## 過去の記録

### 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.
[ 講演参考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.

### 2018年11月26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

DGA-Models of variations of mixed Hodge structures (JAPANESE)
[ 講演概要 ]
Mixed Hodge structureは（Projectiveとは限らない)代数多様体のコホモロジー等に現れる非常に重要な構造です。Variations of mixed Hodge structures(VMHS)とは複素多様体をパラメーターとして複素幾何学的に良い振る舞いをしながら変化するMixed Hodge structureたちのことです。今回のお話ではこのVMHSの代数的なモデルについて考えてみたいと思いいます。具体的にはMorganの Mixed Hodge diagramと呼ばれるケーラー多様体のde Rham複体（あるいは対数的 de Rham複体）を積構造込みで模した代数的な対象に対して、”(Unipotent)VMHSのようなもの"を定義します。このVMHSのようなものは純粋に代数的に定義されたものであるため、本来のVMHSのようにベースとなる空間のパラメーターごとにMixed Hodge structureをとる（ファイバーをとる）ことを自然にはできません。本講演ではこの"VMHSのようなもの”からいかにファイバーを取るかということをメインテーマにしてお話ししたいと思います。さらに時間があれば、本結果の幾何学的応用についてもお話ししたいと思います。特に今回の結果によりMorganのMixed Hodge structureとHainのMixed Hodge structureの深い関係が見えることをお話ししたいと思います。

### 2018年11月21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
Yves André 氏 (Université Pierre et Marie Curie)
Poncelet games, confinement of algebraic integers, and hyperbolic Ax-Schanuel (ENGLISH)
[ 講演概要 ]
We shall theorize and exemplify the problem of torsion values of sections of abelian schemes. This « unlikely intersection problem », which arises in various diophantine and algebro-geometric contexts, can be reformulated in a non-trivial way in terms of Kodaira-Spencer maps. A key tool toward its general solution is then provided by recent theorems of Ax-Schanuel type (joint work with P. Corvaja, U. Zannier, and partly Z. Gao).

#### 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

Orbit equivalence classes for free actions of free products of infinite abelian groups