Seminar information archive

Research Graduate program Undergraduate education

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

2012/02/29

GCOE Seminars

16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Johannes Elschner (Weierstrass Institute, Germany)
Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)

[ Abstract ]
The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.

2012/02/22

Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takuro Mochizuki (Research Institute for Mathematical Sciences, Kyoto University)
Twistor $D$-module and harmonic bundle (ENGLISH)

[ Abstract ]
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:

1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Bernadette Miara (Université Paris-Est, ESIEE, France)
Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)

[ Abstract ]
We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.
The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.
The main result we obtain is as follows:
i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.
ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.

GCOE Seminars

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)

[ Abstract ]
In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.
Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data
$$
{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert
- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}
$$
where $¥tilde ¥Gamma$ is an arbitrary fixed open set of
$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

2012/02/21

Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (The University of Tokyo)
Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)

[ Abstract ]
Mapping class groups (MCG's), of compact oriented surfaces (possibly
with punctures), have many mysterious features: they behave not only
like higher rank lattices (namely, irreducible lattices in higher rank
algebraic groups); but also like rank one lattices. The following
theorem, the Farb--Kaimanovich--Masur superrigidity, states a rank one
phenomenon for MCG's: "every group homomorphism from higher rank
lattices (such as SL(3,Z) and cocompact lattices in SL(3,R)) into
MCG's has finite image."

In this talk, we show a generalization of the superrigidity above, to
the case where higher rank lattices are replaced with some
(non-arithmetic) matrix groups over general rings. Our main example of
such groups is called the "universal lattice", that is, the special
linear group over commutative finitely generated polynomial rings over
integers, (such as SL(3,Z[x])). To prove this, we introduce the notion
of "property (TT)/T" for groups, which is a strengthening of Kazhdan's
property (T).

We will explain these properties and relations to ordinary and bounded
cohomology of groups (with twisted unitary coefficients); and outline
the proof of our result.

2012/02/20

Functional Analysis Seminar

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jan Philip SOLOVEJ (University of Copenhagen)
Microscopic derivation of the Ginzburg-Landau model (ENGLISH)

[ Abstract ]
I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

2012/02/14

Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Loss (Georgia Institute of Technology)
Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)

2012/02/07

GCOE Seminars

14:00-15:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Piermarco Cannarsa (Mat. Univ. Roma "Tor Vergata")
Controllability results for degenerate parabolic operators (ENGLISH)

[ Abstract ]
UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.