## 過去の記録

### 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/

#### 代数幾何学セミナー

13:30-15:00   数理科学研究科棟(駒場) 122号室

Will Donovan 氏 (IPMU)
Perverse sheaves of categories and birational geometry (English)
[ 講演概要 ]
Kapranov and Schechtman have initiated a program to study perverse sheaves of categories, or perverse schobers. It is expected that examples arise from birational geometry, in particular from webs of flops. I explain progress towards constructing these objects for Grothendieck resolutions (work of the above authors with Bondal), and for 3-folds (joint work of myself and Wemyss).

#### 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

Kähler-Ricci soliton, K-stability and moduli space of Fano
manifolds (JAPANESE)
[ 講演概要 ]
Kähler-Ricci soliton is a kind of canonical metrics on Fano manifolds and is a natural generalization of Kähler-Einstein metric in view of Kähler-Ricci flow.

In this talk, I will explain the following good geometric features of Fano manifolds admitting Kähler-Ricci solitons:
1. Volume minimization, reductivity and uniqueness results established by Tian&Zhu.
2. Relation to algebraic (modified) K-stability estabilished by Berman&Witt-Niström and Datar&Székelyhidi.
3. Moment map picture for Kähler-Ricci soliton (‘real side’)
4. Moduli stack (‘virtual side’) and moduli space of them

A result in 1 is indispensable for the formulation in 3 and 4, and explains why we should consider solitons, beyond Einstein metrics. I also show an essential idea in the construction of the moduli space of Fano manifolds admitting Kähler-Ricci solitons and give some remarks on technical key point.

### 2018年05月16日(水)

#### FMSPレクチャーズ

14:45-15:45   数理科学研究科棟(駒場) 122号室
M.M. Lavrentʼev, Jr. 氏 (Novosibirsk State University)
Some strongly degenerate parabolic equations (joint with Prof. A. Tani) (ENGLISH)
[ 講演概要 ]
We consider some nonlinear 1D parabolic equations with the positive leading coefficient which is not away from zero. "Hyperbolic phenomena" (gradient blowing up phenomena) were reported in literature for such models. We describe special cases of regular solvability for degenerate equations under study.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_MMLavrentev.pdf

### 2018年05月15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

[ 講演概要 ]
Consider a real algebraic variety of real codimension 2 defined by $V:=\{g(\mathbf x,\mathbf y)=h(\mathbf x,\mathbf y)=0\}$ in $\mathbb C^n=\mathbb R^n\times \mathbb R^n$. Put $\mathbf z=\mathbf x+i\mathbf y$ and consider complex valued real analytic function $f=g+ih$. Replace the variables $x_1,y_1\dots, x_n,y_n$ using the equality $x_j=(z_j+\bar z_j)/2,\, y_j=(z_j-\bar z_j)/2i$. Then $f$ can be understood to be an analytic functions of $z_j,\bar z_j$. We call $f$ a mixed function. In this way, $V=\{f(\mathbf z,\bar{\mathbf z})=0\}$ and we can use the techniques of complex analytic functions and the singularity theory developed there. In this talk, we explain basic properties of the singularity of mixed hyper surface $V(f)$ and give several open questions.

### 2018年05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) 128号室

Harmonic map and the Einstein equation in five dimension (JAPANESE)
[ 講演概要 ]
We present a new method in constructing 5-dimensional stationary solutions to the vacuum Einstein equation. In 1917, H. Weyl expressed the Schwarzschild black hole solution using a cylindical coordinate system, and consequently realized that the metric is completely determined by a harmonic function. Since then, the relation between harmonic maps and the Einstein equation has been explored mostly by physicists, which they call the sigma model of the Einstein equation. In this talk, after explaining the historical background, we demonstrate that in 5D, the Einstein spacetimes can have a wide range of black hole horizons in their topological types. In particular we establish an existence theorem of harmonic maps, which subsequently leads to constructions of 5D spacetimes with black hole horizons of positive Yamabe types, namely $S^3$, $S^2 \times S^1$, and the lens space $L(p,q)$. This is a joint work with Marcus Khuri and Gilbert Weinstein.

