Seminar information archive

2014/06/10

Lectures

14:40-16:10   Room #056 (Graduate School of Math. Sci. Bldg.)
Sergei Duzhin (Steklov Institute of Mathematics)
Bipartite knots (ENGLISH)
[ Abstract ]
We give a solution to a part of Problem 1.60 in Kirby's list of open
problems in topology thus proving a conjecture raised in 1987 by
J.Przytycki. A knot is said to be bipartite if it has a "matched" diagram,
that is, a plane diagram that has an even number of crossings which can be
split into pairs that look like a simple braid on two strands with two
crossings. The conjecture was that there exist knots that do not have such
diagrams. I will prove this fact using higher Alexander ideals.
This talk is based on a joint work with my student M.Shkolnikov

Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshifumi Kimura (Graduate School of Mathematics, Nagoya University)
The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)
[ Abstract ]
A system of N point vortices is a Hamiltonian dynamical system with N degrees of freedom,and it is known that under certain parameter and initial conditions, there are self-similar collapse solutions for which N vortices collide at a point while rotating without changing the initial shape of configuration. In this talk, I will introduce such collision solutions and discuss some properties of complex time singularities in relation with those solutions.

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Ken Abe (Nagoya University)
On estimates for the Stokes flow in a space of bounded functions (JAPANESE)
[ Abstract ]
The Stokes equations are well understood on $L^p$ space for various kinds of domains such as bounded or exterior domains, and fundamental to study the nonlinear Navier-Stokes equations. The situation is different for the case $p=\\infty$ since in this case the Helmholtz projection does not act as a bounded operator anymore. In this talk, we show some a priori estimate for a composition operator of the Stokes semigroup and the Helmholtz projection on a space of bounded functions.

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yuka Kotorii (The University of Tokyo)
On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
[ Abstract ]
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥ bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.

2014/06/09

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Ryosuke Takahashi (Nagoya University)
Modified Kähler-Ricci flow on projective bundles (JAPANESE)

Numerical Analysis Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Issei Oikawa (Waseda University)
A hybridized discontinuous Galerkin method with weak stabilization (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

2014/06/06

Colloquium

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikhail Kapranov (Kavli IPMU)
Lie algebras from secondary polytopes (ENGLISH)
[ Abstract ]
The secondary polytope of a point configuration
in the Euclidean space was introduced by Gelfand, Zelevinsky
and the speaker long time ago in order to understand discriminants
of multi-variable polynomials. These polytopes have
a remarkable factorization (or operadic) property: each
face of any secondary polytope is isomorphic to the
product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich
and Y. Soibelman, will explain how the factorization property
can be used to construct Lie algebra-type objects:
$L_¥infty$ and $A_¥infty$-algebras. These algebras
turn out to be related to the problem of deformation
of triangulated categories with semiorthogonal decompositions.

2014/06/04

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Ion Nechita (Univ. Paul Sabatier)
Positive and completely positive maps via free additive powers of probability measures (ENGLISH)

2014/06/03

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuru Takakura (Chuo University)
Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
[ Abstract ]
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
using
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.

2014/06/02

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (Nagano National College of Technology)
Generalized pseudoellipsoids and proper holomorphic mappings between them (JAPANESE)

Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yusuke Nakamura (University of Tokyo)
On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)
[ Abstract ]
We will discuss about the base point free theorem on three-dimensional
pairs defined over the algebraic closure of a finite field.

We know the base point free theorem on arbitrary-dimensional Kawamata
log terminal pairs in characteristic zero. By Birkar and Xu, the base
point free theorem in positive characteristic is known for big line
bundles on three-dimensional Kawamata log terminal pairs defined over
an algebraically closed field of characteristic larger than 5. Over the
algebraic closure of a finite field, a stronger result was proved by Keel.

The purpose of this talk is to generalize the Keel's result. We will
prove the base point free theorem for big line bundles on
three-dimensional log canonical pairs defined over the algebraic closure
of a finite field. This theorem is not valid for another field.

This is joint work with Diletta Martinelli and Jakub Witaszek.

