## Seminar information archive

#### Mathematical Biology Seminar

14:50-16:20   Room #122 (Graduate School of Math. Sci. Bldg.)
Yumi YAHAGI (Tokyo City University)
A probabilistic interpretation of an evolution model of slime bacteria

(JAPANESE)

### 2014/12/16

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Haruya Mizutani (Graduate School of Science, Osaka University)
Global Strichartz estimates for Schr¥”odinger equations on
asymptotically conic manifolds (Japanese)

#### Tuesday Seminar on Topology

17:10-18:10   Room #056 (Graduate School of Math. Sci. Bldg.)
Norio Iwase (Kyushu University)
Differential forms in diffeological spaces (JAPANESE)
[ Abstract ]
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.

### 2014/12/15

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hajime Tsuji (Sophia University)
The limits of Kähler-Ricci flows

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Akiyoshi Sannai (University of Tokyo)
A characterization of ordinary abelian varieties in positive characteristic (JAPANESE)
[ Abstract ]
This is joint work with Hiromu Tanaka. In this talk, we study F^e_*O_X on a projective variety over the algebraic closed field of positive characteristic. For an ordinary abelian variety X, F^e_*O_X is decomposed into line bundles for every positive integer e. Conversely, if a smooth projective variety X satisfies this property and its Kodaira dimension is non-negative, then X is an ordinary abelian variety.

### 2014/12/11

#### Infinite Analysis Seminar Tokyo

15:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Yohei Kashima (Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30
Renormalization group method for many-electron systems (JAPANESE)
[ Abstract ]
We consider quantum many-body systems of electrons
hopping and interacting on a lattice at positive temperature.
As it is possible to write down each order term rigorously in
principle, the perturbation series expansion with the coupling
constant between electrons is thought as a valid method to
compute physical quantities. By directly estimating each term,
one can prove that the perturbation series is convergent if the
coupling constant is less than some power of temperature. This is,
however, a serious constraint for models of interacting electrons
in low temperature. In order to ensure the analyticity of physical
quantities of many-electron systems with the coupling constant in
low temperature, renormalization group methods have been developed
in recent years. As one progress in this direction, we construct a
renormalization group method for the half-filled Hubbard model on a
square lattice, which is a typical model of many-electron, and prove
the following. If the system contains the magnetic flux pi (mod 2 pi)
per plaquette, the free energy density of the system is analytic with
the coupling constant in a neighborhood of the origin and it uniformly
converges to the infinite-volume, zero-temperature limit. It is known
that the flux pi condition is sufficient for the free energy density
to be minimum. Thus, it follows that the same analyticity and the
convergent property hold for the minimum free energy density of the
system.

Genki Shibukawa (Institute of Mathematics for Industory, Kyushu University) 17:00-18:30
Unitary transformations and multivariate special
orthogonal polynomials (JAPANESE)
[ Abstract ]
Investigations into special orthogonal function systems by
using unitary transformations have a long history.
This is, by calculating an image of some unitary transform (e.g. Fourier
trans.) of a known orthogonal system, we derive a new orthogonal system
and obtain its fundamental properties.
This basic concept and technique have been known since ancient times for
a single variable case, and recently these multivariate analogue has
been studied by Davidson, Olafsson, Zhang, Faraut, Wakayama et.al..

In our talk, we introduce the unitary picture for the circular Jacobi
polynomials obtained by Shen, further give a multivariate analogue of
the results of Shen.
These polynomials, which we call multivariate circular Jacobi (MCJ)
polynomials, are generalizations (2-parameter deformation) of the
spherical (zonal) polynomials that are different from the Jack or
Macdonald polynomials, which are well known as an extension of spherical
polynomials.
We also remark that the weight function of their orthogonality relation
coincides with the circular Jacobi ensemble defined by Bourgade,et,al.,
and the modified Cayley transform of the MCJ polynomials satisfy with
some quasi differential equation.
In addition, we can give a generalization of MCJ polynomials as
including the Jack polynomials.
For this generalized MCJ polynomials, we would like to present some
conjectures and problems.

