(Updated, December 2, 2016)
火曜日16:50 -- 18:20, 於: 東京大学大学院数理科学研究科棟(駒場)
1階126号室
幹事: 片岡清臣 , 俣野博
Tel & FAX 03-5465-7029 (K. KATAOKA), 03-5465-7037（H. MATANO）
世話人: 片岡清臣，俣野 博，中村 周，儀我 美一
注意：2015年4月から部屋が１２６に変わっています！ また時間も後ろに２０分ずれました！
(代数解析関係は2004年度より代数解析火曜セミナーとしてこれとは別になりました．ただし時間帯・部屋は共用し原則的に交代で開催します．)
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東京大学解析学公開講座１９９７,東京大学解析学公開講座2001(updated
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2016年12月13日（火）:16:50-18:20 at 126
講師: Hans Christianson 氏 （ノースキャロライナ大学、アメリカ合衆国）
題目: Distribution of eigenfunction mass on some really simple domains
Abstract: Eigenfunctions are fundamental objects of study in spectral geometry and quantum chaos. On a domain or manifold, they determine the behaviour of solutions to many evolution type equations using, for example, separation of variables. Eigenfunctions are very sensitive to background geometry, so it is important to understand what the eigenfunctions look like: where are they large and where are they small? There are many different ways to measure what "large" and "small" mean. One can consider local $L^2$ distribution, local and global $L^p$ distribution, as well as restrictions and boundary values. I will give an overview of what is known, and then discuss some very recent works in progress demonstrating that complicated things can happen even in very simple geometric settings.
2016年12月6日（火）:16:50-18:20 at 126
講師: Horia Cornean 氏 （オールボー大学、デンマーク）
題目: On the trivialization of Bloch bundles and the construction of localized Wannier functions
Abstract: We shall present an introductory lecture on the trivialization of Bloch bundles and its
physical implications. Simply stated, the main question we want to answer is the following:
given a rank $N＼geq 1$ family of orthogonal projections $P(k)$ where $k＼in ＼mathbb{R}^d$,
$P(＼cdot)$ is smooth and $＼mathbb{Z}^d$-periodic, is it possible to construct an orthonormal
basis of its range which consists of vectors which are both smooth and periodic in $k$?
We shall explain in detail the connection with solid state physics.
This is joint work with I. Herbst and G. Nenciu.
2016年11月29日（火）:16:50-18:20 at 126
講師: 庄司 直高 氏（筑波大学D3）
題目: Interior transmission eigenvalue problems on manifolds
2016年10月25日（火）:16:50-18:20 at 126
講師: 山根 英司 氏（関西学院大学 数理科学科）
題目: 可積分離散非線型シュレーディンガー方程式の漸近解析
2016年7月12日（火）:16:50-18:20 at 126
講師: X. P. Wang 氏（フランス・ナント大学）
題目: Gevrey estimates of the resolvent and sub-exponential time-decay
Abstract: 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.
2016年6月28日（火）:16:50-18:20 at 126
講師: G. Raikov 氏（チリ・カトリカ大学）
題目: Discrete spectrum of Schr＼"odinger operators with oscillating decaying potentials
Abstract: I will consider the Schr＼"odinger operator $H_{＼eta W} =
-＼Delta + ＼eta W$, self-adjoint in $L^2(＼re^d)$, $d ＼geq 1$. Here $＼eta$
is a non constant almost periodic function, while $W$ decays slowly
and regularly at infinity. I will discuss the asymptotic behaviour of the
discrete spectrum of $H_{＼eta W}$ near the origin. Due to the
irregular decay of $＼eta W$, there exist some non semiclassical
phenomena; in particular, $H_{＼eta W}$ has less eigenvalues than
suggested by the semiclassical intuition.
2016年6月21日（火）:16:50-18:20 at 126
講師: 廣川 真男 氏（広島大学大学院工学研究院）
題目: 量子 Rabi 模型に対する Hepp-Lieb-Preparata 量子相転移について
Abstract: 本講演では、量子相転移の観点から、量子 Rabi 模型を考察する。Preparata は Hepp-Lieb 量子相転移の
数学的構造に基づき、物質と光の相互作用が強くなると、物質・光相互作用系の基底状態が、量子状態の緩和で
本来放射すべき光子を纏い始め非摂動論的になることを主張した (Hepp-Lieb-Preparata 量子相転移)。
最近、情報通信研究機構の吉原らの回路量子電磁気学の実験で、Hepp-Lieb-Preparata 量子相転移を期待させる
結果が得られた。そこで、所謂、A2 項 (光の場の2乗の項) の問題を含め、吉原らが実験で扱った量子 Rabi 模型を
Hepp-Lieb-Preparata 量子相転移の観点から数理物理学的考察を行う。
2016年6月14日（火）:16:50-18:20 at 126
講師: 新國 裕昭 氏 (前橋工科大学)
題目: Schr¥"odinger operators on a periodically broken zigzag carbon nanotube
2016年4月26日（火）:16:50-18:20 at 126
講師: 松原 宰栄 氏 (東大数理)
題目: On microlocal analysis of Gauss-Manin connections for boundary singularities
2016年4月12日（火）:16:50-18:20 at 126
講師: Jussi Behrndt 氏（Graz工科大学, Austria）
題目: Scattering matrices and Dirichlet-to-Neumann maps
Abstract: In this talk we discuss a recent result on the representation of the
scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be
applied to scattering problems for Schrödinger operators with $＼delta$-type
interactions on curves and hypersurfaces, and scattering problems involving Neumann and
Robin realizations of Schrödinger operators on unbounded domains. In both
applications we obtain formulas for the corresponding scattering matrices in
terms of Dirichlet-to-Neumann maps. This talk is based on joint work with
Mark Malamud and Hagen Neidhardt.
