## 過去の記録

### 2018年06月18日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
Ryszard Nest 氏 (Copenhagen Univ.)
Equivariant index theorem (English)

### 2018年06月13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

Poisson boundary for the discrete affine group (English)

### 2018年06月12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

Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
[ 講演概要 ]
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.

#### 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

Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
[ 講演概要 ]
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.

In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.

The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.

Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.

If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 056号室
Alexander Kupers 氏 (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups

[ 講演概要 ]
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.

### 2018年06月11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

Cohomology of non-pluriharmonic loci (JAPANESE)
[ 講演概要 ]
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.

### 2018年06月06日(水)

#### 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
Nicolas Templier 氏 (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
[ 講演概要 ]
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.

（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06月05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

Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
[ 講演概要 ]
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.

### 2018年06月04日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
Hamilton-Jacobi (HJ)方程式の初期値問題の解の長時間挙動を考えた時に現れる定常問題を，加法的固有値問題と呼ぶ．この加法的固有値問題の粘性解は，一意性が成り立たないことがよく知られている．力学系におけるAubry-Mather理論と粘性解理論との関係を整理することで発展した弱Kolmogorov-Arnold-Moser (KAM) 理論において，Mather集合またはAubry集合上で一致する粘性解は一意的であることが証明された．つまり，これらの集合は，加法的固有値問題の粘性解の一意性集合の役割を果たす．

#### 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

Picardの大定理とManin-Mumford予想(Raynaudの定理) (JAPANESE)
[ 講演概要 ]
Manin-Mumford予想とは，関数体上のMordell予想が解決された後の1960年代後半にManinとMumfordにより(独立に)提示されたもので1983年にM. Raynaudにより『代数体上定義されたアーベル多様体の代数的部分空間$X$内のトージョン点集合$X_{tor}$の$\mathbb{Z}$-閉包は部分群の平行移動の有限和である』という形で解決された．この結果は内容の深さからか多くの研究者の関心を呼び、その後，一般化や種々の別証明がM. Hindry ('88), E. Hrushovski ('96), Pila-Zannier ('08)等により与えられてきた．最後のPila-Zannierがここでの話に関係する．

### 2018年05月31日(木)

#### 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
Olivier Pironneau 氏 (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
[ 講演概要 ]
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.

### 2018年05月30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

Blow-ups and the class field theory for curves (JAPANESE)
[ 講演概要 ]

### 2018年05月29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

A partial order on nu+ equivalence classes (JAPANESE)
[ 講演概要 ]
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.

#### 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
Alessandra Sarti 氏 (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
[ 講演概要 ]
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.

### 2018年05月28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

A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
[ 講演概要 ]
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.

#### 数理人口学・数理生物学セミナー

15:30-16:30   数理科学研究科棟(駒場) 122号室
Sourav Kumar Sasmal 氏 (Department of Physics and Mathematics, Aoyama Gakuin University)
T-cell mediated adaptive immunity in primary dengue infections
[ 講演概要 ]
Currently, dengue virus (DENV) is the most common mosquito-borne viral disease in the world, which is endemic across tropical Asia, Latin America, and Africa. The global DENV incidence is increasing day by day due to climate changing. According to a report, DENV cases increase almost five times since 1980, than the previous 30 years. Mathematical modeling is a common tool for understanding, studying and analyzing the mechanisms that govern the dynamics of infectious disease. In addition, models can be used to study different mitigation measures to control outbreaks. Here, we present a mathematical model of DENV dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T -cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment effect for DENV in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.

[ 参考URL ]
https://www.sciencedirect.com/science/article/pii/S0022519317303211

### 2018年05月25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) 056号室

p進簡約群の法p表現 (日本語)
[ 講演概要 ]

#### 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

De Qi Zhang 氏 (Singapore)
Endomorphisms of normal projective variety and equivariant-MMP (English)
[ 講演概要 ]
We report some recent joint works on polarized or int-amplified endomorphisms f on a normal projective variety X with mild singularities, and prove the pseudo-effectivity of the anti-canonical divisor of X, and the f-equivariance, after replacing f by its power, for every minimal model program starting from X. Fano varieties and Q-abelian varieties turn out to be building blocks having such symmetries. The ground field is closed and of characteristic 0 or at least 7.

