## 過去の記録

### 2013年03月18日(月)

#### 作用素環セミナー

16:00-17:30   数理科学研究科棟(駒場) 118号室

Ultraproducts of von Neumann algebras (JAPANESE)

#### 談話会・数理科学講演会

15:00-17:30   数理科学研究科棟(駒場) 050号室

お茶&Coffee&お菓子: 16:00～16:30 (大講義室ロビー)。

[ 講演概要 ]

[ 講演概要 ]

### 2013年03月15日(金)

#### 作用素環セミナー

15:45-18:00   数理科学研究科棟(駒場) 118号室
Lucio Cirio 氏 (Univ. M\"unster) 15:45-16:45
Infinitesimal 2-Yang-Baxter operators from a categorification
of the Knizhnik-Zamolodchikov connection (ENGLISH)
Sutanu Roy 氏 (Univ. G\"ottingen) 17:00-18:00
Twisted tensor product of $C^*$-algebras (ENGLISH)

#### 数値解析セミナー

10:00-12:15   数理科学研究科棟(駒場) 056号室

http://www.ms.u-tokyo.ac.jp/gcoe/index.html

Irene Vignon-Clementel 氏 (INRIA Paris Rocquencourt )
Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)
[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 作用素環セミナー

14:30-15:30   数理科学研究科棟(駒場) 118号室
Stefano Rossi 氏 (Univ. Roma II)
The connected component of a compact quantum group (ENGLISH)

#### 作用素環セミナー

13:15-14:15   数理科学研究科棟(駒場) 118号室
Jean Roydor 氏 (Univ. Bordeaux)
Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 128号室

Caterina Zeppieri 氏 (Universität Münster)
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)
[ 講演概要 ]
Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.
The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.
The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).

### 2013年03月11日(月)

#### 作用素環セミナー

09:45-12:00   数理科学研究科棟(駒場) 123号室
Tristan Bice 氏 (York Univ.) 09:45-10:45
Traces and Ultrapowers (ENGLISH)
David Penneys 氏 (Univ. Toronto) 11:00-12:00
Constructing subfactors with jellyfish (ENGLISH)

#### 作用素環セミナー

13:30-18:15   数理科学研究科棟(駒場) 123号室
Danny Hey 氏 (Univ. Toronto) 13:30-14:30
Classification and the Toms-Winter Conjecture (ENGLISH)
Stephen Curran 氏 (UCLA) 14:45-15:45
Free probability and planar algebras (ENGLISH)
Rasmus Bentmann 氏 (Univ. Copenhagen) 16:00-17:00
Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)
Luis Santiago-Moreno 氏 (Univ. Oregon) 17:15-18:15
Classifying $C^*$-algebras up to W-stability (ENGLISH)

#### GCOEセミナー

14:45-15:45   数理科学研究科棟(駒場) 123号室
このセミナーはMiniworkshop on Operator Algebras IVの一環として行われます
Stephen Curran 氏 (UCLA)
Free probability and planar algebras (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-4.htm

### 2013年03月08日(金)

#### FMSPレクチャーズ

10:30-12:00   数理科学研究科棟(駒場) 056号室
Benjamin Burton 氏 (The University of Queensland, Australia)
Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)
[ 講演概要 ]
In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.

This is joint work with Melih Ozlen.

### 2013年03月07日(木)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/16.html

### 2013年03月06日(水)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 117号室
Frederic Le Roux 氏 (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
[ 講演概要 ]
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.

### 2013年03月05日(火)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/15.html

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State University)
Uniqueness for inverse boundary value problems by Dirichlet-to
-Neumann map on subboundaries (ENGLISH)
[ 講演概要 ]
We consider inverse boundary value problems for elliptic equations of second order and survey recent results on the uniqueness mainly by partial boundary data. In particular, in two dimensions, we show uniqueness results by means of Dirichlet data supported on an arbitrary subboundary $\\widetilde\\Gamma$ and Neumann data measured on $\\widetilde\\Gamma$. We describe the key idea for the proof: complex geometric optics solutions which are constructed by a Carleman estimate. Also we show the uniqueness by Dirichlet-to-Neumann map on subboundaries in three dimensions.

### 2013年03月04日(月)

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 270号室
M.I. Tribelsky 氏 (Landau Institute)
Resonant Light Scattering by Small Particles (ENGLISH)
[ 講演概要 ]
The problem of light scattering by a small spherical particle is studied within the framework of the exact solution of the Maxwell equations. It is shown that if imaginary part of the dielectric permittivity of the particle is small enough, the problem exhibits sharp giant resonances with very unusual properties. Specifically, the characteristic values of the electric and magnetic fields inside the particle and in its immediate vicinity are singular in the particle size. In non-dissipative case these quantities do not have definite limits when the radius of the particle tends to zero. The field of the Poynting vector in the immediate vicinity of the particle includes singular points, whose number, types and positions are very sensitive to the changes in the incident light frequency. As an example a bifurcation diagram, describing the behavior of the singular points in the vicinity of the dipole resonance for a particle with a certain fixed size is discussed.

