過去の記録 ~11/11本日 11/12 | 今後の予定 11/13~


13:00-16:40   数理科学研究科棟(駒場) 126号室
江夏洋一 氏 (東京理科大学) 13:00-13:30
On a mosquito-borne disease transmission by Wolbachia infection (JAPANESE)
[ 講演概要 ]
Symbiotic bacteria called Wolbachia pipientis inside mosquitoes are experimentally observed to prevent transmission of Zika virus. Wolbachia-infected mosquitoes have been widely released and it is reported that they reduce vector competence for Zika virus.
In order to study dynamical behavior of the population of the mosquitoes, Xue et al. (2017) formulated a system of ODEs and investigated stability of three equilibria; a disease-free
equilibrium, a complete infection equilibrium and an endemic equilibrium. In this presentation, we propose a system of DDEs to investigate the effect of a time lag from the egg stage to the aquatic stage. Out talk is based on a collaborated work with Professor Emiko Ishiwata and Mr. Masatoshi Kanamori.
Don Yueping 氏 (青山学院大学) 13:30-14:00
Delayed feedback controls in an Escherichia coli and Tetrahymena system (ENGLISH)
[ 講演概要 ]
In this talk, we develop a novel mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by Shiga-toxin and neutrophils in a community. By applying the quasi steady state approximation, the proposed model can be reduced to a Lotka-Volterra predator-prey type system with two discrete delays. By investigating the distributions of the roots of the characteristic equation, the local stability as well as Hopf bifurcation are well studied when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delays plane always enlarge as the increase of negative feedback control coefficients, and especially the controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as quasi-periodic behaviors and chaotic behaviours.
大泉嶺 氏 (国立社会保障・人口問題研究所) 14:00-14:30
構造人口モデルにおける固有関数と生活史進化 (JAPANESE)
[ 講演概要 ]
年齢構造モデルの基本であるMacKendrick方程式は, 支配的な特性根に対する左右固
中田行彦 氏 (島根大学) 14:40-15:10
Reinfection epidemic models in a heterogeneous host population (JAPANESE)
[ 講演概要 ]
In our recent studies, interplay of heterogeneous susceptible
population and reinfection indicates fragility of the threshold
phenomena, which is frequently observed in epidemic models, with
respect to the basic reproduction number. To elaborate this aspect, we
formulate a mathematical model by a system of ODEs and analyze its
equilibrium structure. If time permits, we analyze the transient
solution in detail for a special case and discuss the complexity in
the epidemic dynamics induced by the heterogeneous susceptibility.
大森亮介 氏 (北海道大学) 15:10-15:40
Time evolution of Tajima's D of a pathogen during its outbreak (JAPANESE)
[ 講演概要 ]
Tajima’s D measures the selection pressure by calculating the difference between two estimates of genetic diversity in a given sample set of nucleic acid sequences, however, it is believed that Tajima’s D is biased by the population dynamics. To analyze the impact of population dynamics of infectious disease pathogen, which described by the standard SIR model on Tajima’s D, we developed an inductive algorithm for calculating the site-specific nucleotide frequencies from a standard multi-strain susceptible-infective-removed model (both deterministic and stochastic). We show that these frequencies are fully determined by the mutation rate and the initial condition of the frequencies. We prove that the sign of Tajima’s D is independent of the disease population dynamics in the deterministic model. We also show that the stochasticity in the transmission and evolution dynamics induces the dependency of Tajima’s D on the population dynamics of pathogens.
Xu Yaya 氏 (東京大学大学院数理科学研究科) 15:40-16:10
Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)
[ 講演概要 ]
The hepatitis beta virus (HBV) and hepatitis delta viurs (HDV)
are two common forms of viral hepatitis. However HDV is dependent
on coinfection with HBV since replication of HDV requires the hepati-
tis B surface antigen (HBsAg) which can only been produced by HBV.
Here we start with analyzing HBV only model, the dynamics between
healthy cells, HBV infected cells and free HBV.We show that a postive
equilbrium exsits and it's globally asmptotically stable for R0 > 1, an
infection free equilibrium is globally asymptotically stable for R0 < 1.
Then we introduce HDV to form a coinfection model which contains
three more variables, HDV infected cells, coinfected cells and free HDV.
Additionally, we investigate two coinfection models, one without and
one with treatment by oral drugs which are valid for HBV only. We
consider several durgs with variable eciencies. As a result, compari-
son of model simulations indicate that treatment is necessary to taking
contiously for choric infection.