2016年1月5日（火）:16:50-18:20 at 126
講師: Eric Skibsted 氏 (Aarhus University, Denmark)
題目: Stationary scattering theory on manifolds
Abstract: We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).
2015年12月1日（火）:16:50-18:20 at 126
講師: Stéphane Malek 氏 (Université de Lille, France )
題目: On complex singularity analysis for some linear partial differential equations
Abstract: We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables
whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
2015年11月24日（火）:16:50-18:20 at 126
講師: 許 本源 氏 ( 東大数理)
題目: A local analysis of the swirling flow to the axi-symmetric
Navier-Stokes equations near a saddle point and no-slip flat boundary
Abstract: As one of the violent flow, tornadoes occur in many place of the world.
In order to reduce human losses and material damage caused by tornadoes,
there are many research methods. One of the effective methods is
numerical simulations. The swirling structure is significant both in
mathematical analysis and the numerical simulations of tornado.
In this joint work with H. Notsu and T. Yoneda we try to clarify the
swirling structure. More precisely, we do numerical computations on axi-
symmetric Navier-Stokes flows with no-slip flat boundary. We compare a
hyperbolic flow with swirl and one without swirl and observe that the
following phenomenons occur only in the swirl case:
The distance between the point providing the maximum velocity
magnitude $|v|$ and the $z$-axis is drastically changing around some
time (which we call it turning point). An ``increasing velocity phenomenon''
occurs near the boundary and the maximum value of $|v|$ is obtained near
the axis of symmetry and the boundary when time is close to the turning
point.
2015年10月20日（火）:16:50-18:20 at 128 （いつもの126と違います）
講師: Danielle Hilhorst 氏 ( CNRS / University of Paris-Sud)
題目: Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term
Abstract:We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
FMSP lecture
2015年10月15日（木）:15:00～18:00 at 126
講師: David Sauzin 氏 (CNRS, France)
題目: Introduction to 1-summability and resurgence
Abstract : The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.
2015年10月13日（火）:16:50-18:20
講師: David Sauzin 氏 (CNRS, France)
題目: Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto)
Abstract: We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.
なお関連したFMSP lecture を上の通り15日に予定しています．
2015年9月29日（火）:16:50-18:20
講師: Otto Liess 氏 (University of Bologna, Italy)
題目: On the Phragmén-Lindelöf principle for holomorphic functions and factor classes
of higher order complex forms in several complex variables
Abstract:In this talk we will discuss maximum principles in unbounded domains
in one or several complex variables. We will mainly be interested in these principles for
plurisubharmonic (in the one-dimensional case, "subharmonic")
or holomorphic functions, when the principles are of
Phragmen-Lindel{＼"o}f principle (henceforth called "PL") type. It will
turn out that for 2 or more complex variables it will be useful to
study our principles together with associated principles for
factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of
functions. We consider then an open set U in C^n in one or several
complex variables. We assume that we are given two real-valued
continuous functions f and g on U. We say that PL holds for
plurisubharmonic (respectively for holomorphic) functions,
if the following implication is true for every plurisubharmonic
function $ ＼rho $ (respectively for every $ ＼rho $ of form
log |h| with h holomorphic) on U:
if we know that $ ＼rho ＼leq f$ on the boundary of U and if
$ (＼rho - f)$ is bounded on U, then it must follow that
$ ＼rho ＼leq g$ on U. ($＼rho ＼leq f$ on the boundary has the following
meaning: for ever z in the boundary of U and for every sequence of points
y_j in U which tends to z, we have limsup (＼rho - f)(y_j) leq 0.)
A trivial condition under which PL is true, is when there exists a
plurisubharmonic function u on U such that
(*) -g(z) ＼leq u(z) ＼leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical
maximal principle for unbounded domains to the function $ ＼rho'= ＼rho
+u$ to obtain at first $ ＼rho' ＼leq 0$ and then $ ＼rho ＼leq - u ＼leq g$.
It is one of the main goals of the talk to explain how far (*) is from
being also a necessary condition for PL.
Some examples are intended to justify our approach and
applications will be given to problems in convex analysis.
2015年9月8日（火）:16:50-18:20
講師: 水谷 治哉 氏（大阪大学）
題目: 長距離型斥力ポテンシャルを持つシュレディンガー方程式の時間大域的ストリッカーツ評価
Abstract: We will discuss a resent result on global-in-time Strichartz estimates
for Schr＼"odinger equations with slowly decreasing repulsive potentials.
If the potential is of very short-range type, there is a simple method due to
Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case.
The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet.
In particular, we employ both Morawetz type estimates and the methods of microlocal
analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.
2015年7月21日（火）:16:30-18:00
講師: 蘆田 聡平 氏 (京都大学理学研究科)
題目: Born-Oppenheimer approximation for an atom in constant magnetic fields
Abstract: We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.
2015年7月14日（火）:16:30-17:30
講師: Li Yutian 氏 (Hong Kong Baptist Univ.)
題目: Small-time Asymptotics for Subelliptic Heat Kernels
Abstract: Subelliptic operators are the natural generalizations of the Laplace-
Beltrami operators, and they play important roles in geometry, several
complex variables, probability and physics. As in the classical spectral
theory for the elliptic operators, some geometrical properties of the
induced subRiemannian geometry can be extracted from the analysis
of the heat kernels for subelliptic operators. In this talk we shall
review the recent progress in the heat kernel asymptotics for subelliptic
operators. We concentrate on the small-time asymptotics of the heat
kernel on the diagonal, or equivalently, the asymptotics for the trace.
Our interest is to find the exact form of the leading term, and this will
lead to a Weyl’s asymptotic formula for the subelliptic operators.
This is a joint work with Professor Der-Chen Chang.
