## Seminar information archive

#### Lectures

15:15-17:00   Room #123 (Graduate School of Math. Sci. Bldg.)
R. Penner (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
[ Abstract ]
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.

#### PDE Real Analysis Seminar

10:00-11:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Chiun-Chang Lee (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ Abstract ]
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.

### 2012/03/16

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Chun LIU (University of Tokyo / Penn State University)
On Complex Fluids (ENGLISH)
[ Abstract ]
The talk is on the mathematical theories, in particular the energetic variational approaches, of anisotropic complex fluids, such as viscoelastic materials, liquid crystals and ionic fluids in proteins and bio-solutions.

Complex fluids, including mixtures and solutions, are abundant in our daily life. The complicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. We study the underlying energetic variational structures that is common among all these multiscale-multiphysics systems.

In this talk, I will demonstrate the modeling as well as analysis and numerical issues arising from various complex fluids.

### 2012/03/14

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
[ Abstract ]
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.

### 2012/03/13

#### Colloquium

15:00-16:00   Room #050 (Graduate School of Math. Sci. Bldg.)
Aleksandar Ivic (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
[ Abstract ]
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.

#### Mathematical Biology Seminar

14:00-15:00   Room #154 (Graduate School of Math. Sci. Bldg.)
Tsuyoshi Kajiwara (Okayama University)
On construction of Lyapunov functions and functionals (JAPANESE)

### 2012/03/09

#### Infinite Analysis Seminar Tokyo

13:30-14:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Shintarou Yanagida (Kobe Univ.)
On Hall algebra of complexes (JAPANESE)
[ Abstract ]
The topic of my talk is the Hall algebra of complexes,
which is recently introduced by T. Bridgeland.
I will discuss its properties and relation to
auto-equivalences of derived category.
If I have enough time,
I will also discuss the relation
of this Hall algebra to the so-called Ding-Iohara algebra.

### 2012/03/07

#### GCOE Seminars

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

#### GCOE Seminars

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.

#### GCOE Seminars

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

#### 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.)
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.

### 2012/02/03

#### thesis presentations

09:45-11:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Atsushi ITO (Graduate School of Mathematical Sciences University of Tokyo)
(JAPANESE)

#### thesis presentations

11:00-12:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Keijyu SONO (Graduate School of Mathematical Sciences University of Tokyo)
Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions(SL(3,R)の主系列表現に付随する球関数,及び高階Epsteinゼータ関数について)
(JAPANESE)

#### thesis presentations

13:00-14:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Tetsuya ITO (Graduate School of Mathematical Sciences University of Tokyo)
Construction of invariant group orderings from topological point of view(位相幾何の視点からの群の不変順序の構成)
(JAPANESE)

#### thesis presentations

14:15-15:30   Room #118 (Graduate School of Math. Sci. Bldg.)
TIAN Ran (Graduate School of Mathematical Sciences University of Tokyo)
The explicit calculation of Čech cohomology and an extension of Davenport’s inequality(Čechコホモロジーの明示的計算とDavenport不等式の拡張)
(JAPANESE)

#### thesis presentations

09:45-11:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Issei OIKAWA (Graduate School of Mathematical Sciences University of Tokyo)
Hybridized Discontinuous Galerkin Methods for Elliptic Problems(楕円型問題に対するハイブリッド型不連続ガレルキン法の研究)
(JAPANESE)

#### thesis presentations

11:00-12:15   Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi YOKOYAMA (Graduate School of Mathematical Sciences University of Tokyo)
Two-dimensional stochastic Navier-Stokes equations derived from a certain variational problem(ある変分問題から導かれる二次元確率ナビエ・ストークス方程式)
(JAPANESE)

#### thesis presentations

13:00-14:15   Room #128 (Graduate School of Math. Sci. Bldg.)
Shinichiro ITOZAKI (Graduate School of Mathematical Sciences University of Tokyo)
Scattering Theory on Manifolds with Asympotically Polynomially Growing Ends(多項式増大する無限遠境界を持つ多様体上の散乱理論)
(JAPANESE)