過去の記録

過去の記録 ~11/11本日 11/12 | 今後の予定 11/13~

2016年07月28日(木)

博士論文発表会

15:00-16:15   数理科学研究科棟(駒場) 118号室
井上 大輔 氏 (東京大学大学院数理科学研究科)
Calabi-Yau 3-folds in Grassmannians and their I-functions (グラスマン多様体に含まれる3 次元カラビ・ヤウ多様体とそれらのI-関数)
(JAPANESE)

2016年07月27日(水)

数理人口学・数理生物学セミナー

15:00-16:00   数理科学研究科棟(駒場) 128号室
Saki Takahashi 氏 (Princeton University)
The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)
[ 講演概要 ]
As we approach global eradication of poliovirus (Enterovirus C species), its relatives are rapidly emerging as public health threats. One of these viruses, Enterovirus A71 (EV-A71), has been implicated in large outbreaks of hand, foot, and mouth disease (HFMD), a childhood illness that has had a substantial burden throughout East and Southeast Asia over the past fifteen years. HFMD is typically a self-limiting disease, but a small proportion of EV-A71 infections lead to the development of neurological and systemic complications that can be fatal. EV-A71 also exhibits puzzling spatial characteristics: the virus circulates at low levels worldwide, but has so far been endemic and associated with severe disease exclusively in Asia. In this talk, I will present findings from a recent study that we did to characterize the transmission dynamics of HFMD in China, where over one million cases are reported each year. I will then describe recent efforts to explain the observed multi-annual cyclicity of EV-A71 incidence in Japan and to probe the contributions of other serotypes to the observed burden of HFMD. In closing, I will discuss plans for unifying data and modeling to study this heterogeneity in the endemicity of EV-A71, as well as to broadly better understand the spatial and viral dynamics of this group of infections.

2016年07月26日(火)

統計数学セミナー

13:00-14:30   数理科学研究科棟(駒場) 052号室
本講演は大阪大学で行い,東京大学へWeb配信いたします.
Ajay Jasra 氏 (National University of Singapore)
Multilevel Particle Filters
[ 講演概要 ]
In this talk the filtering of partially observed diffusions,
with discrete-time observations, is considered.
It is assumed that only biased approximations of the diffusion can be
obtained, for choice of an accuracy parameter indexed by $l$.
A multilevel estimator is proposed, consisting of a telescopic sum of
increment estimators associated to the successive levels.
The work associated to $\cO(\varepsilon^2)$ mean-square error between
the multilevel estimator and average with respect to the filtering
distribution is shown to scale optimally, for example as
$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the
underlying diffusion approximation.
The method is illustrated on several examples.

2016年07月25日(月)

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
今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.
鈴木文顕 氏 (東大数理)
Birational rigidity of complete intersections (English)
[ 講演概要 ]
A complete intersection defined by s hypersurfaces of degree d_1, ... ,d_s in a projective space P^N is Q-Fano, i.e. normal, Q-factorial, terminal and having an ample anti-canonical divisor, if d_1 + ... + d_s is at most N and it has only mild singularities. Then it is rationally-connected by the results of Kollar-Miyaoka-Mori, Zhang and Hacon-Mckernan. A natural question is to determine its rationality. If its dimension or degree is at most 2, then it is rational. How about the remaining cases?

When d_1 + ... + d_s = N, birational rigidity give one of the most effective ways to tackle this problem. We recall that a Q-Fano variety is birationally superrigid if any birational map to the source of another Mori fiber space is isomorphism. It implies that X is non-rational and Bir(X) = Aut(X). After the works of Iskovskih-Manin, Pukhlikov, Chelt'so and de Fernex-Ein-Mustata, de Fernex proved that every smooth hypersurface of degree N in P^N is birationally superrigid for N at least 4. He also proved birational superrigidity of a large class of singular hypersurfaces of this type.

In this talk, we would like to extend de Fernex's results to complete intersections. As a key step, we generalize Pukhlikov's multiplicity bounds of cycles in hypersurfaces to complete intersections.