2015年5月12日（火）:16:30-18:00
講師: 高棹 圭介 氏 （東大数理）
題目: Brakkeの平均曲率流に対する制約条件付きAllen-Cahn方程式の収束について
(Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow)
Abstract: In this talk we consider the Allen-Cahn equation with constraint. In
1994, Chen and Elliott studied the asymptotic behavior of the solution
of the Allen-Cahn equation with constraint. They proved that the zero
level set of the solution converges to the classical solution of the
mean curvature flow under the suitable conditions on initial data. In
1993, Ilmanen proved the existence of the mean curvature flow via the
Allen-Cahn equation without constraint in the sense of Brakke. We proved
the same conclusion for the Allen-Cahn equation with constraint.
2015年4月21日（火）:16:30-18:00
講師: 松原 宰栄 氏 （東大数理）
題目: 留数カレントと定数係数線形遅延微分方程式系の一般論について
Abstract: We introduce the ring of differential operators with constant
coefficients and commensurate time lags (we use the terminology D$＼Delta$
operators from now) initially defined by H. Gl＼"using-L＼"ur＼ss en for
ordinary $D＼Delta$ operators and observe that various function modules
enjoy good cohomological properties over this ring. %After revising the
notion of the residue current in the spirit of M. Andersson and E.
Wulcan, we introduce the multidimensional version of the ring D$＼Delta$
operators.
Combining this ring theoretic observation with the integral
representation technique developed by M. Andersson, we solve a certain
type of division with bounds. In the last chapter, we prove the
injectivity property of various function modules over this ring as well
as spectral synthesis type theorems for $D＼Delta$ equations.
2014年12月16日（火）:16:30-18:00
講師: 水谷 治哉 氏（大阪大学・理学研究科）
題目: Global Strichartz estimates for Schr＼”odinger equations on
asymptotically conic manifolds
2014年12月2日（火）:16:30-18:00
講師: Xavier Cabre 氏（ICREA and UPC, Barcelona）
題目: New isoperimetric inequalities with densities
arising in reaction-diffusion problems
Abstract: In joint works with X. Ros-Oton and J. Serra, the study of the
regularity of stable solutions to reaction-diffusion problems
has led us to certain Sobolev and isoperimetric inequalities
with weights. We will present our results in these new
isoperimetric inequalities with the best constant, that we
establish via the ABP method. More precisely, we obtain
a new family of sharp isoperimetric inequalities with weights
(or densities) in open convex cones of R^n. Our results apply
to all nonnegative homogeneous weights satisfying a concavity
condition in the cone. Surprisingly, even that our weights are
not radially symmetric, Euclidean balls centered at the origin
(intersected with the cone) minimize the weighted isoperimetric
quotient. As a particular case of our results, we provide with
new proofs of classical results such as the Wulff inequality and
the isoperimetric inequality in convex cones of Lions and Pacella.
Furthermore, we also study the anisotropic isoperimetric problem
for the same class of weights and we prove that the Wulff shape
always minimizes the anisotropic weighted perimeter under the
weighted volume constraint.
2014年11月25日（火）:16:30-18:00
講師: 伊藤 健一 氏（神戸大・理学研究科）
題目: Stationary scattering theory on manifold with ends
2014年9月9日（火）:16:30-18:00
講師: Hatem Zaag 氏（CNRS / University of Paris Nord）
題目: Energy methods and blow-up rate for semilinear wave equations
in the superconformal case
Abstract: In a series of papers with Mohamed Ali Hamza (University of Tunis-el
Manar), we consider the semilinear wave equations with power
nonlinearity.
In the subconformal and the conformal case, we consider perturbations
with lower order terms and modify the Lyapunov functional Antonini and
Merle designed for the unperturbed case. We also find a blow-up
criterion for the equation. As a consequence, we bound the Lyapunov
functional. Thanks to interpolations in Sobolev spaces and a
Gagliardo-Nirenberg inequality, we bound the solution in the
self-similar variable, which gives a sharp bound on the blow-up rate.
Surprisingly, our approach works in the superconformal case (still
Sobolev subcritical), leading to a new bound on the blow-up rate,
which improves the bound of Killip, Stoval and Visan.
2014年6月10日（火）:16:30-18:00
講師: 阿部 健 氏（名古屋大）
題目: On estimates for the Stokes flow in a space of bounded functions
Abstract: The Stokes equations are well understood on $L^p$ space for
various kinds of domains such as bounded or exterior domains, and fundamental
to study the nonlinear Navier-Stokes equations. The situation is different for the
case $p=＼infty$ since in this case the Helmholtz projection does not act as a
bounded operator anymore. In this talk, we show some a priori estimate for a
composition operator of the Stokes semigroup and the Helmholtz projection
on a space of bounded functions.
2014年5月27日（火）:16:30-18:00
講師: 宮崎 洋一 氏 （日本大学歯学部）
題目: 楕円型方程式の正則性定理と領域の滑らかさ
(The regularity theorem for elliptic equations and the smoothness of domains)
Abstract: We consider the Dirichlet boundary problem for a strongly elliptic
operator of order $2m$ with non-smooth coefficients, and prove the regularity
theorem for $L_p$-based Sobolev spaces when the domain has a boundary of
limited smoothness. Compared to the known results, we can weaken the
smoothness assumption on the boundary by $m-1$.
2014年5月13日（火）:16:30-18:00
講師: 岡田 靖則 氏 （千葉大学大学院理学研究科）
題目: Ultra-differentiable classes and intersection theorems
Abstract: There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).
2014年4月22日（火）:16:30-18:00
講師: 筒井 容平 氏 （東大数理）
題目: Bounded small solutions to a chemotaxis system with
non-diffusive chemical
(拡散性を有しない誘因因子に対する走化性方程式の小さな有界な解)
Abstract: We consider a chemotaxis system with a logarithmic
sensitivity
and a non-diffusive chemical substance. For some chemotactic
sensitivity
constants, Ahn and Kang proved the existence of bounded
global solutions
to the system. An entropy functional was used in their
argument to control
the cell density by the density of the chemical
substance. Our purpose is to
show the existence of bounded global
solutions for all the chemotactic
sensitivity constants. Assuming the
smallness on the initial data in some
sense, we can get uniform
estimates for time. These estimates are used to
extend local solutions.
