## 過去の記録

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30

[ 講演概要 ]
K(n)局所安定ホモトピー圏はスペクトラムの安定ホモトピー圏の基本構成単位と考えられる。この講演ではMorava E理論とその安定化群との関係が明確になるようなK(n)局所安定ホモトピー圏のモデルを構成する。そのために、Behrens-Davisにより研究された副有限群Gに対する離散対称Gスペクトラムについて考える。そして、K(n)局所安定ホモトピー圏が、離散対称G_nスペクトラムの圏におけるE_nの離散モデル上の加群のホモトピー圏の中に実現されることを示す。

### 2018年12月17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

Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)
[ 講演概要 ]
This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.

### 2018年12月14日(金)

#### 代数幾何学セミナー

10:30-11:30   数理科学研究科棟(駒場) 123号室
Zhi Jiang 氏 (Fudan)
On the birationality of quint-canonical systems of irregular threefolds of general type (English)
[ 講演概要 ]
It is well-known that the quint-canonical map of a surface of general type is birational.
We will show that the same result holds for irregular threefolds of general type. The proof is based on
a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi
type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.

### 2018年12月12日(水)

#### 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
Gaëtan Chenevier 氏 (CNRS, Université Paris-Sud)
A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)
[ 講演概要 ]
I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.

（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．今回はパリからの中継です．）

### 2018年12月11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
Marek Fila 氏 (Comenius University in Bratislava)
Solutions with moving singularities for equations of porous medium type (English)
[ 講演概要 ]
We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions. This is a joint work with Jin Takahashi and Eiji Yanagida.

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30

On non-singular solutions to the normalized Ricci flow on four-manifolds (JAPANESE)
[ 講演概要 ]
A solution to the normalized Ricci flow is called non-singular if the solution exists for all time and the Riemannian curvature tensor is uniformly bounded. In 1999, Richard Hamilton introduced it as an important special class of solutions and proved that the underlying 3-manifold is geometrizable in the sense of Thurston. In this talk, we will discuss properties of 4-dimensional non-singular solutions from a gauge theoretical point of view. In particular, we would like to explain gauge theoretical invariants give rise to obstructions to the existence of 4-dimensional non-singular solutions.

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 117号室

A Pieri-type formula and a factorization formula for K-k-Schur functions
[ 講演概要 ]
We give a Pieri-type formula for the sum of K-k-Schur functions \sum_{\mu\le\lambda}g^{(k)}_{\mu} over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, which sum we denote by \widetilde{g}^{(k)}_{\lambda}. As an application of this, we also give a k-rectangle factorization formula \widetilde{g}^{(k)}_{R_t\cup\lambda}=\widetilde{g}^{(k)}_{R_t} \widetilde{g}^{(k)}_{\lambda}
where R_t=(t^{k+1-t}), analogous to that of k-Schur functions s^{(k)}_{R_t\cup \lambda}=s^{(k)}_{R_t}s^{(k)}_{\lambda}.

### 2018年12月10日(月)

#### 東京確率論セミナー

17:00-18:00   数理科学研究科棟(駒場) 号室

Nikolaos Zygouras 氏 (University of Warwick)
Random polymer models and classical groups (ENGLISH)
[ 講演概要 ]
The relation between polymer models at zero temperature and characters of the general linear group GL_n(R) has been known since the first breakthroughs in the field around the KPZ universality through the works of Johansson, Baik, Rains, Okounkov and others. Later on, geometric liftings of the GL_n(R) characters appeared in the study of positive temperature polymer models in the form of GL_n(R)-Whittaker functions. In this talk I will describe joint works with E. Bisi where we have established that Whittaker functions associated to the orthogonal group SO_{2n+1}(R) can be used to describe laws of positive temperature polymers when their end point is free to lie on a line. Going back to zero temperature, we will also see that characters of other classical groups such as SO_{2n+1}(R); Sp_{2n}(R); SO_{2n}(R) do play a role in describing laws of polymers in various geometries. This occurence might be surprising given the length of time these models have been studied.
[ 参考URL ]

### 2018年12月07日(金)

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 002号室

### 2018年12月06日(木)

#### 東京無限可積分系セミナー

16:00-17:00   数理科学研究科棟(駒場) 002号室
Francesco Ravanini 氏 (University of Bologna)
Integrability and TBA in non-equilibrium emergent hydrodynamics (ENGLISH)
[ 講演概要 ]
The paradigm of investigating non-equilibrium phenomena by considering stationary states of emergent hydrodynamics has attracted a lot of attention in the last years. Recent proposals of an exact approach in integrable cases, making use of TBA techniques, are presented and discussed.

