## Seminar information archive

### 2010/06/24

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Thomas Sinclair (Vanderbilt Univ.)
Strong solidity of factors from lattices in SO(n,1) and SU(n,1) (ENGLISH)
[ Abstract ]
Generalizing techniques found in Ozawa and Popa,
On a class of II$_1$ factors with at most one Cartan subalgebra, II''
(Amer. J. Math., to appear), we show that the group factors of ICC
lattices in SO(n,1) and SU(n,1), $n\\ge2$, are strongly solid. If
time permits, we will also discuss applications to $L^2$-rigidity.

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Hideki Murakawa (University of Toyama)
Reaction-diffusion approximation to nonlinear diffusion problems (JAPANESE)

#### GCOE Seminars

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

### 2010/06/23

#### GCOE Seminars

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Reference URL ]
http://www.infsup.jp/utnas/

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Hideki Murakawa (University of Toyama)
Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2010/06/22

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
[ Abstract ]
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.

### 2010/06/21

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Toru Tsukioka (Osaka Prefecture University)
Pseudo-index and minimal length of extremal rays for Fano manifolds (JAPANESE)
[ Abstract ]
The minimum of intersection numbers of the anticanonical
divisor with rational curves on a Fano manifold is called pseudo-index.
In view of the fact that the geometry of Fano manifolds is governed by
its extremal rays, it is important to consider the extremal rational
curves. In this talk, we show that for Fano 4-folds having birational
contractions, the minimal length of extremal rays coincides with the
pseudo-index.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Sachiko HAMANO (Fukushima Univ)
A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

### 2010/06/17

#### GCOE lecture series

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)

#### Classical Analysis

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Teruhisa Tsuda (University of Kyushu)
On a class of the Schlesinger systems (JAPANESE)

### 2010/06/16

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Luc Illusie (Universite de Paris-Sud)
Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)
[ Abstract ]
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.

### 2010/06/15

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
Sato's counterexample and the structure of generalized functions (JAPANESE)
[ Abstract ]
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuhiro Ichihara (Nihon University)
On exceptional surgeries on Montesinos knots
(joint works with In Dae Jong and Shigeru Mizushima) (JAPANESE)
[ Abstract ]
I will report recent progresses of the study on exceptional
surgeries on Montesinos knots.
In particular, we will focus on how homological invariants (e.g.
khovanov homology,
knot Floer homology) on knots can be used in the study of Dehn surgery.

### 2010/06/14

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Yongnam Lee (Sogang University)
Slope of smooth rational curves in an anticanonically polarized Fano manifold (ENGLISH)
[ Abstract ]
Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuko MATSUMOTO (Osaka Prefecture University)
Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

### 2010/06/11

#### Colloquium

17:00-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Masaaki Umehara (Osaka University)
The Gauss-Bonnet Theorem and singular points on surfaces (JAPANESE)
[ Abstract ]
We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.

### 2010/06/10

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Christian Klingenberg (Wuerzburg 大学 )
Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models
[ Abstract ]
In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.

In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions

u_t + f(u, x)_x = 0 .

We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.

In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (IPMU)
Random groups and nonarchimedean lattices (JAPANESE)

### 2010/06/09

#### Number Theory Seminar

16:15-17:15   Room #052 (Graduate School of Math. Sci. Bldg.)
Richard Hain (Duke University)
Universal mixed elliptic motives (ENGLISH)
[ Abstract ]
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.

#### Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Fabrice Orgogozo (CNRS, École polytechnique)
Constructibilité uniforme des images directes supérieures en
cohomologie étale
(ENGLISH)
[ Abstract ]
Motivé par une remarque de N. Katz sur le lien entre la
torsion de la Z_ℓ-cohomologie étale et les ultraproduits de groupes de
F_ℓ-cohomologie, nous démontrons un théorème d'uniformité en ℓ pour la
constructibilité des images directes supérieures entre schémas de type fini
sur un trait excellent. (Un tel théorème avait été considéré par
O. Gabber il y a plusieurs années déjà.)
La méthode est maintenant classique : on utilise des
théorèmes de A. J. de Jong et un peu de log-géométrie.

(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted from IHES by the internet.)

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Junichi Matsumoto (National Institute of Advanced Industrial Science and Technology)
A bubble finite-element method with orthogonal property and applications to flow problems (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/saito/

#### GCOE Seminars

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)

[ Reference URL ]
http://www.infsup.jp/utnas/

#### Seminar on Probability and Statistics

15:00-16:10   Room #000 (Graduate School of Math. Sci. Bldg.)
KAMATANI, Kengo (Graduate school of Mathematical Sciences, Univ. of Tokyo)
Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)
[ Abstract ]
We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.

This talk will be held at IT Studio.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

### 2010/06/08

#### Lie Groups and Representation Theory

17:00-18:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Soji Kaneyuki (Sophia University)
Automorphism groups of causal Makarevich spaces (JAPANESE)
[ Abstract ]
Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov
boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that
of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.
In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.