| 過去の記録 ～05/16
| 本日 05/17
| 今後の予定 05/18～
| 談話会・セミナー ホーム
| 東大数理 ホーム
| 数理へのアクセス |
14:50 - 16:00 数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
鈴木 大慈 氏 (東京大学)
『 PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model 』(JAPANESE)
スパース加法モデルの推定法として,マルチプルカーネル学習(MKL)が提案されているが, 本発表ではそのベイズ的な変種について考察し,PAC-Bayesの手法を用いてその性能解析 を行う.標準的なMKLの解析では,restricted eigenvalue conditionのような強い仮定をデザ インに課するが,我々はPAC-Bayesの技法を用いてベイズ的なMKLがそのような仮定を設け ないで最適レートを達成することを示す.我々の結果は,近年発展しているガウシアンプロ セス回帰に関する理論を包含しており,PAC-Bayesを使ったより単純な証明を与える.我々 の考える推定量はガウシアンプロセスのスケール混合であり,スケール混合を取ることに よって適応的に最適レートを達成することが示される.また,有限次元のグループラッソに 対応する状況も考え,その収束レートを与える.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html
13:30 - 16:00 数理科学研究科棟(駒場) 123号室
谷口隆 氏 (神戸大学) 13:30 - 14:30
『 算術級数中の3次体の判別式 』(JAPANESE)
3次体の判別式を数える関数は2つ主要項があるが,判別式を算術級数中で数えると,第2主要項に偏りが現れることがある.この必要十分条件を与え,また主要項の公式を与える.証明には,2元3次形式の概均質ベクトル空間のL関数を用いる.(Frank Thorne 氏との共同研究)
都築正男 氏 (上智大学) 15:00 - 16:00
『 Asai L関数の中心値の平均とレベルアスペクト劣凸評価 』(JAPANESE)
10:30 - 12:00 数理科学研究科棟(駒場) 126号室
田島 慎一 氏 (筑波大学)
『 Local cohomology and hypersurface isolated singularities I 』(JAPANESE)
多変数留数に関するGrothendieck local duality と局所コホモロジーに基づくことで, 孤立特異点を持つ超曲面の複素解析的性質を解析することが出来る。本講演では, まず, 局所コホモロジー類の計算法を紹介する。次に, これら局所コホモロジーの応用として, イデアルメンバーシップ判定, スタンダード基底計算, イデアル商計算等が平易にできることを紹介する。数式処理システムRisa/Asirへの実装結果についても報告する。
15:30 - 17:00 数理科学研究科棟(駒場) 122号室
鈴木拓 氏 (早稲田理工)
『 Characterizations of projective spaces and hyperquadrics 』(JAPANESE)
After Mori's works on Hartshorne's conjecture, many results to
characterize projective spaces and hyperquadrics in terms of
positivity properties of the tangent bundle have been provided.
Kov\'acs' conjecture states that smooth complex projective
varieties are projective spaces or hyperquadrics if the $p$-th
exterior product of their tangent bundle contains the $p$-th
exterior product of an ample vector bundle. This conjecture is
the generalization of many preceding results. In this talk, I will
explain the idea of the proof of Kov\'acs' conjecture for varieties
with Picard number one by using a method of slope-stabilities
of sheaves.
17:00 - 18:30 数理科学研究科棟(駒場) 002号室
Emanuel Scheidegger 氏 (The University of Freiburg)
『 Topological Strings on Elliptic Fibrations 』(ENGLISH)
We will explain a conjecture that expresses the BPS invariants
(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau
threefolds in terms of modular forms. In particular, there is a
recursion relation which governs these modular forms. Evidence comes
from the polynomial formulation of the higher genus topological string
amplitudes with insertions.
16:30 - 18:00 数理科学研究科棟(駒場) 118号室
この日だけ部屋を118に変更します.
Norbert Pozar 氏 (Graduate School of Mathematical Sciences, The University of Tokyo)
『 Viscosity solutions for nonlinear elliptic-parabolic problems 』(ENGLISH)
We introduce a notion of viscosity solutions for a general class of
elliptic-parabolic phase transition problems. These include the
Richards equation, which is a classical model in filtration theory.
Existence and uniqueness results are proved via the comparison
principle. In particular, we show existence and stability properties
of maximal and minimal viscosity solutions for a general class of
initial data. These results are new even in the linear case, where we
also show that viscosity solutions coincide with the regular weak
solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a
recent work with Inwon Kim.
16:30 - 18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
http://www.ms.u-tokyo.ac.jp/gcoe/index.html
小山大介 氏 (電気通信大学大学院情報理工学研究科)
『 多重散乱問題に対するDtN有限要素法とSchwarz法 』(JAPANESE)
物体(散乱体)による音波の散乱現象を記述する外部Helmholtz問題に対する数値解法について考える.特に,散乱体が複数ある場合について考える.
