過去の記録

過去の記録 ~03/18本日 03/19 | 今後の予定 03/20~

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
中濱 良祐 氏 (東京大学大学院数理科学研究科)
ベクトル値正則離散系列表現のノルム計算と解析接続 (English)
[ 講演概要 ]
正則離散系列表現は,複素有界対称領域上のベクトル値正則関数空間上に実現される.そのノルムはパラメータが十分大きい場合には収束する積分で表せるが,パラメータが小さくなるとその積分は収束しなくなる.しかし,ノルムを具体的に計算することによって,その小さいパラメータへの解析接続を考えることができ,そのユニタリ化可能性などの性質を論じることができる.本講演ではノルムの具体的な計算に関する結果を扱う.

2015年04月20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
二木 昭人 氏 (東京大学)
Weighted Laplacians on real and complex complete metric measure spaces (Japanese)
[ 講演概要 ]
We compare the weighted Laplacians on real and complex (K¥"ahler) metric measure spaces. In the compact case K¥"ahler metric measure spaces are considered on Fano manifolds for the study of K¥"ahler Ricci solitons while real metric measure spaces are considered with Bakry-¥'Emery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
服部 哲弥 氏 (慶應大学経済学部)
独立確率過程の大数の強法則について (JAPANESE)
[ 講演概要 ]
基礎教科書にある独立実確率変数の大数の強法則を独立な実確率過程に拡張する.
マルチンゲール性などの時間軸方向のσ加法族の性質を仮定せずに成り立つ時間一様な
概収束を目指す.例えば,ビルを建て大量の照明器具を設置し,切れる都度交換するとき,
次に切れるまでの時間分布が(技術改良や原材料の法規制などで)交換時刻に依存する
強度に基づくときに,平均交換回数が一様収束の意味で確定値時間発展に概収束するか,
という問題である.この例のような増加過程の場合は教科書にある各時刻での確率変数の
4次モーメント有界条件だけで一様概収束を得る.マルコフ性等の時間軸方向の良い性質を
仮定しないので,例えば上記の例でビルを建てる時刻も変える2変数確率過程としての
一様強法則も気になるが,サンプルの適切なヘルダー連続性を仮定すれば成り立つ.

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
金光秋博 氏 (東大数理)
Fano 5-folds with nef tangent bundles (日本語)
[ 講演概要 ]
Campana と Peternell は, ネフな接束をもつ Fano 多様体は有理等質多様体で
あると予想した.
渡辺究によって, 5 次元かつ Picard 数が 2 以上のとき, この予想は正しいこ
とが示されている.
一方で, Picard 数が 1 のとき, その上の有理曲線の最小反標準次数 (擬指数)
によって場合分けすることができて, 趙・宮岡・Shepherd-Barron, 宮岡, Hwang,
Mok らの結果から, 5 次元の場合には, 擬指数が 4 であるときを除けば有理等
質多様体であるということがわかっていた.

本講演では, 極小有理曲線族を用いて, 擬指数が 4 である場合について任意次
元で調べる.
その結果として 5 次元のときには Campana と Peternell の予想が正しいこと
が従う.

2015年04月17日(金)

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室
塚本真輝 氏 (京都大学)
ブロディ曲線の成す力学系の平均次元 (日本語)
[ 講演概要 ]
平均次元とは力学系の位相不変量であり,ブロディ曲線とは複素平面から複素射影空間へのリプシッツ正則写像のことである.ブロディ曲線全体は自然に無限次元の力学系を成す.この力学系の平均次元を計算する問題を,グロモフは1999年の論文で開始した.この講演では平均次元の厳密公式を示すことで,この問題に解答を与える.証明の鍵は,リンデンシュトラウスとヴァイスによる平均次元に対する情報理論からのアプローチを応用することである.

