## Seminar information archive

### 2012/10/30

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Tadashi Kawanago (Tokyo Institute of Technology)
Error analysis of Galerkin's method for semilinear partial differential equations (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

#### Tuesday Seminar on Topology

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Koya Shimokawa (Saitama University)
Applications of knot theory to molecular biology (JAPANESE)
[ Abstract ]
In this talk we discuss applications of knot theory to studies of DNA
and proteins.
Especially we will consider (1)topological characterization of
mechanisms of site-specific recombination systems,
(2)modeling knotted DNA and proteins in confined regions using lattice
knots, and
(3)mechanism of topoisomerases and signed crossing changes.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Francis Nier (Univ. Rennes 1)
About the method of characteristics (ENGLISH)
[ Abstract ]
While studying the mean field dynamics of a systems of bosons, one is led to solve a transport equation for a probability measure in an infinite dimensional phase-space. Since those probability measures are characterized after testing with cylindrical or polynomial observables, which make classes which are not invariant after composing with a nonlinear flow. Thus the standard method of characteristics for transport equations cannot be extended at once to the infinite dimensional case. A solution comes from techniques developed for optimal transport and a probabilistic interpretation of trajectories.

#### Lectures

17:00-18:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Frank Lutz (Technische Universität Berlin)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
[ Abstract ]
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).

For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
complicatedness'' of complexes.

### 2012/10/29

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Kento Fujita (RIMS)
The Mukai conjecture for log Fano manifolds (JAPANESE)
[ Abstract ]
The concept of log Fano manifolds is one of the most natural generalization of the concept of Fano manifolds. We will give some structure theorems of log Fano manifolds. For example, we will show that the Mukai conjecture for Fano manifolds implies the log Mukai conjecture' for log Fano manifolds.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Atsuji (Keio University)
Value distribution of meromorphic functions on foliated manifolds,II (JAPANESE)

### 2012/10/26

#### Seminar on Probability and Statistics

14:50-16:00   Room #006 (Graduate School of Math. Sci. Bldg.)
HIROSE, Kei (Graduate School of Engineering Science, Osaka University)
Tuning parameter selection in sparse regression modeling (JAPANESE)
[ Abstract ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html

### 2012/10/23

#### Tuesday Seminar of Analysis

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Elliott Lieb (Princeton Univ.)
Topics in quantum entropy and entanglement (ENGLISH)
[ Abstract ]
Several recent results on quantum entropy and the uncertainty
principle will be discussed. This is partly joint work with Eric Carlen
on lower bounds for entanglement, which has no classical analog, in terms
of the negative of the conditional entropy, S1 - S12, whose negativity,
when it occurs, also has no classical analog. (see arXiv:1203.4719)
It is also partly joint work with Rupert Frank on the uncertaintly
principle for quantum entropy which compares the quantum von Neumann
entropy with the classical entropies with respect to two different
bases. We prove an extension to the product of two and three spaces, which
has applications in quantum information theory. (see arxiv:1204.0825)

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Nariya Kawazumi (The University of Tokyo)
A geometric approach to the Johnson homomorphisms (JAPANESE)
[ Abstract ]
We re-construct the Johnson homomorphisms as an embeddig of the Torelli
group
into the completed Goldman-Turaev Lie bialgebra. Then the image is
included in the
kernel of the Turaev cobracket. In the case where the boundary is
connected,
the Turaev cobracket clarifies a geometric meaning of the Morita traces.
Time permitting, we also discuss the case of holed discs.
This talk is based on a joint work with Yusuke Kuno (Tsuda College).

### 2012/10/22

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Grad. School of Math. Sci., Univ. of Tokyo)
The second main therorem for entire curves into Hilbert modular surfaces (JAPANESE)

### 2012/10/19

#### Seminar on Probability and Statistics

14:50-16:00   Room #006 (Graduate School of Math. Sci. Bldg.)
SHIMIZU, Yasutaka (Graduate School of Engineering Science, Osaka University)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
[ Abstract ]
An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html

### 2012/10/18

#### Seminar on Probability and Statistics

15:15-16:25   Room #006 (Graduate School of Math. Sci. Bldg.)
KATO, Kengo (Department of Mathematics, Graduate School of Science, Hiroshima University)
Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)
[ Abstract ]
This paper aims at developing a quasi-Bayesian analysis
of the nonparametric instrumental variables model, with a focus on the
asymptotic properties of quasi-posterior distributions. In this paper,
instead of assuming a distributional assumption on the data generating
process, we consider a quasi-likelihood induced from the conditional
moment restriction, and put priors on the function-valued parameter.
We call the resulting posterior quasi-posterior, which corresponds to
`Gibbs posterior'' in the literature. Here we shall focus on sieve
priors, which are priors that concentrate on finite dimensional sieve
spaces. The dimension of the sieve space should increase as the sample
size. We derive rates of contraction and a non-parametric Bernstein-von
Mises type result for the quasi-posterior distribution, and rates of
convergence for the quasi-Bayes estimator defined by the posterior
expectation. We show that, with priors suitably chosen, the
quasi-posterior distribution (the quasi-Bayes estimator) attains the
minimax optimal rate of contraction (convergence, respectively). These
results greatly sharpen the previous related work.
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html

#### Lectures

16:00-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Anatoly Yagola (Lomonosov Moscow State University)
Multidimensional ill-posed problems (ENGLISH)
[ Abstract ]
It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.
We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].
Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral
equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].
2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.
This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.

