## 過去の記録

### 2014年06月04日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Ion Nechita 氏 (Univ. Paul Sabatier)
Positive and completely positive maps via free additive powers of probability measures (ENGLISH)

### 2014年06月03日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
[ 講演概要 ]
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年06月02日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)
[ 講演概要 ]
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年05月28日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Gantsooj Batzaya 氏 (東京大学数理科学研究科)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Poisson boundary of monoidal categories (ENGLISH)

#### 数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 128号室

)

[ 講演概要 ]
: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年05月27日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]
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 $m-1$.

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
[ 講演概要 ]
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群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Schubert加群の構造とSchubert加群によるfiltrationについて (JAPANESE)
[ 講演概要 ]

また, この研究のもともとの動機はSchubert多項式に関するある問題を考えていたことなので, それについても話す予定です.

### 2014年05月22日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Boris Hasselblatt 氏 (Tufts Univ)
Godbillon-Vey invariants for maximal isotropic foliations (ENGLISH)
[ 講演概要 ]
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年05月21日(水)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Shenghao Sun 氏 (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
[ 講演概要 ]
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.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Group approximation in Cayley topology and coarse geometry
part I: coarse embeddings of amenable groups (ENGLISH)

### 2014年05月20日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
[ 講演概要 ]
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.

#### 統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 052号室

[ 講演概要 ]

[ 参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html

### 2014年05月19日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

On degenerations of Ricci-flat Kähler manifolds (JAPANESE)

### 2014年05月17日(土)

#### 調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.

[ 講演概要 ]
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).

Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)
[ 講演概要 ]
Heisenberg群上のsub-Laplacianに対する熱核およびSchroedinger核の構成について

またHeisenberg群の群演算にパラメータを、極限操作でユークリッド空間になるように入れたときの、熱核やSchrodinger核に極限操作を行ったときの振る舞いについて考察する。

### 2014年05月15日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Gap theorems for compact gradient Sasaki Ricci solitons (JAPANESE)
[ 講演概要 ]
In this talk we give some necessary and sufficient conditions for compact gradient Sasaki-Ricci solitons to be Sasaki-Einstein. Our result may be considered as a Sasaki geometry version of recent works by H. Li, and M. Fern¥'andez-L¥'opez-E. Garc¥'ia-Rio.

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 050号室
Cédric Villani 氏 (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature
― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ 講演概要 ]
Optimal transport theory, non-Euclidean geometry and statistical physics met fifteen years ago with the discovery that Ricci curvature can be studied quantitatively thanks to entropy and
Monge-Kantorovich transport.
This unexpected encounter was very fruitful, leading to progress in each of these fields.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html

#### FMSPレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 050号室
Tea: 16:00-16:30 ホワイエにて
Cédric Villani 氏 (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html

### 2014年05月14日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Yul Otani 氏 (Univ. Tokyo)
A Supersymmetric model in AQFT (after Buchholz and Grundling) (ENGLISH)

### 2014年05月13日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Ultra-differentiable classes and intersection theorems (JAPANESE)
[ 講演概要 ]
There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).

#### 統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 052号室
Selma Chaker 氏 (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
[ 講演概要 ]
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
[ 参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
[ 講演概要 ]
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Ivan Cherednik 氏 (The University of North Carolina at Chapel Hill, RIMS
)
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
[ 講演概要 ]
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.

The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).

The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due

to Braverman and Finkelberg (algebraic theory of affine flag varieties).