#### 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

Chordal Komatu-Loewner equation for a family of continuously growing hulls (JAPANESE)
[ 講演概要 ]
Loewner方程式は，複素平面上の単連結な領域における単葉函数族の極値問題に古くから用いられてきた．近年では，統計力学模型のスケーリング極限を記述する確率的Loewner発展(SLE)の構成に応用され，函数論，確率論，数理物理と様々な分野にまたがって注目を受けている．本講演ではこの方程式を多重連結領域へと拡張したKomatu-Loewner方程式について紹介する．特に，先行研究の結果を「連続な」増大殻(hull)へ一般化することで，これまで上手く扱えなかった多重連結領域上の問題に対し新たなアプローチが得られる様子を概説する．

### 2018年05月11日(金)

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

#### 講演会

13:00-14:00   数理科学研究科棟(駒場) 123号室
Alex Youcis 氏 (University of California, Berkeley)
The Langlands-Kottwitz method for deformation spaces of Hodge type
[ 講演概要 ]
Cohomology of global Shimura varieties is an object of universal importance in the Langlands program. Given a Shimura datum (G,X) and a (sufficiently nice) representation ¥xi of G, one obtains an l-adic sheaf F_{¥xi,l} on Sh(G,X) with a G(A_f)-structure. Thus, in the standard way, the cohomology group H^*(Sh(G,X),F_¥xi) has an admissible action of Gal(¥overline{E}/E) ¥times G(A_f), where E=E(G,X) is the reflex field of (G,X). Extending work of Kottwitz, Scholze, and others we discuss a method for computing the traces of this action, more specifically of an element ¥tau ¥times g where ¥tau ¥in W_{E_¥mathfrak{p}} for some prime ¥mathfrak{p} of E dividing p and g ¥in G(A_f^p) ¥times G(Z_p), in terms of a weighted point count on the Shimura variety's special fiber, as well as the traces of various local Shimura varieties over E_¥mathfrak{p}, at least in the case when (G,X) is a abelian-type Shimura datum unramified at p.

#### 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

(日本語)
[ 講演概要 ]

（１）の証明にはHutchings等によるEmbedded Contact Homologyの理論，（２）の証明にはMarques-Neves等によるAlmgren-Pitts理論の最近の進展を用いる．これらは技術的には相当異なる理論であるが，どちらも無限次元空間上のMorse理論（あるいはmin-max理論）といえるもので，結果として定義されるmin-max値はいくつかのよく似た性質を満たす．特に，これらのmin-max値の漸近挙動から多様体の体積が復元されるという性質（Laplacianの固有値に対するWeylの法則の類似）が，いずれの証明においても重要な役割を果たす．

### 2018年05月10日(木)

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 123号室

Sug Woo Shin 氏 (University of California, Berkeley)
Introduction to the Langlands-Rapoport conjecture (ENGLISH)
[ 講演概要 ]
In 1970s Langlands envisioned a program to compute the Hasse-Weil zeta functions of Shimura varieties as an alternating product of automorphic L-functions, which in particular implies the meromorphic continuation and functional equation for the zeta functions. In 1987, Langlands and Rapoport formulated a precise and far-reaching conjecture describing the set of points of Shimura varieties modulo p as an essential step towards the goal. The program has been largely carried out by Langlands, Kottwitz, and others for PEL-type Shimura varieties with striking applications to the local and global Langlands correspondences (which in turn led to further applications). We have started to understand the more general Hodge-type and abelian-type cases only recently, thanks to Kisin's work on the Langlands-Rapoport conjecture in the good reduction case. The lecture aims to give a gentle introduction to his seminal paper. After a brief introduction, the lecture is divided into four parts.
(i) Shimura varieties: We introduce Shimura varieties of Hodge type and abelian type and their integral models.
(ii) Statement of the conjecture: After setting up the language of
Galois gerbs, we state the Langlands-Rapoport conjecture.
(iii) Sketch of Kisin's proof: We sketch Kisin's proof of the conjecture for Shimura varieties of Hodge type.
(iv) Counting fixed points: Following forthcoming work of Kisin, Y. Zhu, and the speaker, we explain how to apply the Langlands-Rapoport conjecture to count fixed-points of
Hecke-Frobenius correspondences.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_SugWooShin.pdf

#### 講演会

11:00-12:00   数理科学研究科棟(駒場) 123号室
Alexander Bertoloni Meli 氏 (University of California, Berkeley)
The Cohomology of Rapoport-Zink Spaces of EL-Type

[ 講演概要 ]
I will discuss Rapoport-Zink spaces of EL-type and how to explicitly compute a certain variant of their cohomology in terms of the local Langlands correspondence for general linear groups. I will then show how this computation can be used to resolve certain cases of a conjecture of Harris.