GCOE Seminars

Seminar information archive ~03/28Next seminarFuture seminars 03/29~


Seminar information archive

2013/01/11

11:15-12:15   Room #123 (Graduate School of Math. Sci. Bldg.)
An Speelman (KU Leuven)
Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

2012/12/19

15:45-16:45   Room #118 (Graduate School of Math. Sci. Bldg.)
Mihaita Berbec (KU Leuven)
$W^*$-superrigidity for left-right wreath products (ENGLISH)

2012/11/19

15:30-17:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
Linearisable mappings (ENGLISH)
[ Abstract ]
We present a series of results on linearisable second-order mappings.
Three distinct families of such mappings do exist: projective, mappings of Gambier type and mappings which we have dubbed "of third kind".
Our starting point are the linearisable mappings belonging to the QRT family. We show how they can be linearised and how in some cases their explicit solution can be constructed. We discuss also the growth property of these mappings, a property intimately related to linearisability.
In the second part of the talk we address the question of the extension of these mappings to a non-autonomous form.
We show that the QRT invariant can also be extended (to a quantity which depends explicitly on the independent variable). Using this non-autonomous form we show that it is possible to construct the explicit solution of all third-kind mappings. We discuss also the relation of mappings of the third kind to Gambier-type mappings. We show that a large subclass of third-kind mappings can be considered as the discrete derivative of Gambier-type ones.

2012/11/16

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Dietmar Bisch (Vanderbilt University)
Subfactors with small Jones index (ENGLISH)

2012/07/19

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State Univ.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.

2012/05/07

14:30-16:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Takuma Akimoto (Keio university, Global environmental leaders program)
Distributional behaviors of time-averaged observables in anomalous diffusions (subdiffusion and superdiffusion) (ENGLISH)
[ Abstract ]
In anomalous diffusions attributed to a power-law distribution,
time-averaged observables such as diffusion coefficient and velocity of drift are intrinsically random. Anomalous diffusion is ubiquitous phenomenon not only in material science but also in biological transports, which is characterized by a non-linear growth of the mean square displacement (MSD).
(subdiffusion: sublinear growth, super diffusion: superlinear growth).
It has been known that there are three different mechanisms generating subdiffusion. One of them is a power-law distribution in the trapping-time distribution. Such anomalous diffusion is modeled by the continuous time random walk (CTRW). In CTRW, the time-averaged MSD grows linearly with time whereas the ensemble-averaged MSD does not. Using renewal theory, I show that diffusion coefficients obtained by single trajectories converge in distribution. The distribution is the Mittag-Leffler (or inverse Levy) distribution [1,2].
In superdiffusion, there are three different mechanisms. One stems from positive correlations in random walks; the second from persistent motions in random walks, called Levy walk; the third from very long jumps in random walks, called Levy flight.
If the persistent time distribution obeys a power law with divergent mean in Levy walks, the MSD grows as t^2 whereas the mean of positions is zero. When an external bias is added in Levy walks, the response to bias (velocity of drift) appears in the distribution, which is what we term a distributional response [3]. The distribution is the generalized arcsine distribution.
These distributional behaviors open a new window to dealing with the average (ensemble or time average) in single particle tracking experiments.

[1] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
[2] T. Miyaguchi and T. Akimoto, Phys. Rev. E 83, 031926 (2011).
[3] T. Akimoto, Phys. Rev. Lett. 108, 164101 (2012)

2012/03/07

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Kazufumi Ito (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
[ Abstract ]
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.

2012/03/06

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Weierstrass Institute, Berlin)
On the phase field approach to shape and topology optimization (ENGLISH)
[ Abstract ]
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.

2012/03/06

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Thomas Petzold (Weierstrass Institute, Berlin)
Finite element simulations of induction hardening of steel parts (ENGLISH)
[ Abstract ]
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.

2012/02/29

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

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.

2012/02/22

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 $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

2012/02/07

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.

2011/12/27

13:30-14:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Yichao Zhu (University of Oxford)
The Modelling of Dislocations in the Early Stage of the Metal Fatigue (ENGLISH)
[ Abstract ]
Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of
fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.

2011/12/27

14:30-15:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Manabu Machida (University of Michigan)
Wave Transport in Random Media and Inverse Problems (ENGLISH)
[ Abstract ]
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

2011/12/09

11:40-12:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Wolfgang Koenig (Weierstrass Institute Berlin)
Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)
[ Abstract ]
We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

2011/12/09

14:00-14:50   Room #122 (Graduate School of Math. Sci. Bldg.)
Roman Kotecky (Charles University Prague/University of Warwick)
Gradient Gibbs models with non-convex potentials (ENGLISH)
[ Abstract ]
A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

2011/12/09

15:00-15:50   Room #122 (Graduate School of Math. Sci. Bldg.)
Stefano Olla (University Paris - Dauphine)
Einstein relation and linear response for random walks in random environment (ENGLISH)

2011/11/16

10:00-11:00   Room #270 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
All you never really wanted to know about QRT, but were foolhardy enough to ask (ENGLISH)
[ Abstract ]
We discuss various extensions of the famous QRT second order, first degree, integrable mapping. We show how these extensions can be combined. A discussion of integrable correspondences related to these extended QRT mappings is also presented.

2011/10/20

16:30-18:00   Room #270 (Graduate School of Math. Sci. Bldg.)
O. Emanouilov (Colorado State University)
On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)
[ Abstract ]
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.

2011/08/12

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Benny Hon (Department of Mathematics City University of Hong Kong)
Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)
[ Abstract ]
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

2011/03/08

15:00-16:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Dimitri Yafaev (Univ. Rennes 1)
Diagonal singularities of the scattering matrix and the inverse problem at a fixed energy (ENGLISH)

2011/03/04

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets (ENGLISH)
[ Abstract ]
We discuss the inverse boundary value problem of determining the conductivity in two dimensions from the pair of all input Dirichlet data supported on an open subset S1 and all the corresponding Neumann data measured on an open subset S2.
We prove the global uniqueness under some additional geometric condition, in the case where the intersection of S_1 and S_2 has no interior points, and we prove also the uniqueness for a similar inverse problem for the stationary Schr"odinger equation.
The key of the proof isthe construction of appropriate complex geometrical optics solutions using Carleman estimates with a singular weight.

2011/02/14

13:00-14:00   Room #270 (Graduate School of Math. Sci. Bldg.)
Jin Cheng (Fudan University)
Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)
[ Abstract ]
The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

2010/12/22

11:00-12:00   Room #570 (Graduate School of Math. Sci. Bldg.)
Mourad Bellassoued (Faculté des Sciences de Bizerte)
Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)
[ Abstract ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).

< Previous 12345 Next >