## ͊wΗjZ~i[(Tuesday Seminar of Analysis)

(Updated, April 19, 2013)
Ηj16:30 -- 18:00, : ww@Ȋwȓ() 1K128
: Љb , 씎
Tel & FAX 03-5465-7029 (K. KATAOKA), 03-5465-7037iH. MATANOj
bl: ЉbC C C m

ӁF2007N4畔ςĂ܂I

(㐔͊֌W2004Nx㐔͉ΗjZ~i[ƂĂƂ͕ʂɂȂ܂DԑсE͋pIɌŊJÂ܂D)
Back to Seminar Information Page.
Back to Graduate School of Mathematical Sciences, the University of Tokyo

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2013N521i΁j:16:30~18:00
@ut: W (吔)
@: 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.

2012N124i΁j:16:30~18:30
1. ut: Alexander Vasiliev (Department of Mathematics, University of Bergen, Norway)
@ : Evolution of smooth shapes and the KP hierarchy

2. ut: Irina Markina (Department of Mathematics, University of Bergen, Norway)
@ : 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.

2012N116i΁j:16:30~18:00
@ut: Thierry Ramond (Univ. Paris, Orsay)
@: Resonance free domains for homoclinic orbits

2012N1030i΁j:16:30~18:00
@ut: Francis Nier (Univ. Rennes 1)
@: 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.

2012N1023i΁j:16:30~18:00 ̓̂() 1K002
@ut: Elliott Lieb (Princeton Univ.)
@: 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)

2012N717i΁j:16:30~18:00
@ut: O ikwj
@: 2~̈ɂLiouville-Gel'fand̔񋅑Ώ̉̍\
Abstract: w֐Ɏȉ~^iLiouville-Gel'fandj
ɂčl@B2̉~̈ł́A̔̕񋅑Ώ̂ȉΏ̉

ēꂽʂЉB

2012N710i΁j:16:30~18:00
@ut: z ikwj
@: Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition
Abstract: {uł́Ax񈳏kŜ̉^LqStokes
̈ɂۓɁAGreenɑ\̈Ɉˑ

@ϕ́ÄۓɔŗLl̑Qߋ𖾎Iɕ\
Weyl̑QߌƊ֘AȂǁÄۓɂđϗLp
̂ƂēoĂB{uɂāA܂͓ƂāAȉ~
^ōł{IȃvXDirichletɑ΂ϕ
ɂČyǍɎ匋ʂłStokesɂ

2012N626i΁j:16:30~18:00
@ut: ɓ@ i}gwj
@: 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).

2012N522i΁j:16:30~18:00 at 118*
@ut: Norbert Pozar i吔j
@:Viscosity solutions for nonlinear elliptic-parabolic problems
Abstract: 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.
(̓PPWɂȂ܂DԈႦ̂Ȃ悤ɁI)

2012N515i΁j:16:30~18:00
@ut: J iswE͌j
@: 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.

2012N214i΁j:16:30~18:00
@ut: Michael Loss iGeorgia Institute of Technologyj
@: Symmetry results for Caffarelli-Kohn-Nirenberg inequalities

2012N131i΁j:16:30~18:00
@ut: Michel Chipot (University of Zurich)
@: 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 H^{-1}.

2011N1220i΁j:16:30~18:00
@ut: Gueorgui Raykov iEJ\bNwj
@: 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 .

2011N1213i΁j:16:30~18:00
@ut:Wolfram Bauer iQbQwj
@: Trivializable subriemannian structures and spectral analysis of associated operators

2011N118i΁j:16:30~18:00
@ut: V S i吔i{wpUʌPDjj
@: mIۓp@݂̎̑̕ Ӑɂ
Abstract: {uł́A񈳏kj[ĝ̉^Lq
Δɉ@ImIۓmΔ ̎
݂̑ƈӐɂčl@B j[ĝƂẮAS
όxe\̑傫̙p ̌ňˑp@̂l
@AmIۓƂĂ LFGl@B Necas-Malek-
Ruzicka('93)ɂāAmIO͍𔺂ȂA Ɋւ
Ďꂽ݂̑ƈӐ̎咣A mIۓ
ɑ΂ĎB ݂̑̏ؖ́AKLߎɂēꂽ
̗ɑ΂āA ɓ̌ABirkholder-Davis-Gundy̕sȂ
ɂA ̗̃RpNgƋyсA̕񂪎
A ̎悪アӖŖƂƂłȂB
ȂA{úAgcLiswjƂ̋ɊÂB

2011N1011i΁j:16:30~18:00
@ut: aco G icwi{wpUʌPDjj
@: dݕtTrudinger-Moser^s̍ŗǒ萔Ɋւ
Abstract: uł́AĎdݕtTrudinger-Moser^s
ŗǒ萔Ƌɍl@B
d݂Ȃ̏ꍇ́A Adachi -Tanaka, Proc. Amer. Math. Soc. (1999),
ɂSԏ̃XP[sςTrudinger-Moser^s
ŗǒ萔ƋɓoĂAX͏dݕtTrudinger-Moser^
sւ̊g݂B
2ōl@A̋Ǐyё݂̑ؖB

2011N712i΁j:16:30~18:00
@ut: iȑwj
@: 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).