Grote [J. Comput. Phys. 201, 630--650 (2004)]は,各散乱体を囲む複数の人工境界を導入し, その上で多重DtN(Dirichlet-to-Neumann)写像を定式化し,その写像を用いた境界条件を人工境界上で課し, 元の問題を人工境界で囲まれた複数の互いに素な有界領域における問題に帰着させ,有限要素法で解くという方法を見出した.
本講演では,この方法の事前誤差評価を与える.問題は正定値性を持たないので,誤差評価の導出にはSchatzの方法を用いる.その際,共役問題の解の正則性が必要になるが,問題は非対称なので,その正則性に関する考察もあらたに必要になる.また,この方法で用いられる領域分割に基づく並列Schwarz法を紹介し,その収束性などについても述べる.
17:10 - 18:10 数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム
入谷 寛 氏 (京都大学)
『 Gamma Integral Structure in Gromov-Witten theory 』(JAPANESE)
The quantum cohomology of a symplectic
manifold undelies a certain integral local system
defined by the Gamma characteristic class.
This local system originates from the natural integral
local sysmem on the B-side under mirror symmetry.
In this talk, I will explain its relationships to the problem
of analytic continuation of Gromov-Witten theoy (potentials),
including crepant resolution conjecture, LG/CY correspondence,
modularity in higher genus theory.
10:30 - 11:30 数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Xingfei Xiang 氏 (East China Normal University)
『 $L^p$ Estimates of the Vector Fields and their Applications 』(ENGLISH)
For $1< p < \infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \infty$. As an application of the $L^p$ estimates, the Global $\dv-\curl$ lemma in Sobolev spaces of negative indices is given.
16:40 - 17:40 数理科学研究科棟(駒場) 056号室
三井健太郎 氏 (東京大学数理科学研究科)
『 Simply connected elliptic surfaces 』(JAPANESE)
We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.
14:00 - 15:30 数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Chicago)
『 Generic vanishing theory and connections with derived categories 』(ENGLISH)
I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)
16:30 - 17:30 数理科学研究科棟(駒場) 002号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
『 Quasi-Monte Carlo methods: deterministic is often better than random 』(ENGLISH)
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.
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.
河邑 紀子 氏 (University of North Texas) 13:30 - 15:00
『 The Takagi function - a survey 』(JAPANESE)
More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.
寺澤 祐高 氏 (東京大学) 15:30 - 17:00
『 Dyadic, classical and martingale harmonic analysis II 』(JAPANESE)
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.
For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\"onen-P\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).
10:30 - 12:00 数理科学研究科棟(駒場) 126号室
田島 慎一 氏 (筑波大学)
『 Local cohomology and hypersurface isolated singularities II 』(JAPANESE)
局所コホモロジーの孤立特異点への応用として
・$\mu$-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。
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)
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.
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
中村 伊南沙 氏 (学習院大学,日本学術振興会)
『 Triple linking numbers and triple point numbers of torus-covering $T^2$-links 』(JAPANESE)
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
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.
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)
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)
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.
14:00 - 15:30 数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Chicago)
『 Derived categories and cohomological invariants I 』(ENGLISH)
(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.
15:30 - 17:00 数理科学研究科棟(駒場) 122号室
渡辺究 氏 (埼玉大学)
『 Smooth P1-fibrations and Campana-Peternell conjecture 』(ENGLISH)
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.
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
久野 雄介 氏 (津田塾大学)
『 A generalization of Dehn twists 』(JAPANESE)
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).
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)
14:00 - 15:30 数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Chicago)
『 Derived categories and cohomological invariants II 』(ENGLISH)
(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.
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
野坂 武史 氏 (京都大学 数理解析研究所, 日本学術振興会)
『 Topological interpretation of the quandle cocycle invariants of links 』(JAPANESE)
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.
16:40 - 17:40 数理科学研究科棟(駒場) 056号室
三原朋樹 氏 (東京大学数理科学研究科)
『 Singular homologies of non-Archimedean analytic spaces and integrals along cycles 』(JAPANESE)
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。
15:30 - 17:00 数理科学研究科棟(駒場) 122号室
山ノ井克俊 氏 (東京工業大学)
『 TBA 』(JAPANESE)
16:40 - 17:40 数理科学研究科棟(駒場) 056号室
時本一樹 氏 (東京大学数理科学研究科)
『 On the reduction modulo p of representations of a quaternion division algebra over a p-adic field 』(JAPANESE)
The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.
In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.
The simplest case has already been treated by Vign¥'eras. We deal with more cases.
15:30 - 17:00 数理科学研究科棟(駒場) 122号室
小木曽啓示 氏 (大阪大学)
『 TBA 』(JAPANESE)
16:40 - 17:40 数理科学研究科棟(駒場) 056号室
Patrick Forré 氏 (東京大学数理科学研究科)
『 Higher dimensional class field theory over (higher) local fields 』(ENGLISH)
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
岡 睦雄 氏 (東京理科大学)
『 Contact structure of mixed links 』(JAPANESE)
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
15:30 - 17:00 数理科学研究科棟(駒場) 122号室
Damian Brotbek 氏 (東京大学)
『 TBA 』(ENGLISH)