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 128号室

### 2018年12月05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
Frederic Latremoliere 氏 (Univ. Denver)
The Gromov-Hausdorff Propinquity

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 002号室

#### 統計数学セミナー

13:00-15:00   数理科学研究科棟(駒場) 156号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 2:Representation results for the Gaussian processes. Financial applications of fractional Brownian motion

[ 講演概要 ]
Arbitrage with fBm: why it appears. How to present any contingent claim via self-financing strategy on the financial market involving fBm. Absence of arbitrage for the mixed models. Fractional -Uhlenbeck and fractional Cox-Ingersoll-Ross processes as the models for stochastic volatility.

#### 統計数学セミナー

15:00-17:00   数理科学研究科棟(駒場) 156号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 3:Statistical parameter estimation for the diffusion processes and in the models involving fBm

[ 講演概要 ]
Drift parameter estimation in the standard diffusion model and its strong consistency. Hurst and drift parameter estimation in the models involving fBm and in the mixed models. Asymptotic properties. Estimation of the diffusion parameter.

### 2018年12月04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
Vincent Florens 氏 (Université de Pau et des Pays de l'Adour)
Slopes and concordance of links (ENGLISH)
[ 講演概要 ]
We define the slope of a link associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima-Yamasaki η-function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. We present several examples and discuss the invariance by concordance. Joint with A. Degtyarev and A. Lecuona.

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 002号室

#### 統計数学セミナー

15:00-17:00   数理科学研究科棟(駒場) 126号室
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev)
Lecture 1: Elements of fractional calculus
How to connect the fractional Brownian motion to the Wiener process. Stochastic integration w.r.t. fBm and stochastic differential equations involving fB
[ 講演概要 ]
Fractional integrals and fractional derivatives. Wiener and stochastic integration w.r.t. the fractional Brownian motion. Representations of fBm via a Wiener process and vice versa. Elements of the fractional stochastic calculus. Stochastic differential equations involving fBm: existence, uniqueness, properties of the solutions. Simplest models: fractional Ornstein-Uhlenbeck and fractional Cox-Ingersoll-Ross processes.

### 2018年12月03日(月)

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 002号室

#### 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

[ 講演概要 ]

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
Ali Baklouti 氏 (Sfax 大学)
Monomial representations of discrete type and differential operators. (English)
[ 講演概要 ]
Let $G$ be an exponential solvable Lie group and $\tau$ a monomial representation of $G$, an induced representation from a connected closed subgroup of $G$ of a unitary character. It is well known that $\tau$ disintegrates into irreducible factors and the multiplicities of each isotypic component are explicitly determined. In the case where $G$ is nilpotent, these multiplicities are either finite or infinite almost everywhere, with respect to the disintegration's measure. We associate to $\tau$ an algebra of differential operators and it is shown that in the nilpotent case, the commutativity of this algebra is equivalent to the finiteness of the multiplicities of $\tau$. In the exponential case, we define the notion of monomial representation of discrete type. In this case, we show that such an equivalence does not hold and this answers a question posed by M. Duflo. This is a joint work with H. Fujiwara and J. Ludwig.

### 2018年11月30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) 002号室

[ 講演概要 ]

(i) 非線形随伴法を利用した漸近解析：非線形随伴法を利用した漸近解析として，退化粘性HJ方程式の長時間挙動，ディスカウント近似の極限に関する結果について紹介する．

### 2018年11月28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

Localization of signature for singular fiber bundles

### 2018年11月27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

Frobenius summands and the finite F-representation type (TBA)
[ 講演概要 ]
We are motivated by a question arising from commutative algebra, asking what kind of
graded rings in positive characteristic p have finite F-representation type. In geometric
setting, this is related to the problem to looking out for Frobenius summands. Namely,
given aline bundle L on a projective variety X, we want to know how many and what
kind of indecomposable direct summands appear in the direct sum decomposition of
the iterated Frobenius push-forwards of L. We will consider the problem in the following
two cases, although the present situation in (2) is far from satisfactory.
(1) two-dimensional normal graded rings (a joint work with Ryo Ohkawa)
(2) the anti-canonical ring of a quintic del Pezzo surface

#### 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

Fixed points for group actions on non-positively curved spaces (JAPANESE)
[ 講演概要 ]
In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.