This talk is partially based on joint work with Yoshie
Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel＼'azquez (Univ. of Bonn).
2014年1月28日（火）:16:30-18:00 (東大数理GCOE seminarと共催)
講師: Arnaud Ducrot 氏 （University of Bordeaux）
題目: Asymptotic behaviour of a non-local diffusive logistic equation
Abstract: In this talk we investigate the long time behaviour of a logistic
type equation modelling the motion of cells. The equation we consider
takes into account birth and death process using a simple logistic effect
as well as a non-local motion of cells using non-local Darcy’s law with
regular kernel. Using the periodic framework we first investigate the
well-posedness of the problem before deriving some information about
its long time behaviour. The lack of asymptotic compactness of the
system is overcome by making use of Young measure theory. This
allows us to conclude that the semiflow converges for the Young
measure topology.
2014年1月21日（火）:16:30-18:00
講師: 浜向 直 氏 （東大数理）
題目: An improved level set method based on comparison with a signed distance function
Abstract: In the classical level set method, a slope of a solution to level set
equations can be close to zero as time develops even if the initial
slope is large, and this prevents one from computing interfaces given as
the level set of the solution. To overcome this issue we introduce an
improved equation by adding an extra term to the original equation.
Then, by applying a comparison principle to the signed distance function
to the interface, we prove that, globally in time, the slope of a
solution of the initial value problem is preserved near the zero level set.
2014年1月14日（火）:16:30-18:00
講師: 伊藤 健一 氏 （筑波大学）
題目: Threshold properties for one-dimensional discrete Schr\"odinger operators
Abstract: We study the relation between the generalized eigenspace and the asymptotic
expansion of the resolvent around the threshold $0$ for the one-dimensional discrete
Schr\"odinger operator on $\mathbb Z$. We decompose the generalized eigenspace
into the subspaces corresponding to the eigenstates and the resonance states only by
their asymptotics at infinity, and classify the coefficient operators of the singlar part of
resolvent expansion completely in terms of these eigenspaces. Here the generalized
eigenspace we consider is largest possible. For an explicit computation of the resolvent
expansion we apply the expansion scheme of Jensen-Nenciu (2001). This talk is based
on the recent joint work with Arne Jensen (Aalborg University).
2013年12月17日（火）:16:30-18:00
講師: Fabricio Macia 氏 （マドリッド工科大学）
題目: Dispersion and observability for completely integrable Schrödinger flows
Abstract: I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger
equations that are obtained as the quantization of a completely integrable Hamiltonian system.
The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus.
Our results are obtained through a detailed analysis of semiclassical measures corresponding to
sequences of solutions, which is performed using a two-microlocal approach.
This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.
2013年12月10日（火）:16:30-18:00
講師: Abel Klein 氏 (UC Irvine)
題目: Quantitative unique continuation principle, local behavior of solutions,
and bounds on the density of states for Schr\"odinger operators
Abstract: We establish bounds on the density of states measure for Schr\"odinger operators. These are deterministic
results that do not require the existence of the density of states measure, or, equivalently, of the integrated
density of states. The results are stated in terms of a ``density of states outer-measure'' that always exists,
and provides an upper bound for the density of states measure when it exists. We prove log-H\"older continuity
for this density of states outer-measure in one, two, and three dimensions for Schr\"odinger operators, and in
any dimension for discrete Schr\"odinger operators. Our proofs use a quantitative unique continuation principle
and the local behavior of approximate solutions of the stationary Schr\"odinger equation.
(Joint work with Jean Bourgain.)
References: Jean Bourgain and Abel Klein: Bounds on the density of states for
Schr\"odinger operators. Invent. Math. 194, 41-72 (2013).
2013年11月26日（火）:16:30-18:00
講師: 水谷 治哉 氏 (学習院大)
題目: Global Strichartz estimates for Schr\"odinger equations with long range metrics
Abstract: We consider Schr\"odinger equations on the asymptotically Euclidean space
with the long-range condition on the metric.
We show that if the high energy resolvent has at most polynomial growth with respect to the energy,
then global-in-time Strichartz estimates, outside a large compact set, hold.
Under the non-trapping condition we also discuss global-in-space Strichartz estimates.
This talk is based on a joint work with J.-M. Bouclet (Toulouse University).
2013年11月19日（火）:16:30-18:00
講師: Alexander Pushnitski 氏 (ロンドン大学キングスカレッジ)
題目: Inverse spectral problem for positive Hankel operators
Abstract: Hankel operators are given by (infinite) matrices with entries
$a_{n+m}$ in $\ell^2$. We consider inverse spectral problem
for bounded self-adjoint positive Hankel operators.
A famous theorem due to Megretskii, Peller and Treil asserts
that such operators may have any continuous spectrum of
multiplicity one or two and any set of eigenvalues of multiplicity
one. However, more detailed questions of inverse spectral
problem, such as the description of isospectral sets, have never
been addressed. In this talk I will describe in detail the
direct and inverse spectral problem for a particular sub-class
of positive Hankel operators. The talk is based on joint work
with Patrick Gerard (Paris, Orsay).
2013年7月9日（火）:16:30-18:00（この日のみ数理棟１１８号室です．）
講師: Tom\'as Lungenstrass 氏 (Pontificia Universidad Catolica de Chile)
題目: A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
(Joint work with Georgi Raikov)
Abstract:The Landau Hamiltonian describes the dynamics of a two-dimensional
charged particle subject to a constant magnetic field. Its spectrum
consists in eigenvalues of infinite multiplicity given by $B(2q+1)$, $q\in Z_+$. We
consider perturbations of this operator by including a continuous
electric potential that decays slowly at infinity (as $|x|^{-\rho}$, $0<\rho<1$).