18:00-19:00   数理科学研究科棟(駒場) 056号室
Javier Fresán 氏 (École polytechnique)
Exponential motives (ENGLISH)
[ 講演概要 ]
What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the étale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums.
Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an étale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).

(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.)


17:00-17:45   数理科学研究科棟(駒場) 470号室
Anar Rahimov 氏 (The Institute of Control Systems of ANAS and Baku State University)
An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)
[ 講演概要 ]
We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.
[ 講演参考URL ]



10:30-11:30   数理科学研究科棟(駒場) 056号室
Alex Mahalov 氏 (Arizona State University)
Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics (English)
[ 講演概要 ]
We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework by bootstrapping from global regularity of the averaged stochastic resonant equations. The averaged covariance operator couples stochastic and wave effects. We also present theoretical results for 3D nonlinear dynamics.


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
清水 達郎 氏 (京都大学数理解析研究所)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
[ 講演概要 ]



10:30-12:00   数理科学研究科棟(駒場) 128号室
大沢 健夫 氏 (名古屋大学)
Nishino's rigidity theorem and questions on locally pseudoconvex maps
[ 講演概要 ]
Nishino proved in 1969 that locally Stein maps with fibers $\cong \mathbb{C}$ are locally trivial. Yamaguchi gave an alternate proof of Nishino's theorem which later developed into a the theory of variations of the Bergman kernel. The proofs of Nishino and Yamaguchi will be reviewed and questions suggested by the result will be discussed. A new application of the $L^2$ extension theorem will be also presented in this context.



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
川村 一宏 氏 (筑波大学)
Derivations and cohomologies of Lipschitz algebras (JAPANESE)
[ 講演概要 ]
For a compact metric space M, Lip(M) denotes the Banach algebra of all complex-valued Lipschitz functions on M. Motivated by a classical work of de Leeuw, we define a compact, not necessarily metrizable, Hausdorff space \hat{M} so that each point of \hat{M} induces a derivation on Lip(M). To some extent, \hat{M} may be regarded as "the space of directions." We study, by an elementary method, the space of derivations and continuous Hochschild cohomologies (in the sense of B.E. Johnson and A.Y. Helemskii) of Lip(M) with coefficients C(\hat{M}) and C(M). The results so obtained show that the behavior of Lip(M) is (naturally) rather different than that of the algebra of smooth/C^1 functions on M.


15:30-17:00   数理科学研究科棟(駒場) 122号室
佐藤 謙太 氏 (東大数理)
Ascending chain condition for F-pure thresholds on a fixed strongly F-regular germ (English or Japanese)
[ 講演概要 ]
For a germ of a variety in positive characteristic and a non-zero ideal sheaf on the variety, we can define the F-pure threshold of the ideal by using Frobenius morphisms, which measures the singularities of the pair. In this talk, I will show that the set of all F-pure thresholds on a fixed strongly F-regular germ satisfies the ascending chain condition. This is a positive characteristic analogue of the "ascending chain condition for log canonical thresholds" in characteristic 0, which was recently proved by Hacon, McKernan, and Xu.



