## Seminar information archive

### 2010/10/04

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hideyuki ISHI (Nagoya Univ)
The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)
[ Abstract ]
For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.
Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

### 2010/09/28

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Pavel Exner (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ Abstract ]
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.

### 2010/09/14

#### Infinite Analysis Seminar Tokyo

10:30-14:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Shintarou Yanagida (Kobe Univ.) 10:30-11:30
AGT conjectures and recursion formulas (JAPANESE)
classification of solutions to the reflection equation associated to
trigonometrical $R$-matrix of Belavin (JAPANESE)

### 2010/09/13

#### Infinite Analysis Seminar Tokyo

10:30-15:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Masahiro Kasatani (Tokyo Univ.) 10:30-11:30
Polynomial representations of DAHA of type $C^¥vee C$ and boundary qKZ equations (JAPANESE)
[ Abstract ]
First I will review basic facts about
the double affine Hecke algebra of type $C^¥vee C$
and its polynomial representation.
Next I will intrduce a boundary qKZ equation
and construct its solution in terms of the polynomial representation.
CFT, Isomonodromy deformations and Nekrasov functions (JAPANESE)
[ Abstract ]
This talk is an introduction to the relation between conformal filed
theories
and super symmetric gauge theories (Alday-Gaiotto-Tachikawa conjecture)
from the point of view of differential equations (in particular
isomonodromy
deformations).
Katsuhisa Mimachi (Tokyo Institute of Technology) 14:30-15:30
Twisted de Rham theory---resonances and the non-resonance (JAPANESE)

### 2010/09/12

#### Infinite Analysis Seminar Tokyo

10:30-17:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Hideaki Morita (Muroran Institute of Technology) 10:30-11:30
A factorization formula for Macdonald polynomials at roots of unity (JAPANESE)
[ Abstract ]
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
Junichi Shiraishi (Tokyo Univ.) 13:00-14:00
W algebras and symmetric polynomials (JAPANESE)
[ Abstract ]
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
Koji Hasegawa (Tohoku Univ.) 14:30-15:30
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
[ Abstract ]
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
Yasuhide Numata (Graduate School of Information Science and Technology, Tokyo Univ.) 16:00-17:00
On a bijective proof of a factorization formula for Macdonald
polynomials at roots of unity (JAPANESE)
[ Abstract ]
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)

### 2010/09/11

#### Infinite Analysis Seminar Tokyo

13:00-17:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Masahiko Ito (School of Science and Technology for Future Life, Tokyo Denki University) 13:00-14:00
Three-term recurrence relations for a $BC_n$-type basic hypergeometric function and their application (JAPANESE)
[ Abstract ]
$BC_n$-type basic hypergeometric series are a certain $q$-analogue
of an integral representation for the Gauss hypergeometric function.
They are defined as multiple $q$-series satisfying Weyl group symmetry of type $C_n$,
and they are a multi-sum generalization of the basic hypergeometric series
in a class of what is called (very-)well-poised. In my talk I will explain
an explicit expression for the $q$-difference system of rank $n+1$
satisfied by a $BC_n$-type basic hypergeometric series with 6+1 parameters
as first order simultaneous $q$-difference equations with a concrete basis.
For this purpose I introduce two types of symmetric Laurent polynomials
which I call the $BC$-type interpolation polynomials. The polynomials satisfy
three-term relations like a contiguous relation for the Gauss hypergeometric
function. As an application, I will show another proof for the product formula
of the $q$-integral introduced by Gustafson.
Masatoshi Noumi (Kobe Univ.) 14:30-15:30
TBA (JAPANESE)
Masato Taki (YITP Kyoto Univ.) 16:00-17:00
AGT conjecture and geometric engineering (JAPANESE)

### 2010/09/09

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
[ Abstract ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.

This is Part 3 of a 3-part lecture.

### 2010/09/06

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Prof. Remke Kloosterman (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
[ Abstract ]
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.

### 2010/09/04

#### Lectures

09:30-11:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
[ Abstract ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.

This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.

#### Lectures

11:10-12:40   Room #126 (Graduate School of Math. Sci. Bldg.)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
[ Abstract ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.

This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.

### 2010/09/03

#### Lectures

14:30-15:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Luc Robbiano (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
[ Abstract ]
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.

One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.

If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.

### 2010/09/01

#### Lie Groups and Representation Theory

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Bernhard M\"uhlherr (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
[ Abstract ]
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.

In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.

#### thesis presentations

16:30-17:45   Room #123 (Graduate School of Math. Sci. Bldg.)
Naoki IMAI (Graduate School of Mathematical Sciences the University of Tokyo )
On the moduli spaces of finite flat models of Galois representations (JAPANESE)

### 2010/08/06

#### Lectures

15:30-17:45   Room #370 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University) 15:30-16:30
A Spectral Method for Space--
Time Fractional Diffusion Equation (ENGLISH)
Mourad Choulli (University of Metz) 16:45-17:45
A multidimensional Borg-Levinson theorem (ENGLISH)

#### GCOE Seminars

15:00-16:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Matthieu Alfaro (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
[ Abstract ]
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.

### 2010/08/05

#### Lectures

16:30-17:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems (ENGLISH)

#### Lectures

16:30-17:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Yongzhi Steve Xu (University of Louisville, USA)
Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)

### 2010/07/30

#### GCOE Seminars

16:30-17:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
[ Abstract ]
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.

### 2010/07/29

#### Algebraic Geometry Seminar

14:30-16:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masahiro Futaki (The University of Tokyo)
Homological Mirror Symmetry for 2-dimensional toric Fano stacks (JAPANESE)
[ Abstract ]
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).

We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.

We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).

### 2010/07/28

#### 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.)
Issei Oikawa (University of Tokyo)
Hybridized discontinuous Galerkin method for a convection-diffusion equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2010/07/27

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ayumu Inoue (Tokyo Institute of Technology)
Quandle homology and complex volume
(Joint work with Yuichi Kabaya) (JAPANESE)
[ Abstract ]
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.

#### thesis presentations

16:00-17:15   Room #123 (Graduate School of Math. Sci. Bldg.)
Ryoko TOMIYASU (graduate school of Mathematical Sciences)
On some algebraic properties of CM-types of CM-fields and their reflexes (JAPANESE)

### 2010/07/22

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Owen Sizemore (UCLA)
$W^*$ Rigidity for actions of wreath product groups (ENGLISH)
[ Abstract ]
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.

### 2010/07/20

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Keiko Kawamuro (University of Iowa)
A polynomial invariant of pseudo-Anosov maps (JAPANESE)
[ Abstract ]
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)