The spectrum of the perturbed operator consists of eigenvalue clusters
which accumulate to the Landau levels. We provide estimates for the
rate at which the clusters shrink as we move up the energy levels.
Further, we obtain an explicit description of the asymptotic density
of eigenvalues for asymptotically homogeneous long-range potentials in
terms of a mean-value transform of the associated homogeneous
function.
2013年5月21日（火）:16:30-18:00
講師: 上坂 正晃 氏 (東大数理)
題目: Homogenization in a Thin Layer with an Oscillating Interface and Highly Contrast Coefficients
Abstract: We consider the homogenization problem of the elliptic boundary value problem in a thin domain which has a high and low conductivity zones. In our model, two media
are separated by a highly oscillating interface. The asymptotic behavior is governed by the order of the thickness of the domain, oscillation period of the interface and contrast between two media. In this talk, we show that the limit problem is changed by these parameters. We also introduce the two-scale convergence result in a thin domain which is the key ingredient of the proof.
2012年12月4日（火）:16:30-18:30
1. 講師: Alexander Vasiliev 氏 (Department of Mathematics, University
of Bergen, Norway)
題目: Evolution of smooth shapes and the KP hierarchy
2. 講師: Irina Markina 氏 (Department of Mathematics, University
of Bergen, Norway)
題目: Group of diffeomorphisms of the unit circle and sub-Riemannian
geometry
Abstract1: We consider a homotopic evolution in the space
of smooth
shapes starting from the unit circle. Based on the Loewner-Kufarev
equation we give a Hamiltonian formulation of this evolution and
provide conservation laws. The symmetries of the evolution are
given
by the Virasoro algebra. The 'positive' Virasoro generators span
the
holomorphic part of the complexified vector bundle over the space
of
conformal embeddings of the unit disk into the complex plane and
smooth on the boundary. In the covariant formulation they are
conserved along the Hamiltonian flow. The 'negative' Virasoro
generators can be recovered by an iterative method making use
of the
canonical Poisson structure. We study an embedding of the
Loewner-Kufarev trajectories into the Segal-Wilson Grassmannian,
construct the tau-function, the Baker-Akhiezer function, and finally,
give a class of solutions to the KP hierarchy, which are invariant
on
Loewner-Kufarev trajectories.
Abstract2: We consider the group of sense-preserving diffeomorphisms
of the unit
circle and its central extension - the Virasoro-Bott group as
sub-Riemannian manifolds. Shortly, a sub-Riemannian manifold is
a
smooth manifold M with a given sub-bundle D of the tangent bundle,
and
with a metric defined on the sub-bundle D. The different sub-bundles
on considered groups are related to some spaces of normalized
univalent functions. We present formulas for geodesics for different
choices of metrics. The geodesic equations are generalizations
of
Camassa-Holm, Huter-Saxton, KdV, and other known non-linear PDEs.
We
show that any two points in these groups can be connected by a
curve
tangent to the chosen sub-bundle. We also discuss the similarities
and
peculiarities of the structure of sub-Riemannian geodesics on
infinite
and finite dimensional manifolds.
2012年11月6日（火）:16:30-18:00
講師: Thierry Ramond 氏 (Univ. Paris, Orsay)
題目: Resonance free domains for homoclinic orbits
2012年10月30日（火）:16:30-18:00
講師: Francis Nier 氏 (Univ. Rennes 1)
題目: About the method of characteristics
Abstract: While studying the mean field dynamics of a systems
of bosons,
one is led to solve a transport equation for a probability measure
in an infinite
dimensional phase-space. Since those probability measures are
characterized
after testing with cylindrical or polynomial observables, which
make classes
which are not invariant after composing with a nonlinear flow.
Thus the standard
method of characteristics for transport equations cannot be extended
at once
to the infinite dimensional case. A solution comes from techniques
developed
for optimal transport and a probabilistic interpretation of trajectories.
2012年10月23日（火）:16:30-18:00 この日のみ(駒場) 1階002号室
講師: Elliott Lieb 氏 (Princeton Univ.)
題目: Topics in quantum entropy and entanglement
Abstract: Several recent results on quantum entropy and the uncertainty
principle will be discussed. This is partly joint work with Eric
Carlen
on lower bounds for entanglement, which has no classical analog,
in terms
of the negative of the conditional entropy, S1 - S12, whose negativity,
when it occurs, also has no classical analog. (see arXiv:1203.4719)
It is also partly joint work with Rupert Frank on the uncertaintly
principle for quantum entropy which compares the quantum von
Neumann
entropy with the classical entropies with respect to two different
bases. We prove an extension to the product of two and three spaces,
which
has applications in quantum information theory. (see arxiv:1204.0825)
2012年7月17日（火）:16:30-18:00
講師: 菅 徹 氏（東北大学）
題目: 2次元円環領域におけるLiouville-Gel'fand方程式の非球対称解の構造
Abstract: 指数関数を非線形項に持つ非線形楕円型方程式（Liouville-Gel'fand方程式）
について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解
から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関
して得られた結果を紹介する。
2012年7月10日（火）:16:30-18:00
講師: 牛越 惠理佳 氏（東北大学）
題目: Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition
Abstract: 本講演では、遅い非圧縮粘性流体の運動を記述したStokes
方程式におけるHadamard変分公式の導出について考察する。ここで、
Hadamard変分公式とは、1908年にHadamardによって提唱された、
領域にある摂動をさせた時に、Green函数に代表される領域に依存す
る函数が、どのような摂動をするのかを表現したものである。
変分公式は、領域摂動に伴う固有値の漸近挙動を明示的に表現した
Weylの漸近公式と関連があるなど、領域摂動問題において大変有用な
ものとして導出されてきた。本講演において、まずは導入として、楕円
型方程式で最も基本的なラプラス方程式のDirichlet問題に対する変分公
式について言及し、その後に主結果であるStokes方程式における
Hadamard変分公式について述べる。
2012年6月26日（火）:16:30-18:00
講師: 伊藤 健一 氏（筑波大学）
題目: Absence of embedded eigenvalues for the Schr\"odinger
operator on manifold with ends
Abstract: We consider a Riemannian manifold with, at least, one
expanding end, and prove the absence of $L^2$-eigenvalues for
the Schr\"odinger operator above some critical value. The
critical
value is computed from the volume growth rate of the end and the
potential behavior at infinity. The end structure is formulated
abstractly in terms of some convex function, and the examples
include asymptotically Euclidean and hyperbolic ends. The proof
consists of a priori superexponential decay estimate for eigenfunctions
and the absence of superexponentially decaying eigenfunctions,
both of which employs the Mourre-type commutator argument. This
talk
is based on the recent joint work with E.Skibsted (Aarhus University).
