## 過去の記録

### 2012年06月13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

Singular homologies of non-Archimedean analytic spaces and integrals along cycles (JAPANESE)
[ 講演概要 ]
Berkovichの非アルキメデス的解析空間に新たな特異ホモロジーを定義し、そのホモロジーにおけるサイクルに沿った正則微分形式の積分という新たな概念を考える。Tate曲線においては標準的な体積形式dz/zの積分により周期が得られることを確かめる。

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 122号室
Sunder Sethuraman 氏 (University of Arizona)
A KPZ equation for zero-range interactions (ENGLISH)
[ 講演概要 ]
We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

#### 講演会

11:00-15:30   数理科学研究科棟(駒場) 128号室
S. Harase, et. al. 氏 (Tokyo Institute of Technology/JSPS)
Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)
[ 講演参考URL ]

### 2012年06月12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

Topological interpretation of the quandle cocycle invariants of links (JAPANESE)
[ 講演概要 ]
Carter et al. introduced many quandle cocycle invariants
combinatorially constructed from link-diagrams. For connected quandles of
finite order, we give a topological meaning of the invariants, without
some torsion parts. Precisely, this invariant equals a sum of "knot
colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten
invariant. Moreover, our approach involves applications to compute "good"
torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy
groups of rack spaces.

#### 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

Conformally invariant systems of differential operators of non-Heisenberg parabolic type (ENGLISH)
[ 講演概要 ]
Minkowski space上のwave operatorはconformally invariant operatorの典型的な例である。

conformal invarianceがそのsystemに一般化された (conformally invariant systems)。
このセミナーではmaximal non-Heisenberg parabolicを使って、
その様なsecond order differential operatorのsystemを作りたい。
またconformally invariant systemは、あるgeneralized Verma module間のhomomorphismを誘導するが、もし時間が許せばそれについても述べたい。

#### 講演会

09:50-17:10   数理科学研究科棟(駒場) 118号室
Josef Dick, et. al. 氏 (Univ. New South Wales)
Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)
[ 講演参考URL ]

### 2012年06月11日(月)

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Changzheng Li 氏 (Kavli IPMU)
Quantum cohomology of flag varieties (ENGLISH)
[ 講演概要 ]
In this talk, I will give a brief introduction to the quantum cohomology of flag varieties first. Then I will introduce a Z^2-filtration on the quantum cohomology of complete flag varieties. In the end, we will study the quantum Pieri rules for complex/symplectic Grassmannians, as applications of the Z^2-filtration.

#### 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
Damian BROTBEK 氏 (University of Tokyo)
Differential forms on complete intersections (ENGLISH)
[ 講演概要 ]
Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

### 2012年06月09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.

) 13:30-15:00
Cauchy積分に関する最近の話題(Muscaluらの仕事)
(JAPANESE)
[ 講演概要 ]

) 15:30-17:00
Ill-posedness for the nonlinear Schr\\"odinger equations in one
space dimension
(JAPANESE)
[ 講演概要 ]
In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1$. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.

### 2012年06月08日(金)

#### GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Derived categories and cohomological invariants II (ENGLISH)
[ 講演概要 ]
(Abstract for both Parts I and II)
I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Bong Lian 氏 (Brandeis University)
Period Integrals and Tautological Systems (ENGLISH)
[ 講演概要 ]
We develop a global Poincar\\'e residue formula to study
period integrals of families of complex manifolds. For any compact
complex manifold $X$ equipped with a linear system $V^*$ of
generically smooth CY hypersurfaces, the formula expresses period
integrals in terms of a canonical global meromorphic top form on $X$.
Two important ingredients of this construction are the notion of a CY
principal bundle, and a classification of such rank one bundles.
We also generalize the construction to CY and general type complete
intersections. When $X$ is an algebraic manifold having a sufficiently
large automorphism group $G$ and $V^*$ is a linear representation of
$G$, we construct a holonomic D-module that governs the period
integrals. The construction is based in part on the theory of
tautological systems we have developed earlier. The approach allows us
to explicitly describe a Picard-Fuchs type system for complete
intersection varieties of general types, as well as CY, in any Fano
variety, and in a homogeneous space in particular. In addition, the
approach provides a new perspective of old examples such as CY
complete intersections in a toric variety or partial flag variety. The
talk is based on recent joint work with R. Song and S.T. Yau.

### 2012年06月05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

A generalization of Dehn twists (JAPANESE)
[ 講演概要 ]
We introduce a generalization
of Dehn twists for loops which are not
necessarily simple loops on an oriented surface.
Our generalization is an element of a certain
enlargement of the mapping class group of the surface.
A natural question is whether a generalized Dehn twist is
in the mapping class group. We show some results related to this question.
This talk is partially based on a joint work
with Nariya Kawazumi (Univ. Tokyo).

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (CNRS, Orsay)
Random walk on reductive groups II (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

#### 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
GCOE lectures
Yves Benoist 氏 (CNRS and Orsay)
Random walk on reductive groups (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

### 2012年06月04日(月)

#### 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

Smooth P1-fibrations and Campana-Peternell conjecture (ENGLISH)
[ 講演概要 ]
We give a complete classification of smooth P1-fibrations
over projective manifolds of Picard number 1 each of which admit another
smooth morphism of relative dimension one.
Furthermore, we consider relations of the result with Campana-Peternell conjecture
on Fano manifolds with nef tangent bundle.

#### 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

Log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans. (JAPANESE)
[ 講演概要 ]

### 2012年06月01日(金)

#### GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Derived categories and cohomological invariants I (ENGLISH)
[ 講演概要 ]
(Abstract for both Parts I and II)
I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

### 2012年05月31日(木)

#### 統計数学セミナー

14:50-16:05   数理科学研究科棟(駒場) 006号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/05.html

### 2012年05月30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
Valentina Di Proietto 氏 (東京大学数理科学研究科)
Kernel of the monodromy operator for semistable curves (ENGLISH)
[ 講演概要 ]
For a semistable curve, we study the action of the monodromy operator on the first log-crystalline cohomology group. In particular we examine the relation between the kernel of the monodromy operator and the first rigid cohomology group, in the case of trivial coefficients, giving a new proof of a theorem of B. Chiarellotto and in the case of certain unipotent F-isocrystals as coefficients.
This is a joint work in progress with B. Chiarellotto, R. Coleman and A. Iovita.

#### 講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the fourth of four lectures planned on 5/25, 5/28, 5/29 and 5/30.
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012年05月29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

Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
(JAPANESE)
[ 講演概要 ]
The triple linking number of an oriented surface link was defined as an
torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (CNRS, Orsay)
Random walk on reductive groups. (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

#### 講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the third of four lectures; the first is the colloquium on May 25th(Fri) 16:30--17:30 at 002 and the second is on May 28th(Mon).
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012年05月28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

Local cohomology and hypersurface isolated singularities II (JAPANESE)
[ 講演概要 ]

・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.

#### 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
Mihnea Popa 氏 (University of Illinois at Chicago)
Generic vanishing and linearity via Hodge modules (ENGLISH)
[ 講演概要 ]
I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.