## Seminar information archive

### 2011/10/29

#### Infinite Analysis Seminar Tokyo

11:00-14:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Alexander Orlov (Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00-12:00
CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae﻿ and Orthogonal Polynomials both in Odd and Even Variables
(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)
[ Abstract ]
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. ﻿We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.
Yasuho Masuda (Kobe Univ. ) 13:30-14:30
Kernel function identities associated with van Diejen's $q$-difference operators
and transformation formulas for multiple $q$-hypergeometric series (JAPANESE)

### 2011/10/26

#### Seminar on Probability and Statistics

15:00-16:10   Room #000 (Graduate School of Math. Sci. Bldg.)
SEI, Tomonari (Department of Mathematics, Keio University)
Statistical models constructed by optimal stationary coupling (JAPANESE)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

### 2011/10/25

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
[ Abstract ]
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.

We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.

We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.

This is a joint work with Toshitake Kohno.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Localization of Cohomological Induction (ENGLISH)
[ Abstract ]
Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,
principal series representations and Zuckerman's modules of
semisimple Lie groups.
Hecht, Milicic, Schmid, and Wolf proved that modules induced from
one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.
In this talk, we show a similar result for modules induced from
more general representations.

### 2011/10/22

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Leonid Rybnikov (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
[ Abstract ]
Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Anton Zabrodin (
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
[ Abstract ]
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.

### 2011/10/20

#### GCOE Seminars

16:30-18:00   Room #270 (Graduate School of Math. Sci. Bldg.)
On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)
[ Abstract ]
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.

### 2011/10/19

#### Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Suslin (Northwestern University)
K_2 of the biquaternion algebra (ENGLISH)
[ Reference URL ]
http://www.ihes.fr/~abbes/SGA/suslin.pdf

### 2011/10/17

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshinobu Kamishima (Tokyo Metropolitan University)
Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)

### 2011/10/12

#### Seminar on Probability and Statistics

15:00-16:10   Room #000 (Graduate School of Math. Sci. Bldg.)
SUZUKI, Taiji (University of Tokyo)
On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

### 2011/10/11

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Gael Meigniez (Univ. de Bretagne-Sud, Chuo Univ.)
Making foliations of codimension one,
thirty years after Thurston's works
(ENGLISH)
[ Abstract ]
In 1976 Thurston proved that every closed manifold M whose
Euler characteristic is null carries a smooth foliation F of codimension
one. He actually established a h-principle allowing the regularization of
Haefliger structures through homotopy. I shall give some accounts of a new,
simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
On the best constant of the weighted Trudinger-Moser
type inequality (JAPANESE)

### 2011/10/07

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Takeshi Katsura (Keio University)
Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)

### 2011/10/05

#### Seminar on Mathematics for various disciplines

10:00-11:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Chun Liu (University of Tokyo / Pennsylvania State University)
Energetic Variational Approaches for Ionic Fluids (ENGLISH)
[ Abstract ]
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.

### 2011/10/04

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshifumi Matsuda (The University of Tokyo)
Relatively quasiconvex subgroups of relatively hyperbolic groups (JAPANESE)
[ Abstract ]
Relative hyperbolicity of groups was introduced by Gromov as a
generalization of word hyperbolicity. Motivating examples of relatively
hyperbolic groups are fundamental groups of noncompact complete
hyperbolic manifolds of finite volume. The class of relatively
quasiconvex subgroups of a realtively hyperbolic group is defined as a
genaralization of that of quasicovex subgroups of a word hyperbolic
group. The notion of hyperbolically embedded subgroups of a relatively
hyperbolic group was introduced by Osin and such groups are
characterized as relatively quasiconvex subgroups with additional
algebraic properties. In this talk I will present an introduction to
relatively quasiconvex subgroups and discuss recent joint work with Shin
-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.

### 2011/09/20

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Clara Loeh (Univ. Regensburg)
Functorial semi-norms on singular homology (ENGLISH)
[ Abstract ]
Functorial semi-norms on singular homology add metric information to
homology classes that is compatible with continuous maps. In particular,
functorial semi-norms give rise to degree theorems for certain classes
of manifolds; an invariant fitting into this context is Gromov's
simplicial volume. On the other hand, knowledge about mapping degrees
allows to construct functorial semi-norms with interesting properties;
for example, so-called inflexible simply connected manifolds give rise
to functorial semi-norms that are non-trivial on certain simply connected
spaces.

### 2011/08/12

#### GCOE Seminars

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Benny Hon (Department of Mathematics City University of Hong Kong)
Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)
[ Abstract ]
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

### 2011/08/03

#### thesis presentations

10:00-11:15   Room #123 (Graduate School of Math. Sci. Bldg.)
Yoshinori GONGYO (Graduate School of Mathematical Sciences the University of Tokyo)
Abundance conjecture and canonical bundle formula (JAPANESE)

### 2011/07/29

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Shihoko Ishii (Graduate School of Mathematical Sciences, University of Tokyo)
Arc spaces and algebraic geometry (JAPANESE)

### 2011/07/27

#### Number Theory Seminar

16:00-18:15   Room #123 (Graduate School of Math. Sci. Bldg.)
Takeshi Saito (University of Tokyo) 16:00-17:00
Discriminants and determinant of a hypersurface of even dimension (ENGLISH)
[ Abstract ]
The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Dennis Eriksson (University of Gothenburg) 17:15-18:15
Multiplicities of discriminants (ENGLISH)
[ Abstract ]
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.

### 2011/07/21

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Univ. Tokyo)
Almost completely isometric maps and applications (ENGLISH)

### 2011/07/14

#### Operator Algebra Seminars

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (IPMU)
New perspectives for the local index formula in noncommutative geometry (ENGLISH)

### 2011/07/13

#### Seminar on Probability and Statistics

15:00-16:10   Room #002 (Graduate School of Math. Sci. Bldg.)
YATA, Kazuyoshi (Institute of Mathematics, University of Tsukuba)
Statistical Inference for High-Dimension, Low-Sample-Size Data (JAPANESE)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html

### 2011/07/12

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Masaharau Kobayashi (Tokyo University of Science)
The inclusion relation between Sobolev and modulation spaces (JAPANESE)
[ Abstract ]
In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.
Joint work with Mitsuru Sugimoto (Nagoya University).

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Keiko Kawamuro (University of Iowa)
The self linking number and planar open book decomposition (ENGLISH)
[ Abstract ]
I will show a self linking number formula, in language of
braids, for transverse knots in contact manifolds that admit planar
open book decompositions. Our formula extends the Bennequin's for
the standar contact 3-sphere.

### 2011/07/11

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Chiba (University of Tokyo)
Kobayashi hyperbolic imbeddings into toric varieties (JAPANESE)