2012年5月22日（火）:16:30-18:00 at 118*
講師: Norbert Pozar 氏 （東大数理）
題目:Viscosity solutions for nonlinear elliptic-parabolic problems
Abstract: ﾊWe introduce a notion of viscosity solutions for a
general class of
elliptic-parabolic phase transition problems. These include the
Richards equation, which is a classical model in filtration theory.
Existence and uniqueness results are proved via the comparison
principle. In particular, we show existence and stability properties
of maximal and minimal viscosity solutions for a general class
of
initial data. These results are new even in the linear case, where
we
also show that viscosity solutions coincide with the regular weak
solutions introduced in [Alt&Luckhaus 1983]. This talk is
based on a
recent work with Inwon Kim.
(この日だけ部屋が１１８になります．お間違えのないように！)
2012年5月15日（火）:16:30-18:00
講師: 水谷 治哉 氏（京都大学・数理解析研究所）
題目: Strichartz estimates for Schr\"odinger equations with
variable
coefficients and unbounded electromagnetic potentials
Abstract:In this talk we consider the Cauchy problem for Schr\"odinger
equations with variable coefficients and unbounded potentials.
Under the
assumption that the Hamiltonian is a long-range perturbation of
the free
Schr\"odinger operator, we construct an outgoing parametrix
for the
propagator near infinity, and give applications to sharp Strichartz
estimates.
The basic idea is to combine the standard approximation by using
a time
dependent modifier, which is not in the semiclassical regime,
with the
semiclassical approximation of Isozaki-Kitada type. We also show
near
sharp Strichartz estimates without asymptotic conditions by using
local
smoothing effects.
2012年2月14日（火）:16:30-18:00
講師: Michael Loss 氏 （Georgia Institute of Technology）
題目: Symmetry results
for Caffarelli-Kohn-Nirenberg inequalities
2012年1月31日（火）:16:30-18:00
講師: Michel Chipot 氏 (University of Zurich)
題目: Obstacle problems in unbounded domains
Abstract:We will present a formulation of obstacle problems in
unbounded
domains when the energy method does not work, i.e. whenthe force
does
not belong to ﾊH^{-1}.
2011年12月20日（火）:16:30-18:00
講師: Gueorgui Raykov 氏 （チリ・カソリック大学）
題目: A trace formula for the perturbed Landau Hamiltonian
Abstract: The talk will be based on a joint work with A. Pushnitski
and C. Villegas-Blas, the preprint is available here:
http://arxiv.org/abs/1110.3098 .
2011年12月13日（火）:16:30-18:00
講師:Wolfram Bauer氏 （ゲッチンゲン大学）
題目: Trivializable
subriemannian structures and spectral analysis of associated operators
2011年11月8日（火）:16:30-18:00
講師: 寺澤 祐高 氏 （東京大数理（日本学術振興会特別研究員PD））
題目: 確率的摂動項を持つ冪乗法則流体方程式の弱解の存在と 一意性について
Abstract: 本講演では、非圧縮性非ニュートン流体の運動を記述する
偏微分方程式に加法的確率的摂動項を加えた確率偏微分方程式 の弱解
の存在と一意性について考察する。 非ニュートン流体としては、粘性
が変形速度テンソルの大きさの冪乗 の形で依存する冪乗法則流体を考
察し、確率的摂動項としては 有色雑音を考察する。 Necas-Malek-
Ruzicka('93)において、確率的外力項を伴わない、 決定方程式に関し
て示された弱解の存在と一意性の主張を、 確率的摂動項を持つ方程式
に対して示す。 解の存在の証明は、ガレルキン近似によって得られた
解の列に対して、 伊藤の公式、Birkholder-Davis-Gundyの不等式など
により、 解の列のコンパクト性を示すこと及び、解の部分列が収束し
、 その収束先が方程式を弱い意味で満たすことを示すことでなされる。
なお、本講演は、吉田伸生氏（京都大学）との共同研究に基づく。
2011年10月11日（火）:16:30-18:00
講師: 和田出 秀光 氏 （早稲田大学（日本学術振興会特別研究員PD））
題目: 重み付きTrudinger-Moser型不等式の最良定数に関して
Abstract: 同講演では、斉次重み付きTrudinger-Moser型不等式を
最良定数と共に考察する。
重みなしの場合は、 Adachi -Tanaka, Proc. Amer. Math. Soc. (1999),
により全空間上のスケール不変なTrudinger-Moser型不等式が
最良定数と共に導出されており、我々は重み付きTrudinger-Moser型
不等式への拡張を試みる。
更に、重み付きTrudinger-Moser型不等式の偏微分方程式への
応用として、重み付き指数型非線形項を伴うKlein-Gordon方程式を
2次元で考察し、同方程式の局所解及び大域解の存在を証明する。
2011年7月12日（火）:16:30-18:00
講師: 小林 政晴 氏 （東京理科大学）
題目: The inclusion relation between Sobolev and modulation spaces
Abstract: In this talk, we consider the inclusion relations between
the $L^p$-Sobolev spaces and the modulation spaces. As an application,
we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\alpha}$
between $L^p$-Sobolev spaces and modulation spaces.