2015年04月15日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
Juan Orendain 氏 (UNAM/Univ. Tokyo)
On the tricategory of coordinate free conformal nets
(English)

数理人口学・数理生物学セミナー

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (東京大学大学院数理科学研究科)
生活史と個体群動態の数理:~一回繁殖生物における個体差と環境収容力への影響~
(JAPANESE)
[ 講演概要 ]
生活史と個体群動態の関係は密接である.例えば、ネズミの個体数と象の個体数
が歴然としているのは、成熟年齢やサイズなど個体の持つ生活史の特性が、双方
とも異なる事に起因すると考えられている.しかし、それら個体の特性が個体群
動態に与える影響は十分に理解されているとは言い難い.構造人口模型はそれら
個体と集団を繋げる数理モデルとして注目されてきた.本研究は、齢構造とサイ
ズ構造、両方を考慮した構造人口模型を考える.具体的には、人口規模の増大が
種内競争により、個々のサイズ成長率の期待値を減少させる生育過程を考える.
また、この種をあるサイズに達したときに繁殖する一回繁殖生物と仮定する.こ
れらの仮定から生成された構造人口模型の定常状態を環境収容力と考え、サイズ
の成長率の分散(個体差)が環境収容力とそこでの個体群構造への影響を解析し
たい.

2015年04月14日(火)

諸分野のための数学研究会

13:30-14:30   数理科学研究科棟(駒場) 056号室
※ 通常の時間と異なります。
長谷川 洋介 氏 (東京大学生産技術研究所 機械・生体系部門 講師)
熱流体工学と最適化数理の接点
[ 講演概要 ]
我々の身の回りの流れの多くは、高いレイノルズ数を有し、乱流状態である。
乱流を正確に予測し、自在に制御することができれば、環境予測や省エネルギーに大きく貢献できる。
本講演では、最も基礎的な系の一つである、壁に沿って流れる乱流(壁乱流)を対象として、最適制御理論の応用事例、有限のセンサ情報に基づく熱流動場の逆推定等に関する最近の試みを紹介する。
また、ミクロな気液二相流や微粒子が分散した懸濁液の蒸発プロセス等、工学的に重要であり、また現象としても興味深い事例を時間の許す限り紹介する。

トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
中村 信裕 氏 (学習院大学)
Pin(2)-monopole invariants for 4-manifolds (JAPANESE)
[ 講演概要 ]
The Pin(2)-monopole equations are a variant of the Seiberg-Witten equations
which can be considered as a real version of the SW equations. A Pin(2)-mono
pole version of the Seiberg-Witten invariants is defined, and a special feature of
this is that the Pin(2)-monopole invariant can be nontrivial even when all of
the Donaldson and Seiberg-Witten invariants vanish. As an application, we
construct a new series of exotic 4-manifolds.

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
田中 雄一郎 氏 (九州大学マス・フォア・インダストリ研究所)
複素球多様体へのコンパクトリー群の可視的作用について (English)
[ 講演概要 ]
With the aim of uniform treatment of multiplicity-free representations of Lie groups, T. Kobayashi introduced the theory of visible actions on complex manifolds.

In this talk we consider visible actions of a compact real form U of a connected complex reductive algebraic group G on G-spherical varieties. Here a complex G-variety X is said to be spherical if a Borel subgroup of G has an open orbit on X. The sphericity implies the multiplicity-freeness property of the space of polynomials on X. Our main result gives an abstract proof for the visibility of U-actions. As a corollary, we obtain an alternative proof for the visibility of U-actions on linear multiplicity-free spaces, which was earlier proved by A. Sasaki (2009, 2011), and the visibility of U-actions on generalized flag varieties, earlier proved by Kobayashi (2007) and T- (2013, 2014).

2015年04月13日(月)

東京確率論セミナー

16:50-17:50   数理科学研究科棟(駒場) 128号室
Hans Rudolf Kuensch 氏 (ETH Zurich)
Modern Monte Carlo methods -- Some examples and open questions (ENGLISH)
[ 講演概要 ]
Probability and statistics once had strong relations, but in recent years the two fields have moved into opposite directions. Despite this, I believe that both fields would profit if they continued to interact. Monte Carlo methods are one topic that is of interest to both probability and statistics: Statisticians use advanced Monte Carlo methods, and analyzing these methods is a challenge for probabilists. I will illustrate this, using as examples rare event estimation by sample splitting, approximate Bayesian computation and Monte Carlo filters.

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
安福 悠 氏 (日本大学)
Campana's Multiplicity and Integral Points on P^2 (English)
[ 講演概要 ]
We analyze when the complements of (possibly reducible) curves in P^2 have Zariski-dense integral points. The analysis utilizes the structure theories for affine surfaces based on logarithmic Kodaira dimension. When the log Kodaira dimension is one, an important role is played by Campana's multiplicity divisors for fibrations, but there are some subtleties. This is a joint work with Aaron Levin (Michigan State).

