## 過去の記録

#### 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
Pablo Ramacher 氏 (Marburg University)
SINGULAR EQUIVARIANT ASYMPTOTICS AND THE MOMENTUM MAP. RESIDUE FORMULAE IN EQUIVARIANT COHOMOLOGY (ENGLISH)
[ 講演概要 ]
Let M be a smooth manifold and G a compact connected Lie group acting on M by isometries. In this talk, we study the equivariant cohomology of the cotangent bundle of M, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain residue formulae. In case of compact symplectic manifolds with a Hamiltonian G-action, similar residue formulae were derived by Jeffrey, Kirwan et al..

### 2014年06月16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

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
A.P. Veselov 氏 (Loughborough, UK and Tokyo)
Universal formulae for Lie groups and Chern-Simons theory (ENGLISH)
[ 講演概要 ]
In 1990s Vogel introduced an interesting parametrization of simple
Lie algebras by 3 parameters defined up to a common multiple and
permutations. Numerical characteristic is called universal if it can be
expressed in terms of Vogel's parameters (example - the dimension of Lie
algebra). I will discuss some universal formulae for Lie groups
and Chern-Simons theory on 3D sphere.
The talk is based on joint work with R.L. Mkrtchyan and A.N. Sergeev.

### 2014年06月11日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室

Finiteness of K-area and the dual of the Baum-Connes conjecture (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 ]

### 2014年06月10日(火)

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 056号室
Sergei Duzhin 氏 (Steklov Institute of Mathematics)
Bipartite knots (ENGLISH)
[ 講演概要 ]
We give a solution to a part of Problem 1.60 in Kirby's list of open
problems in topology thus proving a conjecture raised in 1987 by
J.Przytycki. A knot is said to be bipartite if it has a "matched" diagram,
that is, a plane diagram that has an even number of crossings which can be
split into pairs that look like a simple braid on two strands with two
crossings. The conjecture was that there exist knots that do not have such
diagrams. I will prove this fact using higher Alexander ideals.
This talk is based on a joint work with my student M.Shkolnikov

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)
[ 講演概要 ]
A system of N point vortices is a Hamiltonian dynamical system with N degrees of freedom,and it is known that under certain parameter and initial conditions, there are self-similar collapse solutions for which N vortices collide at a point while rotating without changing the initial shape of configuration. In this talk, I will introduce such collision solutions and discuss some properties of complex time singularities in relation with those solutions.

#### 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

On estimates for the Stokes flow in a space of bounded functions (JAPANESE)
[ 講演概要 ]
The Stokes equations are well understood on $L^p$ space for various kinds of domains such as bounded or exterior domains, and fundamental to study the nonlinear Navier-Stokes equations. The situation is different for the case $p=\\infty$ since in this case the Helmholtz projection does not act as a bounded operator anymore. In this talk, we show some a priori estimate for a composition operator of the Stokes semigroup and the Helmholtz projection on a space of bounded functions.

#### 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

On relation between the Milnor's $¥mu$-invariant and HOMFLYPT
polynomial (JAPANESE)
[ 講演概要 ]
Milnor introduced a family of invariants for ordered oriented link,
called $¥bar{¥mu}$-invariants. Polyak showed a relation between the $¥ bar{¥mu}$-invariant of length 3 sequence and Conway polynomial.
Moreover, Habegger-Lin showed that Milnor's invariants are invariants of
string link, called $¥mu$-invariants. We show that any $¥mu$-invariant
of length $¥leq k$ can be represented as a combination of HOMFLYPT
polynomials if all $¥mu$-invariant of length $¥leq k-2$ vanish.
This result is an extension of Polyak's result.

### 2014年06月09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

Modified Kähler-Ricci flow on projective bundles (JAPANESE)

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
ハイブリッド型不連続Galerkin(HDG)法とは、要素内部の未知量に加え、要素間境界上の未知量を導入して定式化を行うという、新しいタイプの不連続Galerkin法である。本講演では、従来のHDG法の安定化項を弱めることによって得られる新手法(弱安定化HDG法)を紹介する。 弱安定化HDG法の理論誤差解析や、ガウス型数値積分公式による実装法、数値計算結果などについて示す。非適合有限要素法との関連性についても述べる。
[ 講演参考URL ]
http://www.infsup.jp/utnas/

### 2014年06月06日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 056号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。ඁ

Mikhail Kapranov 氏 (Kavli IPMU)
Lie algebras from secondary polytopes (ENGLISH)
[ 講演概要 ]
The secondary polytope of a point configuration
in the Euclidean space was introduced by Gelfand, Zelevinsky
and the speaker long time ago in order to understand discriminants
of multi-variable polynomials. These polytopes have
a remarkable factorization (or operadic) property: each
face of any secondary polytope is isomorphic to the
product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich
and Y. Soibelman, will explain how the factorization property
can be used to construct Lie algebra-type objects:
$L_¥infty$ and $A_¥infty$-algebras. These algebras
turn out to be related to the problem of deformation
of triangulated categories with semiorthogonal decompositions.

### 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)