2014/05/28

Number Theory Seminar

16:40-17:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Gantsooj Batzaya (University of Tokyo)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Ochanomizu University)
Poisson boundary of monoidal categories (ENGLISH)

Mathematical Biology Seminar

14:50-16:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Keisuke Ejima (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo
)
Modeling the social contagion: The obesity epidemic and its control (JAPANESE)
[ Abstract ]
:As an obesity epidemic has grown worldwide, a variety of
intervention programs have been considered, but a scientific approach
to comparatively assessing the control programs has still to be
considered. The present study aims to describe an obesity epidemic by
employing a simple mathematical model that accounts for both social
contagion and non-contagious hazards of obesity, thereby comparing the
effectiveness of different types of interventions.
An epidemiological model is devised to describe the time- and
age-dependent risk of obesity, the hazard of which is dealt with as
both dependent on and independent of obesity prevalence, and
parameterizing the model using empirically observed data. The
equilibrium prevalence is investigated as our epidemiological outcome,
assessing its sensitivity to different parameters that regulate the
impact of intervention programs and qualitatively comparing the
effectiveness. We compare the effectiveness of different types of
interventions, including those directed to never-obese individuals
(i.e. primary prevention) and toward obese and ex-obese individuals
(i.e. secondary prevention).
The optimal choice of intervention programs considerably varies with
the transmission coefficient of obesity, and a limited
transmissibility led us to favour preventing weight gain among
never-obese individuals. An abrupt decline in the prevalence is
expected when the hazards of obesity through contagious and
non-contagious routes fall into a particular parameter space, with a
high sensitivity to the transmission potential of obesity from person
to person. When a combination of two control strategies can be
selected, primary and secondary preventions yielded similar population
impacts and the superiority of the effectiveness depends on the
strength of the interventions at an individual level.
The optimality of intervention programs depends on the contagiousness
of obesity. Filling associated data gaps of obesity transmission would
help systematically understand the epidemiological dynamics and
consider required control programs.

2014/05/27

Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoichi Miyazaki (NIHON UNIVERSITY, SCHOOL OF DENTISTRY)
The regularity theorem for elliptic equations and the smoothness of domains (JAPANESE)
[ Abstract ]
We consider the Dirichlet boundary problem for a strongly elliptic operator of order $2m$ with non-smooth coefficients, and prove the regularity theorem for $L_p$-based Sobolev spaces when the domain has a boundary of limited smoothness. Compared to the known results, we can weaken the smoothness assumption on the boundary by $m-1$.

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ege Fujikawa (Chiba University)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
[ Abstract ]
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki Watanabe (the University of Tokyo, Graduate School of Mathematical Sciences)
On the structure of Schubert modules and filtration by Schubert modules
(JAPANESE)
[ Abstract ]
One of the methods for studying Schubert polynomials is using
Schubert modules introduced by Kraskiewicz and Pragacz.
In this seminar I will talk about a new result on the structure of
Schubert modules, and give a criterion for a module to have a filtration by Schubert modules.
I will also talk about a problem concerning Schubert polynomials
which motivated this research.

2014/05/22

Geometry Colloquium

10:00-11:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Boris Hasselblatt (Tufts Univ)
Godbillon-Vey invariants for maximal isotropic foliations (ENGLISH)
[ Abstract ]
The combination of a contact structure and an orientable maximal isotropic foliation gives rise to m+1 Godbillon-Vey invariants for an m+1-dimensional maximal isotropic foliation that are of interest with respect to geometric rigidity: by studying these jointly, we give new proofs of famous "rigidity'' results from the 1980s that require only a very few simple lines of reasoning rather than the elaborate original proofs.

2014/05/21

Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Shenghao Sun (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
[ Abstract ]
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.

Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (Tohoku Univ.)
Group approximation in Cayley topology and coarse geometry
part I: coarse embeddings of amenable groups (ENGLISH)

2014/05/20

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Shintaro Kuroki (The Univeristy of Tokyo)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
[ Abstract ]
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya
Masuda.

Seminar on Probability and Statistics

13:00-14:10   Room #052 (Graduate School of Math. Sci. Bldg.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Maximum likelihood type estimation of diffusion processes with non synchronous observations contaminated by market microstructure noise (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html

2014/05/19

Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shigeharu Takayama (University of Tokyo)
On degenerations of Ricci-flat Kähler manifolds (JAPANESE)

2014/05/17

Harmonic Analysis Komaba Seminar

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yohei Tsutsui (The University of Tokyo) 13:30-15:00
Bounded small solutions to a chemotaxis system with non-diffusive chemical (JAPANESE)
[ Abstract ]
We consider a chemotaxis system with a logarithmic sensitivity and a non-diffusive chemical substance. For some chemotactic sensitivity constants, Ahn and Kang proved the existence of bounded global solutions to the system. An entropy functional was used in their argument to control the cell density by the density of the chemical substance. Our purpose is to show the existence of bounded global solutions for all the chemotactic sensitivity constants. Assuming the smallness on the initial data in some sense, we can get uniform estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu Univ.) and Juan J.L. Vel\\'azquez (Univ. of Bonn).
Toshinao Kagawa (Tokyo City University) 15:30-17:00
Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)

2014/05/15

Geometry Colloquium

10:00-11:30   Room #122 (Graduate School of Math. Sci. Bldg.)