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
Frédéric Campana 氏 (Université de Lorraine)
An orbifold version of Miyaoka's semi-positivity theorem and applications (English)
[ 講演概要 ]
This `orbifold' version of Miyaoka's theorem says that if (X,D)
is a projective log-canonical pair with K_X+D pseudo-effective,
then its 'cotangent' sheaf $¥Omega^1(X,D)$ is generically semi-positive.
The definitions will be given. The original proof of Miyaoka, which
mixes
char 0 and char p>0 arguments could not be adapted. Our proof is in char
0 only.

A first consequence is when (X,D) is log-smooth with reduced boudary D,
in which case the cotangent sheaf is the classical Log-cotangent sheaf:
if some tensor power of $¥omega^1_X(log(D))$ contains a 'big' line
bundle, then K_X+D is 'big' too. This implies, together with work of
Viehweg-Zuo,
the `hyperbolicity conjecture' of Shafarevich-Viehweg.

The preceding is joint work with Mihai Paun.

A second application (joint work with E. Amerik) shows that if D is a
non-uniruled smooth divisor in aprojective hyperkaehler manifold with
symplectic form s,
then its characteristic foliation is algebraic only if X is a K3 surface.
This was shown previously bt Hwang-Viehweg assuming D to be of general
type. This result has some further consequences.

2015年04月10日(金)

統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 128号室
Yacine Ait-Sahalia 氏 (Princeton University)
Principal Component Analysis of High Frequency Data (joint with Dacheng Xiu)
[ 講演概要 ]
We develop a methodology to conduct principal component analysis of high frequency financial data. The procedure involves estimation of realized eigenvalues, realized eigenvectors, and realized principal components and we provide the asymptotic distribution of these estimators. Empirically, we study the components of the constituents of Dow Jones Industrial Average Index, in a high frequency version, with jumps, of the Fama-French analysis. Our findings show that, excluding jump variation, three Brownian factors explain between 50 and 60% of continuous variation of the stock returns. Their explanatory power varies over time. During crises, the first principal component becomes increasingly dominant, explaining up to 70% of the variation on its own, a clear sign of systemic risk.

2015年04月08日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
木田良才 氏 (東大数理)
On treeable equivalence relations arising from the Baumslag-Solitar groups
(English)

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
安田正大 氏 (大阪大学)
Integrality of $p$-adic multiple zeta values and application to finite multiple zeta values.
(English)
[ 講演概要 ]
I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.
(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.)

2015年04月07日(火)

トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : 16:30-17:00 Common Room
植田 一石 氏 (東京大学大学院数理科学研究科)
Potential functions for Grassmannians (JAPANESE)
[ 講演概要 ]
Potential functions are Floer-theoretic invariants
obtained by counting Maslov index 2 disks
with Lagrangian boundary conditions.
In the talk, we will discuss our joint work
with Yanki Lekili and Yuichi Nohara
on Lagrangian torus fibrations on the Grassmannian
of 2-planes in an n-space,
the potential functions of their Lagrangian torus fibers,
and their relation with mirror symmetry for Grassmannians.

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Bent Orsted 氏 (Aarhus University)
Branching laws and elliptic boundary value problems
(English)
[ 講演概要 ]
Classically the Poisson transform relates harmonic functions in the complex upper half plane to their boundary values on the real axis. In some recent work by Caffarelli et al. some new generalizations of this appears in connection with the fractional Laplacian. In this lecture we
shall explain how the symmetry-breaking operators introduced by T. Kobayashi for studying branching laws may shed new light on the situation for elliptic boundary value problems. This is based on joint work with J. M\"o{}llers and G. Zhang.

2015年04月06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
吉川 謙一 氏 (京都大学)
Analytic torsion for K3 surfaces with involution (Japanese)
[ 講演概要 ]
In 2004, I introduced a holomorphic torsion invariant for 2-elementary K3 surfaces, i.e., K3 surfaces with involution. In the talk, I will report a recent progress in this invariant. Namely, for all possible deformation types, the holomorphic torsion invariant viewed as a function on the moduli space, is expressed as the product of an explicit Borcherds lift and an explicit Siegel modular form. If time permits, I will interpret the result in terms of the BCOV invariant, i.e., the genus-one string amplitude in B-model, for Calabi-Yau threefolds of Borcea-Voisin. This is a joint work with Shouhei Ma.