16:00-17:30   数理科学研究科棟(駒場) 128号室
岡村 和樹 氏 (京都大学 数理解析研究所)
Some results for range of random walk on graph with spectral dimension two (JAPANESE)
[ 講演概要 ]
We consider the range of random walk on graphs with spectral dimension two. We show that a certain weak law of large numbers hold if a recurrent graph satisfies a uniform condition. We construct a recurrent graph such that the uniform condition holds but appropriately scaled expectations fluctuate. Our result is applicable to showing LILs for lamplighter random walks in the case that the spectral dimension of the underlying graph is two.


16:45-18:15   数理科学研究科棟(駒場) 126号室
Pieter Naaijkens 氏 (UC Davis)
Subfactors and wiretapping channels



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Sang-hyun Kim 氏 (Seoul National University)
Diffeomorphism Groups of One-Manifolds (ENGLISH)
[ 講演概要 ]
Let a>=2 be a real number and k = [a]. We denote by Diff^a(S^1) the group of C^k diffeomorphisms such that the k--th derivatives are Hölder--continuous of exponent (a - k). For each real number a>=2, we prove that there exists a finitely generated group G < Diff^a(S^1) such that G admits no injective homomorphisms into Diff^b(S^1) for any b>a. This is joint work with Thomas Koberda.


15:30-17:00   数理科学研究科棟(駒場) 122号室
田中 公 氏 (東大数理)
Kodaira vanishing theorem for Witt canonical sheaves (English)
[ 講演概要 ]
We establish an analogue of the Kodaira vanishing theorem in terms of de Rham-Witt complex. More specifically, given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf.


16:50-18:20   数理科学研究科棟(駒場) 117号室
小山大介 氏 (電気通信大学大学院情報理工学研究科)
Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
[ 講演概要 ]
A Hybrid discontinuous Galerkin (HDG) method for linear elasticity problems has been introduced by Kikuchi et al. [Theor. Appl. Mech. Japan, vol.57, 395--404 (2009)], [RIMS Kokyuroku, vol.1971, 28--46 (2015)]. We consider to seek numerical solutions of the plane strain problem by the HDG method, especially in the case when materials are nearly incompressible, that is, when the first Lam\'e parameter $\lambda$ is large. In this talk, we consider two cases when the HDG method uses a lifting term and does not use it. When the lifting term is used, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, we have to take an interior penalty parameter of order $\lambda$ as $\lambda$ tends to infinity, in order to guarantee the coercivity of the bilinear form. Taking such an interior penalty parameter causes volumetric locking phenomena. We thus conclude that the lifting term is essential for avoiding the volumetric locking in the HDG method.



16:00-17:30   数理科学研究科棟(駒場) 128号室
Antar Bandyopadhyay 氏 (Indian Statistical Institute)
Random Recursive Tree, Branching Markov Chains and Urn Models (ENGLISH)
[ 講演概要 ]
In this talk, we will establish a connection between random recursive tree, branching Markov chain and urn model. Exploring the connection further we will derive fairly general scaling limits for urn models with colors indexed by a Polish Space and show that several exiting results on classical/non-classical urn schemes can be easily derived out of such general asymptotic. We will further show that the connection can be used to derive exact asymptotic for the sizes of the connected components of a "random recursive forest", obtained by removing the root of a random recursive tree.

[This is a joint work with Debleena Thacker]


10:30-12:00   数理科学研究科棟(駒場) 128号室
細野 元気 氏 (東京大学)
On the proof of the optimal $L^2$ extension theorem by Berndtsson-Lempert and related results
[ 講演概要 ]
We will present the recent progress on the Ohsawa-Takegoshi $L^2$ extension theorem. A version of the Ohsawa-Takegoshi $L^2$ extension with a optimal estimate has been proved by Blocki and Guan-Zhou. After that, by Berndtsson-Lempert, a new proof of the optimal $L^2$ extension theorem was given. In this talk, we will show an optimal $L^2$ extension theorem for jets of holomorphic functions by the Berndtsson-Lempert method. We will also explain the recent result about jet extensions by McNeal-Varolin. Their proof is also based on Berndtsson-Lempert, but there are some differences.