### 2018年05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

Sign-changing solutions for a one-dimensional semilinear parabolic problem (Japanese)
[ 講演概要 ]
This talk is concerned with a nonlinear parabolic equation on a bounded interval with the homogeneous Dirichlet or Neumann boundary condition. Under rather general conditions on the nonlinearity, we consider the blow-up and global existence of sign-changing solutions. It is shown that there exists a nonnegative integer $k$ such that the solution blows up in finite time if the initial value changes its sign at most $k$ times, whereas there exists a stationary solution with more than $k$ zeros. The proof is based on an intersection number argument combined with a topological method.

### 2018年05月23日(水)

#### 統計数学セミナー

14:00-15:10   数理科学研究科棟(駒場) 052号室
Lorenzo Mercuri 氏 (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
[ 講演概要 ]
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.

An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.

#### 統計数学セミナー

15:30-16:40   数理科学研究科棟(駒場) 052号室
Emanuele Guidotti 氏 (University of Milan)
Latest Development in yuimaGUI - Interactive Platform for Computational Statistics and Finance

[ 講演概要 ]
The yuimaGUI package provides a user-friendly interface for the yuima package, including additional tools related to Quantitative Finance. It greatly simplifies tasks such as estimation and simulation of stochastic processes, data retrieval, time series clustering, change point and lead-lag analysis. Today we are going to discuss the latest development in yuimaGUI, extending the Platform with multivariate modeling and simulation, Levy processes, Point processes, broader model selection tools and more general distributions thanks to the new yuima-Law object.

### 2018年05月22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

A discrete game interpretation for curvature flow equations with dynamic boundary conditions (日本語)
[ 講演概要 ]
A game-theoretic approach to motion by curvature was proposed by Kohn and Serfaty in 2006. They constructed a family of deterministic discrete games, whose value functions converge to the unique solution of the curvature flow equation. In this talk, we develop this method to provide an interpretation for the associated dynamic boundary value problems by including in the game setting a kind of nonlinear reflection near the boundary. We also discuss its applications to the fattening phenomenon. This talk is based on joint work with N. Hamamuki at Hokkaido University.

#### 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

[ 講演概要 ]
Atiyah-Singerの指数定理は，閉多様体上の解析的指数と位相的指数が一致することを主張する，微分トポロジーの金字塔の一つである．私の研究目標は，その指数理論の無限次元多様体版を与えることである．そのためには，できるだけ単純な場合から始めるのが自然であるため，次の問題を考えることにした：円周Tのループ群LTが，「固有かつ余コンパクトに」作用している無限次元多様体に対するLT同変指数理論を，KK理論的な観点から構築せよ．いまだにこの問題の解決には至っていないが，arXiv:1701.06055，arXiv:1709.06205 では，「関数空間」と見なせるHilbert空間を始めとする，解析的指数理論を構築するのに不可欠な対象をいくつか構成した．本講演では，この問題に対する現時点での結果を説明する．

### 2018年05月21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

Christopher Hacon 氏 (Utah/Kyoto)
Towards the termination of flips. (English)
[ 講演概要 ]
The minimal model program (MMP) predicts that if $X$ is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps
$X=X_0-->X_1-->X_2-->...-->X_n$ known as divisorial contractions and flips whose output $\bar X=X_n$ is a minimal model so that $K_{\bar X}$ is a nef $Q$-divisor i.e it intersects all curves $C\subset \bar X$ non-negatively: $K_{\bar X}\cdot C\geq 0$.
The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e. there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.
[ 参考URL ]
https://www.math.utah.edu/~hacon/