENTUM MAP. RESIDUE FORMULAE IN EQUIVARIANT COHOMOLOGY (ENGLISH)
[ 講演概要 ]
Let M be a smooth manifold and G a compact connected Lie group acting on M by isometries. In this talk, we study the equivariant cohomology of the cotangent bundle of M, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain residue formulae. In case of compact symplectic manifolds with a Hamiltonian G-action, similar residue formulae were derived by Jeffrey, Kirwan et al..

### 2014年06月16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) 126号室

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
A.P. Veselov 氏 (Loughborough, UK and Tokyo)
Universal formulae for Lie groups and Chern-Simons theory (ENGLISH)
[ 講演概要 ]
In 1990s Vogel introduced an interesting parametrization of simple
Lie algebras by 3 parameters defined up to a common multiple and
permutations. Numerical characteristic is called universal if it can be
expressed in terms of Vogel's parameters (example - the dimension of Lie
algebra). I will discuss some universal formulae for Lie groups
and Chern-Simons theory on 3D sphere.
The talk is based on joint work with R.L. Mkrtchyan and A.N. Sergeev.

### 2014年06月11日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室

Finiteness of K-area and the dual of the Baum-Connes conjecture (ENGLISH)

#### 数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2014年06月10日(火)

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 056号室
Sergei Duzhin 氏 (Steklov Institute of Mathematics)
Bipartite knots (ENGLISH)
[ 講演概要 ]
We give a solution to a part of Problem 1.60 in Kirby's list of open
problems in topology thus proving a conjecture raised in 1987 by
J.Przytycki. A knot is said to be bipartite if it has a "matched" diagram,
that is, a plane diagram that has an even number of crossings which can be
split into pairs that look like a simple braid on two strands with two
crossings. The conjecture was that there exist knots that do not have such
diagrams. I will prove this fact using higher Alexander ideals.
This talk is based on a joint work with my student M.Shkolnikov

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)
[ 講演概要 ]
A system of N point vortices is a Hamiltonian dynamical system with N degrees of freedom,and it is known that under certain parameter and initial conditions, there are self-similar collapse solutions for which N vortices collide at a point while rotating without changing the initial shape of configuration. In this talk, I will introduce such collision solutions and discuss some properties of complex time singularities in relation with those solutions.

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

On estimates for the Stokes flow in a space of bounded functions (JAPANESE)
[ 講演概要 ]
The Stokes equations are well understood on $L^p$ space for various kinds of domains such as bounded or exterior domains, and fundamental to study the nonlinear Navier-Stokes equations. The situation is different for the case $p=\\infty$ since in this case the Helmholtz projection does not act as a bounded operator anymore. In this talk, we show some a priori estimate for a composition operator of the Stokes semigroup and the Helmholtz projection on a space of bounded functions.

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
[ 講演概要 ]
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥ bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.