If we have time, we also describe a unitary picture of Meixner,
Charlier and Krawtchouk polynomials which are typical examples of
discrete orthogonal systems, and mention their multivariate analogue.

### 2014/12/10

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Akitaka Kishimoto (Hokkaido Univ.)
Approximately inner flows on $C^*$-algebras (English)

#### FMSP Lectures

16:00-17:30   Room #118 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
[ Abstract ]
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.

### 2014/12/09

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Koji Fujiwara (Kyoto University)
Stable commutator length on mapping class groups (JAPANESE)
[ Abstract ]
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.

Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.

### 2014/12/08

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masatake Tomari (Nihon University)
On maximal ideal cycle and fundamental cycle of normal two-dimensional quasi-homogeneous singularities, and singularities with star-shaped resolution (JAPANESE)

### 2014/12/04

#### Geometry Colloquium

17:00-18:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Ryushi Goto (Osaka University)
Deformations and the moduli spaces of generalized complex manifolds (JAPANESE)

### 2014/12/03

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yuki Arano (Univ. Tokyo)
Central property (T) for $SU_q(2n+1)$
(English)

#### Lectures

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Xavier Cabre (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities, part II: Detailed proofs and related works (ENGLISH)
[ Abstract ]
This is a sequel to the Tuesday Analysis Seminar on December 2 by the same speaker.
In joint works with X. Ros-Oton and J. Serra, the study of the regularity of stable solutions to reaction-diffusion problems has led us to certain Sobolev and isoperimetric inequalities with weights. We will present our results in these new isoperimetric inequalities with the best constant, that we establish via the ABP method.
More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (or densities) in open convex cones of R^n. Our results apply to all nonnegative homogeneous weights satisfying a concavity condition in the cone. Surprisingly, even that our weights are not radially symmetric, Euclidean balls centered at the origin (intersected with the cone) minimize the weighted isoperimetric quotient. As a particular case of our results, we provide with new proofs of classical results such as the Wulff inequality and the isoperimetric inequality in convex cones of Lions and Pacella. Furthermore, we also study the anisotropic isoperimetric problem for the same class of weights and we prove that the Wulff shape always minimizes the anisotropic weighted perimeter under the weighted volume constraint.

#### Mathematical Biology Seminar

14:50-16:20   Room #122 (Graduate School of Math. Sci. Bldg.)
Toshikazu Kuniya (Graduate School of System Informatics, Kobe University)
Global analysis of age-structured SIS epidemic models with spatial
heterogeneity (JAPANESE)

### 2014/12/02

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yosuke Kubota (The University of Tokyo)
The Atiyah-Segal completion theorem in noncommutative topology (JAPANESE)
[ Abstract ]
We introduce a new perspevtive on the Atiyah-Segal completion
theorem applying the "noncommutative" topology, which deals with
topological properties of C*-algebras. The homological algebra of the
Kasparov category as a triangulated category, which is developed by R.
Meyer and R. Nest, plays a central role. It contains the Atiyah-Segal
type completion theorems for equivariant K-homology and twisted K-theory.
This is a joint work with Yuki Arano.

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Tsubasa Itoh (Tokyo Institute of Technology)
Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner (JAPANESE)
[ Abstract ]
In this talk, the two dimensional Euler flow under a simple symmetry condition with hyperbolic structure in a unit square $D=\{(x_{1}, x_{2}): 0 < x_{1} + x_{2} < \sqrt{2},\ 0<-x_{1} + x_{2} < \sqrt{2}\}$ is considered.
It is shown that the Lipschitz estimate of the vorticity on the boundary is at most single exponential growth near the stagnation point.
(Joint work with Tsuyoshi Yoneda and Hideyuki Miura.)