15:30-16:30   数理科学研究科棟(駒場) 002号室
伊藤由佳理 氏 (IPMU, 名古屋大学)
特異点解消とマッカイ対応 (JAPANESE)
[ 講演概要 ]
本講演では、2次元有理二重点の特異点解消と1979年にJohn McKayが発見した有限群とディンキン図形の関係に基づく2次元のマッカイ対応について紹介し、その後、代数多様体の分類論や超弦理論と共に発展した3次元の特異点解消とマッカイ対応について解説したい。



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
境 圭一 氏 (信州大学)
The space of short ropes and the classifying space of the space of long knots (JAPANESE)
[ 講演概要 ]
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).


10:30-11:30   数理科学研究科棟(駒場) 056号室
Felix Schulze 氏 (University College London)
Optimal isoperimetric inequalities for surfaces in any codimension
in Cartan-Hadamard manifolds (English)
[ 講演概要 ]
Let $(M^n,g)$ be simply connected, complete, with non-positive sectional
curvatures, and $\Sigma$ a 2-dimensional surface in $M^n$. Let $S$ be an area
minimising 3-current such that $\partial S = \Sigma$. We use a weak mean
curvature flow, obtained via elliptic regularisation, starting from
$\Sigma$, to show that $S$ satisfies the optimal Euclidean isoperimetric
inequality: $|S| \leq 1/(6\sqrt{\pi}) |\Sigma|^{3/2}$. We also obtain the
optimal estimate in case the sectional curvatures of $M$ are bounded from
above by $\kappa < 0$ and characterise the case of equality. The proof
follows from an almost monotonicity of a suitable isoperimetric
difference along the approximating flows in one dimension higher.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Frédéric Campana 氏 (Université de Lorraine/KIAS)
Orbifold rational connectedness (English)
[ 講演概要 ]
The first step in the decomposition by canonical fibrations with fibres of `signed' canonical bundle of an arbitrary complex projective manifolds $X$ is its `rational quotient' (also called `MRC' fibration): it has rationally connected fibres and non-uniruled base. In general, the further steps (such as the Moishezon-Iitaka fibration) of this decomposition will require the consideration of 'orbifold base' of fibrations in order to deal with the multiple fibres (as seen already for elliptic surfaces). One thus needs to work in the larger category of (smooth) `orbifold pairs' $(X,D)$ to achieve this decomposition. The aim of the talk is thus to introduce the notions of Rational Connectedness and 'rational quotient' in this context, by means of suitable equivalent notions of negativity for the orbifold cotangent bundle (suitably defined. When $D$ is reduced, this is just the usual Log-version). The expected equivalence with connecting families of `orbifold rational curves' remains however presently open.



10:30-12:00   数理科学研究科棟(駒場) 128号室
新田 泰文 氏 (東京工業大学)
Relative GIT stabilities of toric Fano manifolds in low dimensions
[ 講演概要 ]
In 2000, Mabuchi extended the notion of Kaehler-Einstein metrics to Fano manifolds with non-vanishing Futaki invariant. Such a metric is called generalized Kaehler-Einstein metric or Mabuchi metric in the literature. Recently this metrics were rediscovered by Yao in the story of Donaldson's infinite dimensional moment map picture. Moreover, he introduced (uniform) relative Ding stability for toric Fano manifolds and showed that the existence of generalized Kaehler-Einstein metrics is equivalent to its uniform relative Ding stability. This equivalence is in the context of the Yau-Tian-Donaldson conjecture. In this talk, we focus on uniform relative Ding stability of toric Fano manifolds. More precisely, we determine all the uniformly relatively Ding stable toric Fano 3- and 4-folds as well as unstable ones. This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.