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
謝 賓 氏 (信州大学理学部数学科)
Intermittent property of parabolic stochastic partial differential equations

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
今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.
谷本 祥 氏 (University of Copenhagen)
On the geometry of thin exceptional sets in Manin’s conjecture
[ 講演概要 ]
Manin’s conjecture predicts the asymptotic formula for the counting function of rational points on a Fano variety X after removing the exceptional sets. The original conjecture, which removes a proper closed subset, is wrong due to covering families of subvarieties violating the compatibility of Manin’s conjecture, and its refinement, suggested by Emmanuel Peyre, removes a thin set instead of a closed set. In this talk, first I would like to explain that subvarieties which conjecturally have more points than X only form a thin set using the minimal model program and the boundedness of log Fano varieties. After that, I would like to discuss our conjecture on the birational boundedness of covers violating the compatibility of Manin’s conjecture, and present some results in dimension 2 and 3. This is joint work with Brian Lehmann.

2016年07月22日(金)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
N. Christopher Phillips 氏 (Univ. Oregon)
Radius of comparison for $C^*$ crossed products by free minimal actions of amenable groups

2016年07月19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
渡邊 陽介 氏 (University of Hawaii)
The geometry of the curve graphs and beyond (JAPANESE)
[ 講演概要 ]
The curve graphs are locally infinite. However, by using Masur-Minsky's tight geodesics, one could view them as locally finite graphs. Bell-Fujiwara used a special property of tight geodesics and showed that the asymptotic dimension of the curve graphs is finite. In this talk, I will introduce a new class of geodesics which also has the property. If time permits, I will explain how such geodesics can be adapted in Out(F_n) setting.

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 126号室
宮﨑 弘安 氏 (東京大学大学院数理科学研究科)
Cube invariance of higher Chow groups with modulus (モジュラス付き高次チャウ群のキューブ不変性)
(JAPANESE)

2016年07月13日(水)

社会数理コロキウム

17:00-18:30   数理科学研究科棟(駒場) 002号室
講演終了後2階コモンルームで情報交換会を行います。
伊東 利雄 氏 (富士通研究所)
企業での研究開発の取り組み~数学を使った情報理論、人工知能の研究紹介~ (JAPANESE)
[ 講演概要 ]
情報理論と人工知能の分野の中に、符号理論、圧縮センシング、ニューラルネットワーク
などの技術があり、ガロア体、代数曲線、確率を用いた尤度推定、多様体、L^1ノルム
正則化、微分方程式など様々な数学が用いられています。またこれらの技術はハードディスクや
携帯電話にも応用されています。本講演では、これらの技術から自分が取り組んできた研究に
ついていくつかをご紹介したいと思います。またニューラルネットワークの研究について、
脳神経科学との関わりについても少し触れてみたいと思います。
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20160713.pdf

数理人口学・数理生物学セミナー

15:00-16:00   数理科学研究科棟(駒場) 128演習室号室
Yu Min 氏 (青山学院大学理工学部)
腫瘍免疫系における時間遅れの二元的な役割 (ENGLISH)
[ 講演概要 ]
In this talk, a previous tumor immune interaction model is simplified by considering a relatively weak immune activation, which can still keep the essential dynamics properties. Since the immune activation process is not instantaneous, we incorporate one delay effect for the activation of the effector cells by helper T cells into the model. Furthermore, we investigate the stability and instability region of the tumor-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of effector cells by helper T cells and the helper T cells stimulation rate by the presence of identified tumor antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumor-presence equilibrium. Besides, our results show that the appropriate immune activation time plays a significant role in control of tumor growth.

2016年07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
同じ日の13:30--15:00, 126室で、同講師による標数0の特異点解消の講義があります. We have a complimentary lecture by Matsuki-sensei on the resolution in characteristic 0 (from 13:30-15:00 at room#126).
Kenji Matsuki 氏 (Purdue/RIMS)
Hypersurfaces of maximal contact and jumping phenomenon in the problem of resolution of singularities in positive characteristic (English)
[ 講演概要 ]
According to our approach for resolution of singularities in positive characteristic (called the Idealistic Filtration Program, alias the I.F.P.) the algorithm is divided into the following two steps:

Step 1. Reduction of the general case to the monomial case.