### 2012/10/17

#### Geometry Colloquium

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (Tohoku University)
p-Kazhdan constants and non-expanders (JAPANESE)
[ Abstract ]
In study of graphs and finitely generated groups (as Cayley graphs) as metric spaces with the path metrics, one basic idea is to "linearize" them, more precisely, to embed them into certain Banach spaces in some nice way. Special attention has been paid to embeddings of graphs into Hilbert spaces or l^p spaces. It is a well-known result that a "family of expanders", namely, a family of finite graphs (of unifromly bounded degree) with uniform lower bound of spectral gaps (equivalently, of Cheeger constants), does not coarsely embed into Hilbert spaces, or l^p spaces.
In this talk, we investigate a "family of NON-expanders" coming from Cayley graphs of a family of finitely generated groups. In this setting we define l^p-version of the Kazhdan constant and of the property tau constant for groups, and study the decay rate of p-spectral gap of non-expanders in terms of them. This gives some metric geometrical information on the family. Our main example will be the family of (Cayley graphs of SL_n(Z/k_nZ)), indexed by n>2, for (k_n)_n a sequence of natural numbers>2 and with respect to standard 4-element generating sets. We will start from basic definitions, such as ones of Cayley graphs, expander families, and Kazhdan constants.

#### Lectures

15:00-16:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Vjacheslav Yurko (Saratov University)
Inverse problems for differential operators on spatial networks (ENGLISH)

### 2012/10/16

#### Tuesday Seminar on Topology

17:10-18:10   Room #056 (Graduate School of Math. Sci. Bldg.)
Ken-Ichi Yoshikawa (Kyoto University)
Analytic torsion of log-Enriques surfaces (JAPANESE)
[ Abstract ]
Log-Enriques surfaces are rational surfaces with nowhere vanishing
pluri-canonical forms. We report the recent progress on the computation
of analytic torsion of log-Enriques surfaces.

### 2012/10/15

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
An L^2 estimate on domains and application to Levi-flat surfaces (JAPANESE)

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yoshinori Gongyo (University of Tokyo)
On the moduli b-divisors of lc-trivial fibrations (JAPANESE)
[ Abstract ]
Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro's result on klt-trivial fibrations. Moreover I may explain some applications of canonical bundle formulas. These are joint works with Osamu Fujino.

### 2012/10/12

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Antonio Siconolfi (La Sapienza - University of Rome)
Homogenization on arbitrary manifolds (ENGLISH)
[ Abstract ]
We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.

### 2012/10/09

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Michihiko Fujii (Kyoto University)
The growth series of pure Artin groups of dihedral type (JAPANESE)
[ Abstract ]
In this talk, I consider the kernel of the natural projection from
the Artin group of dihedral type to the corresponding Coxeter group,
that we call a pure Artin group of dihedral type,
and present rational function expressions for both the spherical and
geodesic growth series
of the pure Artin group of dihedral type with respect to a natural
generating set.
Also, I show that their growth rates are Pisot numbers.
This talk is partially based on a joint work with Takao Satoh.

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Takuma Kimura (Waseda University)
On the numerical verification method for parabolic problems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2012/10/06

#### Harmonic Analysis Komaba Seminar

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Shuichi Sato (Kanazawa university) 13:30-15:00
Method of rotations with weight for nonisotropic dilations (JAPANESE)
( ) 15:30-17:00
TBA (JAPANESE)

### 2012/10/05

#### Seminar on Probability and Statistics

14:50-16:00   Room #006 (Graduate School of Math. Sci. Bldg.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)
[ Abstract ]

"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな
"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.
Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,

[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html

### 2012/10/02

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Akito Futaki (The University of Tokyo)
Geometric flows and their self-similar solutions
(JAPANESE)
[ Abstract ]
In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,
namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein
problem. In the second half of this talk we consider the mean curvature flow and its self-similar
solutions, and see common aspects of the two geometric flows.

### 2012/10/01

#### Algebraic Geometry Seminar

13:30-15:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Robert Laterveer (CNRS, IRMA, Université de Strasbourg)
Weak Lefschetz for divisors (ENGLISH)
[ Abstract ]
Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.