16:30-18:00   数理科学研究科棟(駒場) 123号室
中林潤 氏 (横浜市立大学 先端医科学研究センター )
Human Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化 (JAPANESE)
[ 講演概要 ]
今回のセミナーではHuman Immunodeficiency Virus (HIV) の細胞内複製ダイナミクスと感染個体内における進化を取り扱った研究を紹介する。
HIVは+鎖RNAをゲノムとして持つレンチウイルス属に属するレトロウイルスである。RNAを鋳型として逆転写酵素によって産生されたウイルスDNAが、ホストのゲノムにintegrateされ、そこからウイルス遺伝子産物が産生され、最終的にウイルス粒子が複製される。HAART (Highly Active Antiretroviral Therapy) によってHIV感染患者の予後は劇的に改善されたが、いったんintegrateされたprovirusが休眠状態で残存し、何らかのきっかけで再びウイルスを産生することがあり、これがHIV治療の大きな妨げとなっている。Integration siteの決定機構を解明することは、HIVの治療戦略を検討するのに重要である。
HIVのintegration siteはホストのゲノム中に一様ではなく偏って分布していることが知られている。HIV細胞内複製を記述する数理モデルと、これを用いた進化シミュレーションを使って、HIV integration siteの選好性がどのように決定されるか検討した。またデータベースに登録されたHIV integration siteの情報と、ホストのepigenomeデータを統合して網羅的な解析を行い、integration site特異的な塩基配列について検討したので、これらの結果について紹介したい。


13:00-16:00   数理科学研究科棟(駒場) 123号室
二宮嘉行 氏 (九州大学)
[ 講演概要 ]



10:30-11:30   数理科学研究科棟(駒場) 056号室
※ 通常と曜日が異なります。
Kaj Nyström 氏 (Uppsala University)
Boundary value problems for parabolic equations with measurable coefficients (English)
[ 講演概要 ]
In recent joint works with P. Auscher and M. Egert we establish new results concerning boundary value problems in the upper half-space for second order parabolic equations (and systems) assuming only measurability and some transversal regularity in the coefficients of the elliptic part. To establish our results we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green's representation for solutions in natural classes involving square functions and non-tangential maximal functions, well-posedness results with data in $L^2$-Sobolev spaces together with invertibility of layer potentials, and perturbation results. In addition we solve the Kato square root problem for parabolic operators with coefficients of the elliptic part depending measurably on all variables. Using these results we are also able to solve the $L^p$-Dirichlet problem for parabolic equations with real, time-dependent, elliptic but non-symmetric coefficients. In this talk I will briefly describe some of these developments.



15:30-17:00   数理科学研究科棟(駒場) 122号室
Meng Chen 氏 (Fudan )
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
[ 講演概要 ]
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.


16:50-18:20   数理科学研究科棟(駒場) 002号室
石川歩惟 氏 (神戸大学大学院システム情報学研究科)
変分原理に基づくエネルギー保存数値解法と無制約最適化問題への応用 (Japanese)
[ 講演概要 ]
構造保存型数値解法は, 方程式のもつ力学的構造に着目し, その力学的性質を保つようにしてスキームを設計する数値計算法である. 特に, エネルギー保存則を厳密に保つような数値解法はエネルギー保存数値解法と呼ばれ, 離散勾配法などが知られている. 離散勾配法とは, 勾配の性質を引き継ぐよう定義された離散勾配と呼ばれるものをスキームに用いる方法で, この方法によるスキームは安定性に優れたものとなることが多い. その一方, 多くの場合に陰的になり, また, 解析力学における基本原理である変分原理との対応も明らかではない. また, 離散勾配自体の導出も, 容易でない場合もある.
 そこで, 我々は, 離散勾配法の枠組みに変分原理を取り入れたエネルギー保存数値解法を提案してきた. 本講演では, この手法について紹介したのち, 変分原理を活かしたエネルギー散逸系に対する方法への拡張方法について述べる. また, これと離散勾配を自動的に導出する自動離散微分という方法を組み合わせ, 無制約最適化問題の近似解法を設計する. 最後に, 最近の話題として, Lie群上でのスキーム設計手法についても述べる.

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