2011N426i΁j:16:30~18:00
@ut: Љ b i吔j
@: On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles

1116i΁j20iyj21ijɓwȊwȂ
L. Boutet de Monvel搶(University of Paris 6)
Michael Ruzhansky搶(Imperial College London)āA
GCOE㉇̍یW
uMicrolocal analysis and partial differential equationsv
JÂ܂BvO͂łB(japanese, english)
****Fl̂Q劽}܂B

2010N928i΁j:16:30~18:00
@ut: Pavel Exner iCzech Academy of Sciencesj
@: Some spectral and resonance properties of quantum graphs
Abstract: In this talk I will discuss three new results about SchrNodinger 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.

2010N713i΁j:17:00~18:00
@ut: Carlos Villegas Blas iLVRwj
@:On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom
Abstract: Let H be the hydrogen atom Hamiltonian. 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. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
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2010 N 7 12 ()~16 ()F14:40--16:40

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@u: Luca Prelli (Universit{\a} degli Studi di Padova)
^Cg: Sheaves on Subanalytic Sites (2 u)
PF2010 N 6 29 () 16:40--17:40@{wHwx͑Z 1 5 K 151
QF2010 N 7 1 () 16:40--17:40 {wHwx͑Z EFgr 6 K W63
AuXgNgF
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.

2010N622i΁j
@ut: Ivana Alexandrova (East Carolina University)
@: 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. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.

2010N615i΁j
@ut: Fu (hqwZ w玺)
@: 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.

2010N413i΁j
@ut: Jean-Marc Bouclet (gD[[Yw)
@: Strichartz estimates and the Isozaki-Kitada parametrix on asymptotically hyperbolic manifold

2010N126i΁j(12uύXɂȂ܂D)
@ut: Jacob S. Christiansen (Ryn[Qw)
@: Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)

2010N119i΁j
@ut: c (tE)
@: ̗LE Massera ^藝ɂ

2009N121819FWȗIv{ȑuŊJÂ܂B

2009N1124i΁j
@ut: g M (ssw)
@: Analytic Properties of Eigen Values of Daubechies Localization Operator
Abstract: iPjh[xV[Ǎ݉pf̌ŗLl͓̉IAϕ\A
iQjh[xV[Ǎ݉pf̃V{̍ČA
iRjh[xV[Ǎ݉pf̃o[O}[tHbNԂł̕\
ɂďqׂB

2009N915i΁j
@ut: ŉz hS ihqwZw玺)
@: Qw̒Ǐ
(21 pictures; 1(700KB), 2(600KB))
v|FQwƂ́C2̂Eʂ2wɕėԂŁĆu֐͉QwłvƌĂD̍lpƁC
Eʂ̎ԕωLqBirkoff-RottC[ɏĉ邱ƂD

2009N721i΁j
@ut: Georgi Raikov iPUC, Chile)
@: 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.

2009N630i΁j
@ut: Ivana Alexandrova i吔)
@: 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.

2009N62i΁j
@ut: _{ W i吔)
@: K[pf̌j֐ɂ
(30 pictures; 1(800KB), 2(700KB))

2009N526i΁j
@ ut: Myriam Ounaies i Strasbourgww)
@ : Intrepolation problems in H"ormander algebras
(44pictures; 1(900KB), 2(900KB), 3(900KB))
Abstract:
We call Hrmander 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 Hrmander'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.

2009N428i΁j
@ut: m isw)
@ : ^U𔺂VfBK[̔Cӂ̑傫̏f[^ɑ΂̑Qߋik׎Ƃ̋j
(24 pictures; 1(800KB),2(700KB))

2009N120i΁j
@ut: g M (HƑw)
@ : Generating function of eigenvalues of Daubechies Localization Operator
(Daubechies Localization Operator ŗLl̕֐ symbol ֐Čɂ)
(25 pictures; 1(1500KB),2(1600KB))

2009N16i΁j
@ut:  Mj (ߋE嗝H)
@ : CERcnWKBɕt􉽓I\
({A~czqƂ̋)
(25 pictures; 1(800KB),2(800KB))

2008N1125i΁j
@ut: Ovidiu Calin (Eastern Michigan University)
@ : 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.

2008N1111i΁j
@ut: V T (sw)
@ :Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
(13 pictures; 850KB)

͓ʃZ~i[iՎJÁj
2008N1031ij
@ut: Fran\c{c}ois Germinet ipwZW|g[YZj
@ :Poisson statistics for random Schr\"odinger operators
@ԁF17:00 - 18:00
@FȊwȓ 123
iƎԁAꏊقȂ܂Bj

2008N1028i΁j
@ut: Serge Alinhac (pwIZCZ)
@ :Introduction to geometric analysis of hyperbolic equations
@ԁF17:00 - 18:00
@FȊwȓ 123
(17 pictures; 2000KB)
iƎԁAꏊقȂ܂B܂̓RԘAuƂȂ܂BQAR͂ꂼ29, 30ɓAԑтōs܂BȂȀT͌jj14:40~16:40ɁA123Ŕ`U^ɂĂ̒ ̏Wuc܂Bj

2008N1014i΁j(O[oCOEuƂ̋ÂłB)
@ut: George Sell (~l\^w)
@ : Thin 3D Navier-Stokes equations
-Ultimate boundedness of solutions with large data and global attractors-
@ԁF16:00 - 17:30
@FȊwȓ 002
(37 pictures; 1(800KB), 2(800KB), 3(800KB))
iƎԁAꏊقȂ܂Ij
uv|F
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.

2008N520i΁j
@ut: Vania Sordoni ({[jw)
@ : Wave operators for diatomic molecules
(37 photographs;1(600KB),2(600KB),3(600KB))

2008N513i΁j
@ut: Andr\'e Martinez ({[jw)
@ : Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\"ostrand)
(24 photographs; 1(600KB), 2(600KB))