(Imperial College London)
Conference Venue: Room 642 for 10am-1pm, and room 139 for 2pm-6:30pm, Huxley Building, Imperial College London
The Microlocal Day is a new initiative of a short and intensive series of lectures devoted to different aspects of the microlocal analysis and related topics. The program includes research lectures as well as survey lectures aimed at researchers and PhD students interested in the subject. All are welcome to attend.
The previous Microlocal Day #1 was held in June 2010.
Friday, 3 December, 10:40am—1pm, Imperial College, Room 642
Friday, 3 December, 2pm—6:35pm, Imperial College, Room 139
For further information please contact
Michael Ruzhansky at this e-mail address
Suggestion of hotels in the area (Earl’s Court Station, 15 mins walk to Imperial College)
How to get to the Department
of Mathematics, Imperial College
Travel to the tube station Gloucester Road (District, Circle, and Piccadilly Lines).
When you exit the station, turn left along Gloucester Road, crossing Cromwell Road 50 meters from the exit.
After 4-5 minutes walk along Gloucester Road, turn right to Queen's Gate Terrace.
This is a short road leading directly to the entrance of the Huxley Building, at 180 Queen's Gate. We are on floor 6.
Fumihiko Hirosawa (Yamaguchi University) On the energy estimates for second order homogeneous hyperbolic equations with Levi-type conditions
We consider the energy estimates for the Cauchy problem of second order homogeneous
strictly hyperbolic equations with time dependent coefficients. In particular we focus
on the smoothness and interactions of oscillating coefficients, which are crucial for the
energy estimates; we shall call them a kind of Levi-type conditions.
Ilia Kamotski (University of Bath) Boundary value problems in irregular domains and applications
We discuss some aspects of the theory of the linear water waves, some challenges and
Naoto Kumano-go (Kogakuin University) Path integrals for Gaussian processes as analysis on path space by time slicing approximation
We introduce the path integrals for Gaussian processes as an analysis which has functional
integrals and smooth functional derivatives. More precisely, we give a fairly general class of
functionals so that the path integrals for Gaussian processes have a
mathematically rigorous meaning.
For any functional belonging to our class, the time slicing approximation of the path integral
converges uniformly on compact subsets of the configuration space. Our class is closed under
multiplication, translation, real linear transformation and functional
The invariance under translation and orthogonal transformation, the interchange of the order
with Riemann-Stieltjes integrals and limits, the integration by parts and the Taylor expansion
formula with respect to functional differentiation, and the fundamental theorem of calculus
hold in the path
 Naoto Kumano-go, Path integrals for Gaussian processes as analysis on path space by time slicing
approximation, Integration: Mathematical Theory and Applications, Vol. 1, No. 3 (2010), pp.253-278.
Tokio Matsuyama (Tokai University) Dispersion for 3D wave equation with a potential in an exterior domain
In this talk I will introduce the dispersive estimates and Strichartz estimates for 3D wave
equation with a potential in an exterior domain. The dispersive estimates will be proved by
interpolating between pointwise estimates for the propagator and $L^2$ estimates.
The pointwise estimates will be proved by using the spectral representation of the propagator.
The key lemma is the representation formula for the perturbed resolvent of the Schrödinger
operator in terms of the free resolvent in the whole space. By $TT^*$ argument we will
get the Strichartz estimates.
Mitsuru Sugimoto (Nagoya University) On some Lp-type estimates for evolution operators
Mapping properties of unimodular Fourier multiplier describing various type of evolution operators
will be discussed. It is know that they are bounded on modulation spaces while not on Lp-spaces
except for the case p=2. In this talk, the boundedness between Lp-Sobolev spaces and modulation
spaces will be mainly considered. For the purpose, the inclusion relations between Lp-Sobolev
spaces and modulation spaces will be determined explicitly.
Mirko Tarulli (Imperial College London) On the smoothing-Strichartz estimates
We present some a-priori estimates for evolution equations in mixed smoothing-Strichartz spaces.
As an application we discuss Strichartz estimates for magnetic Klein-Gordon.
Naohito Tomita (Osaka University) A Hörmander type multiplier theorem for multilinear operators
In this talk, we consider a Hörmander type multiplier theorem for multilinear operators.
The multipliers in our problem have only the limited smoothness.
Jens Wirth (University of Stuttgart) Phase space analysis for hyperbolic systems
In this talk some aspects of phase space analysis for hyperbolic systems will be discussed.
The main focus will be on diagonalisation and decoupling of pseudo-differential hyperbolic
systems in adapted symbol classes taking care of the structure of the problem at infinity.