Joint work with Mitsuru Sugimoto (Nagoya University).
2011年4月26日（火）:16:30-18:00
講師: 片岡 清臣 氏（東京大数理）
題目: On the system of fifth-order differential equations which
describes surfaces containing six continuous families of circles
11月16日（火）と20日（土）～21日（日）に東京大学数理科学研究科に
L. Boutet de Monvel先生(University of Paris 6)と
Michael Ruzhansky先生(Imperial College London)をお招きして、
GCOE後援の国際研究集会
「Microlocal analysis and partial differential equations」
を開催します。プログラムはこちらです。(japanese,
english)
****皆様のご参加を大歓迎します。
2010年9月28日（火）:16:30-18:00
講師: Pavel Exner 氏（Czech Academy of Sciences）
題目: Some spectral and resonance properties of quantum graphs
Abstract: In this talk I will discuss three new results about
Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand
Brian Davies.
The first one is related to invalidity of the uniform continuation
principle for such
operators. One manifestation of this fact are embedded eigenvalues
due to
rational relations of graph edge lengths. This effect is non-generic
and we show
how geometric perturbations turn these embedded eigenvalues into
resonances.
Then second problem is related to high-energy behavior of resonances:
we extend
a recent result of Davies and Pushnitski to graphs with general
vertex couplings
and find conditions under which the asymptotics does not have
Weyl character.
Finally, the last question addressed here concerns the absolutely
continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent
result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum
is absent
provided the edge length are increasing without a bound along
the tree.
We show that the result remains valid for a large class of vertex
couplings,
but on the other hand, there are nontrivial couplings leading
to an ac spectrum.
2010年7月13日（火）:17:00-18:00
講師: Carlos Villegas Blas 氏（メキシコ国立自治大学）
題目:On a limiting eigenvalue distribution theorem for perturbations
of the hydrogen atom
Abstract: Let H be the hydrogen atom Hamiltonian. ﾊWe will show
that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending
of
the Planck's parameter h. ﾊﾊWe will show that the distribution
of
eigenvalues in those clusters has a semi-classical limit ﾊinvolving
the averages of the principal symbol of Q along the classical
orbits
of the Kepler problem.
注意：いつもより３０分遅く始まります．当日は上智大理工 田原秀敏氏の集中講義もあります．
2010 年 7 月 12 日 (月)~16 日 (金)：14:40--16:40
日本大学での講演会
講演者: Luca Prelli (Universit{\`a} degli Studi di Padova)
タイトル: Sheaves on Subanalytic Sites (2 回講演)
第１回：2010 年 6 月 29 日 (火) 16:40--17:40 日本大学理工学部駿河台校舎 1 号館 5 階 151
教室
第２回：2010 年 7 月 1 日 (木) 16:40--17:40 日本大学理工学部駿河台校舎 ウェルトンビル 6 階
W63 教室
アブストラクト：
Classical sheaf theory is not well suited to study objects which
are
defined by growth conditions as tempered and Whitney functions.
For this reason we have to work in a bigger category where this
kind of
objects are well defined, the category of subanalytic sheaf.
The talk is divided in two parts. In the first one we will introduce
the
notion of subanalytic sheaves and give several examples in order
to show how
they permit to treat more functional objects than classical sheaves.
In the
second we will discuss some applications to D-modules.
2010年6月22日（火）
講師: Ivana Alexandrova 氏 (East Carolina University)
題目: Resonances for Magnetic Scattering by Two Solenoidal Fields
at Large Separation
Abstract: We consider the problem of quantum resonances in magnetic
scattering by two
solenoidal fields at large separation in two dimensions, and we
study how a trajectory
oscillating between the two fields gives rise to resonances near
the real axis when
the distance between two centers of fields goes to infinity. ﾊWe
give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated
explicitly for
scattering by each solenoidal field. ﾊThe study is based on a
new type of complex
scaling method. ﾊAs an application, we also discuss the relation
to semiclassical
resonances in scattering by two solenoidal fields. This is joint
work with Hideo Tamura.
2010年6月15日（火）
講師: 滝口 孝志 氏 (防衛大学校 数学教育室)
題目: Sato's counterexample and the structure of generalized functions
Abstract: In this talk, we discuss the relation between the structure
and the microlocal unique continuation property of generalized
functions. We also mention some applications of the microlocal
unique continuation property.
2010年4月13日（火）
講師: Jean-Marc Bouclet 氏 (トゥールーズ大学)
題目: Strichartz estimates and the Isozaki-Kitada parametrix on
asymptotically hyperbolic manifold
2010年1月26日（火）(12日から講演日変更になりました．)
講師: Jacob S. Christiansen 氏 (コペンハーゲン大学)
題目: Finite gap Jacobi matrices (joint work with Barry Simon and
Maxim Zinchenko)
2010年1月19日（火）
講師: 岡田 靖則 氏 (千葉大・理)
題目: 超函数の有界性と Massera 型定理について
2009年12月18日～19日：研究集会「微分方程式の総合的研究」が本研究科大講義室で開催されます。
2009年11月24日（火）
講師: 吉野 邦生 氏 (東京都市大学)
題目: Analytic Properties of Eigen Values of Daubechies Localization
Operator
Abstract: （１）ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
（２）ドーベシー局在化作用素のシンボルの再現公式、
（３）ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
2009年9月15日（火）
講師: 打越 敬祐 氏（防衛大学校数学教育室)
題目: 渦層の超局所解析
(21 pictures; 1(700KB),
2(600KB))
要旨：渦層とは，2次元流体が界面を境に2層に分かれて流れる状態で，今井功氏は「佐藤超関数は渦層である」と言っている．この考え方を用いると，
界面の時間変化を記述するBirkoff-Rott方程式を，擬微分方程式に書き直して解けることを説明する．
2009年7月21日（火）
講師: Georgi Raikov 氏（PUC, Chile)
題目: Low Energy Asymptotics of the SSF for Pauli Operators with
Non-Constant Magnetic Fields
(23 pictures; 1(700KB),
2(800KB))
Abstract: In my talk, I will consider the 3D Pauli operator with
non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast
enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function
which is proportional to the eigenvalue
counting function at negative energies, and to the scattering
phase at positive energies.
