## 過去の記録

### 2014年07月29日(火)

#### 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
Cyril Houdayer 氏 (ENS Lyon)
Asymptotic structure of free Araki-Woods factors (ENGLISH)

### 2014年07月28日(月)

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Computer assisted analysis of Craik’s and Pehlivan’s 3D dynamical systems (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

### 2014年07月25日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

Mathematical modelling of Tumor Immune System Interaction (JAPANESE)
[ 講演概要 ]
We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,
namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).
By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.
Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.
However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.
We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.
The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.
Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.

#### 博士論文発表会

10:30-11:45   数理科学研究科棟(駒場) 128号室

On the study of front propagation in nonlinear free boundary problems(非線形自由境界問題における波面の伝播の研究) (JAPANESE)

### 2014年07月24日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

メビウス・エネルギーの分解定理 (JAPANESE)
[ 講演概要 ]

すなわち、特異性を持つエネルギー密度の主値積分で定義される。エネルギーが主値積分で与えられるため、変分公式の計算などでは解析的にはデリケートな扱いが必要とされた。

この分解による3つの各部分のメビウス不変性は保たれており、微分幾何的にも興味深い。解析的には、この分解によってメビウス・エネルギーの変分公式とその評価が従来の計算法よりはるかに容易に求められるという利点がある。様々な関数空間上での第一・第二変分公式の評価を紹介する。

### 2014年07月23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
George Elliott 氏 (Univ. Toronto)
The Cuntz semigroup---a critical component for classification? (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07月22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) 056号室
Tea: 16:00 - 16:30 コモンルーム
Jesse Wolfson 氏 (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
[ 講演概要 ]
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.

### 2014年07月19日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

sigma函数の原点でのべき級数展開のHurwitz整性 (JAPANESE)

と Coble の超平面 (JAPANESE)

### 2014年07月17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

Jingyi Chen 氏 (University of British Columbia)
The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)
[ 講演概要 ]
We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.

### 2014年07月16日(水)

#### 東京無限可積分系セミナー

10:30-12:00   数理科学研究科棟(駒場) 002号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the Hilbert scheme to m/n Pieri rules (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.

### 2014年07月15日(火)

#### 東京無限可積分系セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From the shuffle algebra to the Hilbert scheme (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.

### 2014年07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) 126号室
Gopal Prasad 氏 (University of Michigan)
Higher dimensional analogues of fake projective planes (ENGLISH)
[ 講演概要 ]
A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti
number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.

### 2014年07月13日(日)

#### 東京無限可積分系セミナー

14:00-15:00   数理科学研究科棟(駒場) 002号室
Andrei Negut 氏 (Columbia University, Department of Mathematics)
From vertex operators to the shuffle algebra (ENGLISH)
[ 講演概要 ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.

### 2014年07月12日(土)

#### Lie群論・表現論セミナー

13:20-17:00   数理科学研究科棟(駒場) 126号室
Mikhail Kapranov 氏 (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
[ 講演概要 ]
Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).

The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.

Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
[ 講演概要 ]
One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.

Branching Problems of Representations of Real Reductive Groups (ENGLISH)
[ 講演概要 ]
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.

By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.

If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.

#### Lie群論・表現論セミナー

09:30-11:45   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

の特異集合への制限から常微分方程式の研究に興味を持った.
Fuchs型常微分方程式全体の空間にEuler変換などを通じてKac-Moodyルー
ト系のWeyl群が作用することが分かり,局所モノドロミーで決まらない
モジュライ空間の次元を不変量として,群軌道の有限性が明らかになった.
モジュライがないrigidな場合は自明な方程式に変換されるので具体的

と分類への応用がある.これらは分岐のない不確定特異点も許す場合に

まれ,モノドロミーの可約性などがルート系の言葉で一般的に記述でき
る.これらの概説と共に,最近の結果や今後の問題ついて解説する.

Gordan Savin 氏 (the University of Utah) 10:45-11:45
Representations of covering groups with multiplicity free K-types (ENGLISH)
[ 講演概要 ]
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.

### 2014年07月11日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]

として

のですが、
もっと一般の不定値計量をもつ空間では何が起こるでしょうか?
そもそも、大域解析の舞台となる良い空間が存在するのでしょうか。

この談話会では、

1.(局所から大域へ)閉じた空間が存在するか?

2. (スペクトル理論)変形しても音程が変わらないことがある?

という話題をとりあげてみたいと思います。

これらの問題は多岐にわたる数学の分野が関わっていますが、例として

#### FMSPレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf

### 2014年07月08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) 056号室
Tea: 16:00 - 16:30 コモンルーム
Ingrid Irmer 氏 (JSPS, 東京大学大学院数理科学研究科)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
[ 講演概要 ]
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."

#### 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

ABS equations arising from q-P((A2+A1)^{(1)}) (JAPANESE)
[ 講演概要 ]
The study of periodic reductions from ABS equations to discrete Painlevé equations have been investigated by many groups. However, there still remain open questions:
(i) How do we identify the discrete Painlevé equation that would result from applying a periodic reduction to an ABS equation?
(ii) Discrete Painlevé equations obtained by periodic reductions often have insufficient number of parameters. How do we obtain the general case with all essential parameters?
To solve these problems, we investigated the periodic reductions from the viewpoint of Painlevé systems.

In this talk, we show how to construct a lattice where ABS equations arise from relationships between $\\tau$ functions of Painlevé systems and explain how this lattice relates to a hyper cube associated with an ABS equation on each face.
In particular, we consider the $q$-Painlevé equations, which have the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$.

### 2014年07月07日(月)

#### 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

Balanced line bundles (JAPANESE)
[ 講演概要 ]
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.

### 2014年07月03日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

しかし、放物型方程式に関しては時間変数を固定した上での空間変数に関する解の凸性の研究が専らであった。本講演では、放物型冪凸という概念を導入し、冪凸非斉次項をもつ熱方程式の解の時空間変数による凸性について、最近の研究成果を含めて述べる。

#### FMSPレクチャーズ

16:00-18:00   数理科学研究科棟(駒場) 470号室
Gordan Savin 氏 (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf

### 2014年07月01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) 056号室
Tea: 16:00 - 16:30 コモンルーム

Singularities of special Lagrangian submanifolds (JAPANESE)
[ 講演概要 ]
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.

#### 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
(Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
[ 講演概要 ]
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.