Step 2. Solution in the monomial case.

While we have established Step 1 in abritrary dimension, Step 2 becomes very subtle and difficult in positive characteristic. This is in clear contrast to the classical setting in characteristic zero, where the solution in the monomial case is quite easy.

The talk consists of the two parts.

・Part I [13:30--15:00]: This part is mainly for the students, who are not familiar with the classical results in characteristic zero. Through Hironaka's reformulation of the problem of resolution of singularities, we will see how the notion of a hypersurface of maximal contact provides an inductive structure on dimension to the problem, and hence leading to a solution. Since our I.F.P. is closely modelled upon the classical algorithm in characteristic zero, this part should also give some background material and motivation for our approach in positive characteristic.

in

・Part II [15:30--17:00]: This is the main body of my talk. I will proceed according to the following menu.

{\bf Framewrok of the I.F.P.}: First I will explain the framewrok of the I.F.P., which further extends Hironaka's refomulation. The biggest obstacle to establish Step 1 is the fact that, in positive characteristic, a smooth hypersurface of maximal contact does not exist in general. In order to overcome this obstacle, we introduce the notion of the Leading Generator System, which is the collection of multiple singular hypersurfaces of maximal contcat.

{\bf Monomial Case}: As metioned above, then the problem is reduced to the one in the monomial case.

・ {\bf Inductive scheme on the invariant \boldmath$\tau$}: We firstly observe that, by the inductive scheme on the invariant $\tau$, we have only to consider the case with $\tau = 1$, i.e., the case where there is only one single singular hypersurface of maximal contact.

・ {\bf Tight Monomail Case}: We secondly observe that, if we reach the so-called Tight Monomial Case, then we can easily solve the problem.

・ {\bf Introduction of the invariant `` \boldmath$\mathrm{inv}_{\mathrm{MON},real}$''}: Thus our final task is, after arriving at the monimial case with $\tau = 1$, to reach the Tight Monomial Case, which is characterized by $\mathrm{inv}_{\mathrm{MON},real} = 0$.

・ {\bf Moh-Hauser Jumping phenomenon}: The invariant $\mathrm{inv}_{\mathrm{MON},real}$ usually behaves well, i.e., decreases after each blow up. But under some circustances, it strictly increases. I will explain this well-known Moh-Jumping phenomenon by giving a simple example.

・ {\bf Eventual decrease of the jumping peaks}: At last, the problem boils down to analyzing and overcoming the Moh-Hauser Jumping phenomenon. For this purpose, we will present the conjecture of ``Eventual decrease of the jumping peaks'', which is affirmatively solved in dimension 3, and is the current focus of our research in dimension 4.
[ 講演参考URL ]
https://www.math.purdue.edu/people/bio/kmatsuki/home

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
John Parker 氏 (Durham University)
Non-arithmetic lattices (ENGLISH)
[ 講演概要 ]
In this talk I will discuss arithmetic and non-arithmetic lattices and I will give a history of the problem of finding non-arithmetic lattices. I will also briefly describe the construction of new non-arithmetic lattices in SU(2,1) found in my joint workwith Martin Deraux and Julien Paupert.

PDE実解析研究会

10:20-11:00   数理科学研究科棟(駒場) 056号室
通常の開催時間と異なります。
Piotr Rybka 氏 (University of Warsaw)
Special cases of the planar least gradient problem (English)
[ 講演概要 ]
We study the least gradient problem in two special cases:
(1) the natural boundary conditions are imposed on a part of the strictly convex domain while the Dirichlet data are given on the rest of the boundary; or
(2) the Dirichlet data are specified on the boundary of a rectangle. We show existence of solutions and study properties of solution for special cases of the data. We are particularly interested in uniqueness and continuity of solutions.

PDE実解析研究会

14:20-15:00   数理科学研究科棟(駒場) 056号室
通常の開催時間と異なります。
Amru Hussein 氏 (TU Darmstadt)
Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations (English)
[ 講演概要 ]
Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the $L^p$ theory for the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, is developed. This set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of $H^2/p$, $p$, $1 < p < \infty$, satisfying certain boundary conditions. Thus, the general $L^p$ setting admits rougher data than the usual $L^2$ theory with initial data in $H^1$.