### 2013年02月28日(木)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
Stability of the determination of the surface impedance of an
obstacle from the scattering amplitude (ENGLISH)
[ 講演概要 ]
In this joint work with Mourad Bellassoued and Aymen Jbalia, we prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 270号室
Kazufumi Ito 氏 (North Carolina State Univ.)
$L_0$ optimization and Lagrange multiplier (ENGLISH)
[ 講演概要 ]
$L_p$ optimization with $p ¥in[0,1)$ is investigated. The difficulty of natural lack of weak lower-semicontinuity is addressed and the Lagrange multiplier theory is developed. Existence results and necessary optimality conditions are obtained, and the semismooth Newton method using the primal-dual active set is developed. The theory and algorithm are demonstrated for the case of optimal control problems. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved.

### 2013年02月27日(水)

#### GCOEセミナー

10:00-11:00   数理科学研究科棟(駒場) 270号室
Dietmar Hoemberg 氏 (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
[ 講演概要 ]
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.

Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results.

(joint work with K. Krumbiegel and N. Togobytska, WIAS)

### 2013年02月23日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

Ramanujan巡回グラフとHardy-Littlewood予想 (JAPANESE)
[ 講演概要 ]
TBA

[ 講演概要 ]
TBA

### 2013年02月22日(金)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Stefaan Vaes 氏 (KU Leuven)
II$_1$ factors with a unique Cartan subalgebra (ENGLISH)

#### FMSPレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 118号室
Stefaan Vaes 氏 (KU Leuven)
II_1 factors with a unique Cartan subalgebra (ENGLISH)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
Fatiha Alabau-Boussouira 氏 (Université de Lorraine)
Exact insensitizing controls for scalar wave equations and control of coupled systems (ENGLISH)
[ 講演概要 ]
The control of scalar PDE's such as the wave or heat equation is by now well-understood.
It consists in building a source term which can drive the solution from a given initial state to a final (reachable) desired state.
Exact insensitizing control are exact controls which should satisfy an additional requirement:
they should be robust to small unknown perturbations of the initial data. More precisely, they should, as exact controls, drive the solution to the desired state, but they also should insensitize a given measure of the solution to such perturbations. One can show that the existence of exact insensitizing controls for a scalar wave equation is equivalent to the exact controllability by a single control of a system of two wave equations coupled in cascade.
We shall present in this talk the challenging issues and give some recent results and perspectives for the exact insensitizing control of scalar wave equations. We shall also give some more general results on the controllability of coupled systems by a reduced number of controls.

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 270号室
Piermarco Cannarsa 氏 (Univ. Roma II)
Carleman estimates and Lipschitz stability for Grushin-type operators (ENGLISH)
[ 講演概要 ]
The Baouendi-Grushin operator is an important example of a degenerate elliptic operator that has strong connections with almost-riemannian structures. It is also the infinitesimal generator of a strongly continuous semigroup on Lebesgue spaces with very interesting properties from the point of view of control theory. Such properties will be discussed in this lecture, starting with approximate and null controllability.
We will then address the inverse source problem for these operators deriving a Lipschitz stability result.

### 2013年02月21日(木)

#### FMSPレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 056号室
Michael Mascagni 氏 (Florida State University
)
Monte Carlo Methods for Partial Differential Equations: Computing Permeability
(ENGLISH)
[ 講演概要 ]
We present a brief overview of Monte Carlo methods for the solution of elliptic and parabolic partial differential equations (PDEs). We begin with a review of the Feynman-Kac formula, and its use in the probabilistic representation of the solutions of elliptic and parabolic PDEs. We then consider some specific Monte Carlo methods used for obtaining the solution of simple elliptic partial differential equations (PDEs) as part of exterior boundary value problems that arise in electrostatics and flow through porous media. These Monte Carlo methods use Feynman-Kac to represent the solution of the elliptic PDE at a point as the expected value of functionals of Brownian motion trajectories started at the point of interest. We discuss the rapid solution of these equations, in complex exterior geometries, using both the "walk on spheres" and "Greens function first-passage" algorithms. We then concentrate on methods for quickly computing the isotropic permeability using the "unit
capacitance" and "penetration depth'' methods. The first of these methods, requires computing a linear functional of the solution to an exterior elliptic PDE. Both these methods for computing permeability are simple, and provide accurate solutions in a few seconds on laptop-scale computers. We then conclude with a brief look at other Monte Carlo methods and problems that arise on related application areas.