2009年6月30日（火）
講師: Ivana Alexandrova 氏（東京大数理)
題目: The Structure of the Scattering Amplitude for Schrodinger
Operators with a Strong Magnetic Field
(21 pictures; 1(800KB),
2(800KB))
Abstract: We study the microlocal structure of the semi-classical
scattering amplitude for Schrodinger operators with a strong magnetic
field at non-trapping energies. We prove that, up to any order,
the scattering amplitude can be approximated by a semi-classical
pseudodifferential-operator-valued Fourier integral operator.
2009年6月2日（火）
講師: 神本 晋吾 氏（東京大数理)
題目: 無限階擬微分作用素の形式核関数について
(30 pictures; 1(800KB),
2(700KB))
2009年5月26日（火）
講師: Myriam Ounaies 氏 （ Strasbourg大学数学科)
題目: Intrepolation problems in Hｴ"ormander algebras
(44pictures; 1(900KB),
2(900KB),
3(900KB))
Abstract:
We call H嗷mander algebras the spaces $A_p(＼mathbb C)$ of entire
functions $f$ such that, for all $z$ in $＼mathbb C$, ＼[|f(z)|＼le
Ae^{Bp(z)},＼] where $A$ and $B$ are some positive constants (depending
on $f$) and $p$ is a subharmonic weight. We consider the following
interpolation problem : Given a discrete sequence $＼{a_j＼}$ of
complex numbers and a sequence of complex values $＼{b_j＼}$, under
what conditions does there exist a function $f＼in A_p(＼mathbb
C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what
is the trace of $A_p(＼mathbb C)$ on $＼{a_j＼}$ ?
We say that $＼{a_j＼}$ is an interpolating sequence if the trace
is defined by the space of all $＼{b_j＼}$ satisfying $|b_j|＼le
A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use H嗷mander's $L^2$-estimates for the $＼bar＼partial$-equation
to describe the trace when the weight $p$ is radial and doubling
and to characterize the interpolating sequences for more general
weights.
2009年4月28日（火）
講師: 下村 明洋 氏 （首都大学東京)
題目: 非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動（北直泰氏との共同研究）
(24 pictures; 1(800KB),2(700KB))
2009年1月20日（火）
講師: 吉野 邦生 氏 (武蔵工業大学)
題目: Generating function of eigenvalues of Daubechies Localization
Operator
(Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について)
(25 pictures; 1(1500KB),2(1600KB))
2009年1月6日（火）
講師: 青木 貴史 氏 (近畿大理工)
題目: 野海・山田方程式系のWKB解に付随する幾何的構造
(本多尚文氏、梅田陽子氏との共同研究)
(25 pictures; 1(800KB),2(800KB))
2008年11月25日（火）
講師: Ovidiu Calin 氏 (Eastern Michigan University)
題目: Heat kernels for subelliptic operators
(67 pictures; 1(800KB),
2(800KB),
3(800KB),
4(800KB),
5(800KB))
Abstract:
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior
or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels
of
subelliptic operators. The heat kernels of subelliptic operators
are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators
too.
2008年11月11日（火）
講師: 新國 裕昭 氏 (首都大学東京)
題目:Rotation number approach to spectral analysis of the generalized
Kronig-Penney Hamiltonians
(13 pictures; 850KB)
函数解析特別セミナー（臨時開催）
2008年10月31日（金）
講師: Fran\c{c}ois Germinet 氏 （パリ大学セルジポントワーズ校）
題目:Poisson statistics for random Schr\"odinger operators
時間：17:00 - 18:00
部屋：数理科学研究科棟 123号室
（いつもと時間、場所が異なります。）
2008年10月28日（火）
講師: Serge Alinhac 氏 (パリ大学オルセイ校)
題目:Introduction to geometric analysis of hyperbolic equations
時間：17:00 - 18:00
部屋：数理科学研究科棟 123号室
(17 pictures; 2000KB)
（いつもと時間、場所が異なります。またこの日から３日間連続講演となります。第２回、第３回はそれぞれ29, 30日に同じ部屋、時間帯で行われます。なお、この週は月曜から金曜の14:40~16:40に、同じ123号室で非線形分散型方程式についての中西
賢次 氏の集中講議があります。）
2008年10月14日（火）(グローバルCOE講演会との共催です。)
講師: George Sell 氏 (ミネソタ大学)
題目: Thin 3D Navier-Stokes equations
-Ultimate boundedness of solutions with large data and global
attractors-
時間：16:00 - 17:30
部屋：数理科学研究科棟 002号室
(37 pictures; 1(800KB),
2(800KB),
3(800KB))
（いつもと時間、場所が異なります！）
講演要旨：
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,
Dragos Iftimie, and Luan Hoang.
2008年5月20日（火）
講師: Vania Sordoni 氏 (ボローニャ大学)
題目: Wave operators for diatomic molecules
(37 photographs;1(600KB),2(600KB),3(600KB))
2008年5月13日（火）
講師: Andr\'e Martinez 氏 (ボローニャ大学)
題目: Resonances for non-analytic potentials (joint work with
T. Ramond and J. Sj\"ostrand)
(24 photographs; 1(600KB),
2(600KB))