## Seminar information archive

### 2011/01/17

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Dano Kim (KIAS)
L^2 methods and Skoda division theorems (ENGLISH)
[ Abstract ]
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Toshihiro Nose (Kyushu Univ.)
Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)
[ Abstract ]
In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

### 2011/01/13

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Robert Coquereaux (CNRS/CPT)
Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)

### 2011/01/12

#### Number Theory Seminar

16:30-18:45   Room #056 (Graduate School of Math. Sci. Bldg.)
Zhonghua Li (University of Tokyo) 16:30-17:30
On regularized double shuffle relation for multiple zeta values (ENGLISH)
[ Abstract ]
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki (North Carolina University) 17:45-18:45
Spines with View Toward Modular Forms (ENGLISH)
[ Abstract ]
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.

### 2011/01/11

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Nariya Kawazumi (The University of Tokyo)
The Chas-Sullivan conjecture for a surface of infinite genus (JAPANESE)
[ Abstract ]
Let \\Sigma_{\\infty,1} be the inductive limit of compact
oriented surfaces with one boundary component. We prove the
center of the Goldman Lie algebra of the surface \\Sigma_{\\infty,1}
is spanned by the constant loop.
A similar statement for a closed oriented surface was conjectured
by Chas and Sullivan, and proved by Etingof. Our result is deduced
from a computation of the center of the Lie algebra of oriented chord
diagrams.
If time permits, the Lie bracket on the space of linear chord diagrams
will be discussed. This talk is based on a joint work with Yusuke Kuno
(Hiroshima U./JSPS).

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (Univ. Tokyo)
Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Takehiko Kinoshita (RIMS)
Norm estimates of inverse linear ordinary differential operator and its applications (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2010/12/22

#### GCOE Seminars

11:00-12:00   Room #570 (Graduate School of Math. Sci. Bldg.)
Mourad Bellassoued (Faculté des Sciences de Bizerte)
Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)
[ Abstract ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Takashi Hara (University of Tokyo)
Inductive construction of the p-adic zeta functions for non-commutative
p-extensions of totally real fields with exponent p (JAPANESE)
[ Abstract ]
We will discuss how to construct p-adic zeta functions and verify
the main conjecture in special cases in non-commutative Iwasawa theory
for totally real number fields.

The non-commutative Iwasawa main conjecture for totally real number
fields has been verified in special cases by Kazuya Kato,
Mahesh Kakde and the speaker by `patching method of p-adic zeta functions'
introduced by David Burns and Kazuya Kato (Jurgen Ritter and Alfred Weiss
have also constructed the successful example of the main conjecture
under somewhat different formulations).

In this talk we will explain that we can prove the main conjecture
for cases where the Galois group is isomorphic
to the direct product of the ring of p-adic integer and a finite p-group
of exponent p by utilizing Burns-Kato's method and inductive arguments.

Finally we remark that in 2010 Ritter-Weiss and Kakde independently
justified the non-commutative main conjecture
for totally real number fields under general settings.

### 2010/12/21

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Katsuyuki NAOI (Graduate School of Mathematical Sciences, the University of Tokyo)
Some relation between the Weyl module and the crystal basis of the tensor product of fudamental representations (ENGLISH)

### 2010/12/20

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshi Yamaguchi (Shiga Univ*)
Pseudoconvex domains in Hopf surfaces (JAPANESE)

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshinori Gongyo (Univ. of Tokyo)
On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)
[ Abstract ]
I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)

### 2010/12/16

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Marco Merkli (Memorial Univ. Newfoundland)
Evolution of Quantum Dynamical Systems (ENGLISH)

#### Operator Algebra Seminars

15:15-16:15   Room #122 (Graduate School of Math. Sci. Bldg.)
Nicolas Monod (EPFL)
Fixed point theorems and derivations (ENGLISH)