In this study, the linearized Stokes type problem plays a prominent role, and it turns out that it can be treated efficiently using perturbation methods for $H^\infty$-calculus.

解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室
X. P. Wang 氏 (Université de Nantes, France)
Gevrey estimates of the resolvent and sub-exponential time-decay (English)
[ 講演概要 ]
For a class of non-selfadjoint Schrodinger operators satisfying some weighted coercive condition, we prove that the resolvent satisfies the Gevrey estimates at the threshold. As applications, we show that the heat and Schrodinger semigroups decay sub-exponentially in appropriately weighted spaces. We also study compactly supported perturbations of this class of operators where zero may be an embedded eigenvalue.

PDE実解析研究会

12:10-12:50   数理科学研究科棟(駒場) 056号室
通常の開催時間と異なります。
Elio Espejo 氏 (National University of Colombia)
The role of convection in some Keller-Segel models (English)
[ 講演概要 ]
An interesting problem in reaction-diffusion equations is the understanding of the role of convection in phenomena like blow-up or convergence. I will discuss this problem through some Keller-Segel type models arising in mathematical biology and show some recent results.

PDE実解析研究会

11:20-12:00   数理科学研究科棟(駒場) 056号室
通常の開催時間と異なります。
Monika Muszkieta 氏 (Wroclaw University of Science and Technology)
The total variation flow in $H^{−s}$ (English)
[ 講演概要 ]
In the talk, we consider the total variation flow in the Sobolev space $H^{−s}$. We explain the motivation to study this problem in the context of image processing applications and provide its rigorous interpretation under periodic boundary conditions. Furthermore, we introduce a numerical scheme for an approximate solution to this flow which has been derived based on the primal-dual approach and discuses some issues concerning its convergence. We also show and compare results of numerical experiments obtained by application of this scheme for a simple initial data and different values of the index $s$.
This is a join work with Y. Giga.

2016年07月11日(月)

東京確率論セミナー

15:00-18:20   数理科学研究科棟(駒場) 128号室
時間がいつもと異なります.ご注意ください(この日は2つ講演があります).
Jin Feng 氏 (University of Kansas) 15:00-16:30
An introduction to Hamilton-Jacobi equation in the space of probability measures (English)
[ 講演概要 ]
I will discuss Hamilton-Jacobi equation in the space of probability measures.

Two types of applications motivate the issue: one is from the probabilistic large deviation study of weakly interacting particle systems in statistical mechanics, another is from an infinite particle version of the variational formulation of Newtonian mechanics.

In creating respective well-posedness theories, two mathematical observations played important roles: One, the free-particle flow picture naturally leads to the use of the optimal mass transportation calculus. Two, there is a hidden symmetry (particle permutation invariance) for elements in the space of probability measures. In fact, the space of probability measures in this context is best viewed as an infinite dimensional quotient space. Using a natural metric, we are lead to some fine aspects of the optimal transportation calculus that connect with the metric space analysis and probability.

Time permitting, I will discuss an open issue coming up from the study of the Gibbs-Non-Gibbs transitioning by the Dutch probability community.

The talk is based on my past works with the following collaborators: Markos Katsoulakis, Tom Kurtz, Truyen Nguyen, Andrzej Swiech and Luigi Ambrosio.
上山 大信 氏 (明治大学大学院先端数理科学研究科) 16:50-18:20
ある化学反応系のモデリングとそのシミュレーション解析

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
増本周平 氏 (東大数理)
Fraïssé Theory and Jiang-Su algebra

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
藤原宏志 氏 (京都大学大学院情報学研究科)
Towards fast and reliable numerical computations of the stationary radiative transport equation (日本語)
[ 講演概要 ]
The radiative transport equation (RTE) is a mathematical model of near-infrared light propagation in human tissue, and its analysis is required to develop a new noninvasive monitoring method of our body or brain activities. Since stationary RTE describes light intensity depending on a position and a direction, a discretization model of 3D-RTE is essentially a five dimensional problem. Therefore to establish a reliable and practical numerical method, both theoretical numerical analysis and computing techniques are required.