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Xavier Cabre (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities arising in reaction-diffusion problems (English)
[ Abstract ]
In joint works with X. Ros-Oton and J. Serra, the study of the
regularity of stable solutions to reaction-diffusion problems
has led us to certain Sobolev and isoperimetric inequalities
with weights.  We will present our results in these new
isoperimetric inequalities with the best constant, that we
establish via the ABP method.  More precisely, we obtain
a new family of sharp isoperimetric inequalities with weights
(or densities) in open convex cones of R^n. Our results apply
to all nonnegative homogeneous weights satisfying a concavity
condition in the cone. Surprisingly, even that our weights are
not radially symmetric, Euclidean balls centered at the origin
(intersected with the cone) minimize the weighted isoperimetric
quotient. As a particular case of our results, we provide with
new proofs of classical results such as the Wulff inequality and
the isoperimetric inequality in convex cones of Lions and Pacella.
Furthermore, we also study the anisotropic isoperimetric problem
for the same class of weights and we prove that the Wulff shape
always minimizes the anisotropic weighted perimeter under the
weighted volume constraint.

### 2014/12/01

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
Effective and noneffective extension theorems (Japanese)
[ Abstract ]
As an effective extension theorem, I will review the sharp $L^2$ extension theorem explaining the ideas of its proofs due to Blocki and Guan-Zhou. A new proof using the Poincare metric with be given, too. As a noneffective extension theorem, I will talk about an extension theorem from semipositive divisors. It is obtained as an application of an isomorphism theorem which is essentially contained in my master thesis.

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Malte Wandel (RIMS)
Induced Automorphisms on Hyperkaehler Manifolds (ENGLISH)
[ Abstract ]
in this talk I want to report on a joint project with Giovanni Mongardi (Milano). We study automorphisms of hyperkaehler manifolds. All known deformation classes of these manifolds contain moduli spaces of stable sheaves on surfaces. If the underlying surface admits a non-trivial automorphism, it is often possible to transfer this automorphism to a moduli space of sheaves. In this way we obtain a big class of interesting examples of automorphisms of hyperkaehler manifolds. I will present a criterion to 'detect' automorphisms in this class and discuss several applications for the classification of automorphisms of manifolds of K3^[n]- and kummer n-type. If time permits I will try to talk about generalisations to O'Grady's sporadic examples.

#### Numerical Analysis Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yusuke Imoto (Kyushu University)
An error estimate of a generalized particle method for Poisson equations
(日本語)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2014/11/28

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Hiroshi Nishiura (Graduate School of Medicine, The University of Tokyo)
Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue
(JAPANESE)
[ Abstract ]
The basic and effective reproduction numbers offer epidemiological
insights into the growth of generations of infectious disease cases,
informing the required control effort. Recently, the renewal process
model has appeared to be a usefu tool for quantifying the reproduction
numbers in real-time using only case data. Here I present methods,
results and pitfalls of the use of renewal process model, presenting
recent case studies of Ebola virus disease epidemic in West Africa and a
massive epidemic of dengue fever in the summer of Japan 2014.
[ Reference URL ]
http://www.ghp.m.u-tokyo.ac.jp/profile/staff/hnishiura/

### 2014/11/26

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yi-Zhi Huang (Rutgers Univ.)
A program to construct and study conformal field theories (ENGLISH)

#### Lectures

16:00-17:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Mykhaylo Shkolnikov (Princeton University)
Intertwinings, wave equations and beta ensembles (ENGLISH)
[ Abstract ]
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to wave equations and more general hyperbolic partial differential equations. The talk will be devoted to this recent development, as well as an algebraic perspective on intertwinings which, in particular, gives rise to a novel intertwining in beta random matrix theory. Based on joint works with Vadim Gorin and Soumik Pal.

#### Seminar on Probability and Statistics

16:30-17:40   Room #052 (Graduate School of Math. Sci. Bldg.)
KATAYAMA, Shota (Tokyo Institute of Technology)
Sparse and robust linear regression: Iterative algorithm and its statistical convergence

### 2014/11/25

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kenichi Ito (Department of Mathematics, Graduate School of Science, Kobe University)
Stationary scattering theory on manifold with ends (JAPANESE)