#### Lectures

13:00-14:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Sebastien Hitier (BNP Paribas, Head of Quantitative Research, Credit Asia)
Credit Derivatives Modelling and the concept of Background Intensity I (ENGLISH)
[ Abstract ]
Session 1: Introducing background intensity models
- Motivation for the concept of background intensity
- The default realisation marker
- Definition of background filtration and background intensity
- Reformulating the H hypothesis, and Kusuoka’s “remark”
- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models
- Generalised HJM formula for credit
- Definition of conditionally independent defaults
- Diversification effects: results on forward loss distribution
- Stronger conditional independence effect for spot loss
- Existence of a canonical copula
- Properties of the portfolio loss copula

#### Lectures

14:40-16:10   Room #123 (Graduate School of Math. Sci. Bldg.)
Sebastien Hitier (BNP Paribas, Head of Quantitative Research, Credit Asia)
Credit Derivatives Modelling and the concept of Background Intensity II (ENGLISH)
[ Abstract ]
Session 1: Introducing background intensity models
- Motivation for the concept of background intensity
- The default realisation marker
- Definition of background filtration and background intensity
- Reformulating the H hypothesis, and Kusuoka’s “remark”
- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models
- Generalised HJM formula for credit
- Definition of conditionally independent defaults
- Diversification effects: results on forward loss distribution
- Stronger conditional independence effect for spot loss
- Existence of a canonical copula
- Properties of the portfolio loss copula

### 2010/12/14

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kenneth Schackleton (IPMU)
On the coarse geometry of Teichmueller space (ENGLISH)
[ Abstract ]
We discuss the synthetic geometry of the pants graph in
comparison with the Weil-Petersson metric, whose geometry the
pants graph coarsely models following work of Brock’s. We also
restrict our attention to the 5-holed sphere, studying the Gromov
bordification of the pants graph and the dynamics of pseudo-Anosov
mapping classes.

### 2010/12/13

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
An equality estimate for the second main theorem (JAPANESE)

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Sergey Fomin (University of Michigan)
Enumeration of plane curves and labeled floor diagrams (ENGLISH)
[ Abstract ]
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.

This is joint work with Grisha Mikhalkin.

### 2010/12/10

#### Colloquium

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Yoshikazu Giga (The University of Tokyo, Graduate School of Mathematical Sciences)
Hamilton-Jacobi equations and crystal growth (JAPANESE)

### 2010/12/09

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Ryszard Nest (Univ. Copenhagen)
Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)

### 2010/12/07

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (The University of Tokyo)
Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)
[ Abstract ]
In many geometric situations we may encounter the action of
a group $G$ on a manifold $M$, e.g., in the context of foliations. If
the action is free and proper, then the quotient $M/G$ is a smooth
manifold. However, in general the quotient $M/G$ need not even be
Hausdorff. Furthermore, it is well-known that a manifold has structure
invariant under the full group of diffeomorphisms except the
differentiable structure itself. Under these conditions how can one do
diffeomorphism-invariant geometry?

Noncommutative geometry provides us with the solution of trading the
ill-behaved space $M/G$ for a non-commutative algebra which
essentially plays the role of the algebra of smooth functions on that
space. The local index formula of Atiyah-Singer ultimately holds in
the setting of noncommutative geometry. Using this framework Connes
and Moscovici then obtained in the 90s a striking reformulation of the
local index formula in diffeomorphism-invariant geometry.

An important part the talk will be devoted to reviewing noncommutative
geometry and Connes-Moscovici's index formula. We will then hint to on-
going projects about reformulating the local index formula in two new
geometric settings: biholomorphism-invariant geometry of strictly
pseudo-convex domains and contactomorphism-invariant geometry.

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Akitoshi Takayasu (Waseda University)
Numerical verification of existence for solutions to Dirichlet
boundary value problems of semilinear elliptic equations
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2010/12/06

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hajime Ono (Tokyo Univ of Science)
Chow semistability of polarized toric manifolds (JAPANESE)

### 2010/12/04

#### Classical Analysis

09:30-10:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Toshihiko Matsuki (Kyoto University)
Orbit decomposition of multiple flag varieties and representations of of quiver (JAPANESE)