We firstly introduce huge-scale computation examples of RTE with bio-optical data. A high-accurate numerical cubature on the unit sphere and a hybrid parallel computing technique using GPGPU realize fast computation. Secondly we propose a semi-discrete upwind finite volume method to RTE. We also show its error estimate in two dimensions.

This talk is based on joint works with Prof. Y.Iso, Prof. N.Higashimori, and Prof. N.Oishi (Kyoto University).

2016年07月05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
Dulip Piyaratne 氏 (IPMU)
Generalized Bogomolov-Gieseker type inequality for Fano 3-folds (English)
[ 講演概要 ]
Construction of Bridgeland stability conditions on a given smooth projective 3-fold is an important problem. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for Fano 3-folds of Picard rank one due to the works of Macri, Schmidt and Li. However, Schmidt gave a counter-example for a Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality for general Fano 3-folds and why it holds.

Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 128号室
服部 俊昭 氏 (東工大・理・数学)
清水の補題の一般化について
[ 講演概要 ]
SL(n,C)のあるタイプの冪等元を含む部分群が離散部分群になるための必要条件を与える不等式が、n=2の場合(もともとの清水の補題の場合に相当)を拡張する形で得られることと、対応する対称空間へのその群の作用が不等式によって影響を受けることについて去年7月のこのセミナーでお話しいたしました。これはその後の進展の報告です。

2016年07月04日(月)

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
難波 隆弥 氏 (岡山大学大学院自然科学研究科)
Central limit theorems for non-symmetric random walks on nilpotent covering graphs
[ 講演概要 ]
ベキ零群を被覆変換群とするような有限グラフの被覆グラフのことをベキ零被覆グラフと呼ぶ。結晶格子(特に被覆変換群がアーベル群の場合)上のランダムウォークに関してはすでに様々なアプローチが図られ多くの結果が得られている。ベキ零被覆グラフ上のランダムウォークについては、対称な場合に幾つかの極限定理が知られているものの、非対称な場合にはあまり研究が進展していないように思われる。本講演では、ベキ零被覆グラフ上の非対称ランダムウォークを考察し、ある条件下で汎関数中心極限定理が成り立つことを報告する。本講演の内容は、石渡聡氏(山形大)および河備浩司氏(岡山大)との共同研究に基づく。

2016年06月28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
見村 万佐人 氏 (東北大学)
Strong algebraization of fixed point properties (JAPANESE)
[ 講演概要 ]
バナッハ空間(ないしは族)を固定したとき,有限生成群のそれ上の等長作用が常に大域的固定点を持つ,という性質を固定点性質と呼ぶ.ヒルベルト空間全体のなす族を考えたときの固定点性質は,「Kazhdan の性質(T)」と呼ばれる群の剛性と同値であることが知られている.

離散群の線型表現の分類は連続群と違い,群が少しでも複雑になると手に負えない.これが原因で,離散群の固定点性質を直接示すことは当面の間著しく困難であった.Y. Shalom は1999年の論文(Publ. IHES)で,固定点性質を部分群に分けて,最後に“パッチワーク”する,という手法を応用し,上の困難に対し初のブレイクスルーをもたらした.しかし,Shalomのパッチワーク戦略では群の部分群による「有界生成(Bounded Generation)」という厄介な要請が本質的であって(後述するように実はこれは気のせいだったのだが,長年そう信じられてきたように講演者には思われる),この要請がShalomの手法を適用する際の致命的な弱点となっていた.

今回,講演者はShalomのパッチワーク(1999,2006)の思想を発展させて,「有界生成」条件を舞台から追いやることに成功した.講演者の条件は,
部分群たちを広げていくある“ゲーム”の必勝戦略として記述される.講演ではこの“ゲーム”の内容・証明のあらすじをお話したい.これにより,
「有界生成」の成立がわからないような状況でもパッチワーク戦略を適用できうるようになった.系として,いろいろな離散群が強い固定点性質をもつことを示せ,しかも証明も非常にコンセプチュアルである.こうした応用面についても概観したい.

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