2015年03月24日(火)

トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Mina Aganagic 氏 (University of California, Berkeley)
Knots and Mirror Symmetry (ENGLISH)
[ 講演概要 ]
I will describe two conjectures relating knot theory and mirror symmetry. One can associate, to every knot K, one a Calabi-Yau manifold Y(K), which depends on the homotopy type of the knot only. The first conjecture is that Y(K) arises by a generalization of SYZ mirror symmetry, as mirror to the conifold, O(-1)+O(-1)->P^1. The second conjecture is that topological string provides a quantization of Y(K) which leads to quantum HOMFLY invariants of the knot. The conjectures are based on joint work with C. Vafa and also with T.Ekholm, L. Ng.

Lie群論・表現論セミナー

18:00-19:30   数理科学研究科棟(駒場) 126号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
A Gysin formula for Hall-Littlewood polynomials
[ 講演概要 ]
Schubert calculus on Grassmannians is governed by Schur S-functions, the one on Lagrangian Grassmannians by Schur Q-functions. There were several attempts to give a unifying approach to both situations.
We propose to use Hall-Littlewood symmetric polynomials. They appeared implicitly in Hall's study of the combinatorial lattice structure of finite abelian p-groups and in Green's calculations of the characters of GL(n) over finite fields; they appeared explicitly in the work of Littlewood on some problems in representation theory.
With the projection in a Grassmann bundle, there is associated its Gysin map, induced by pushing forward cycles (topologists call it "integration along fibers").
We state and prove a Gysin formula for HL-polynomials in these bundles. We discuss its two specializations, giving better insights to previously known formulas for Schur S- and P-functions.

2015年03月20日(金)

数値解析セミナー

13:30-15:00   数理科学研究科棟(駒場) 122号室
Gadi Fibich 氏 (Tel Aviv University)
Asymmetric Auctions (English)
[ 講演概要 ]
Auctions are central to the modern economy, both on-line and off-line. A fundamental result in auction theory is that when bidders are symmetric (identical), then under quite general conditions, all auctions are revenue equivalent. While it is known that this result does not hold when bidders are asymmetric, the effect of bidders' asymmetry is poorly understood, since asymmetric auctions are much harder to analyze.

In this talk I will discuss the mathematical theory of asymmetric auctions. I will focus on asymmetric first-price auctions, where the mathematical model is given by a nonstandard system of $n$ nonlinear ordinary differential equations, with $2n$ boundary conditions and a free boundary. I will present various analytic and numerical approaches for this system. Then I will present some recent results on asymptotic revenue equivalence of asymmetric auctions.

Joint work with A. Gavious and N. Gavish.

2015年03月19日(木)

FMSPレクチャーズ

9:00-11:00   数理科学研究科棟(駒場) 大講義室号室
これらの講義はPrinceton-Tokyo workshop on Geometric Analysisの一環として3/17~19に行われます。
Matthew Gursky 氏 (Univ. Nortre Dame) 9:00-9:50
Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)
[ 講演概要 ]
In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.
These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.
I will also explain some recent work which attempts to understand the moduli space of critical metrics.
[ 参考URL ]
https://sites.google.com/site/princetontokyo/mini-courses
Gábor Székelyhidi 氏 (Univ. Nortre Dame) 10:10-11:00
Hessian type equations on compact Kähler manifolds (ENGLISH)
[ 講演概要 ]
I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.
[ 参考URL ]
https://sites.google.com/site/princetontokyo/mini-courses

2015年03月18日(水)

FMSPレクチャーズ

9:00-11:00   数理科学研究科棟(駒場) 大講義室号室
これらの講義はPrinceton-Tokyo workshop on Geometric Analysisの一環として3/17~19に行われます。
Matthew Gursky 氏 (Univ. Nortre Dame) 9:00-9:50
Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)
[ 講演概要 ]
In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.
These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.
I will also explain some recent work which attempts to understand the moduli space of critical metrics.
[ 参考URL ]
https://sites.google.com/site/princetontokyo/mini-courses
Gábor Székelyhidi 氏 (Univ. Nortre Dame) 10:10-11:00
Hessian type equations on compact Kähler manifolds (ENGLISH)
[ 講演概要 ]
I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.
[ 参考URL ]
https://sites.google.com/site/princetontokyo/mini-courses

2015年03月17日(火)

FMSPレクチャーズ

13:30-15:00, 15:30-17:30   数理科学研究科棟(駒場) Balcony A, Kavli IPMU号室
3/16 13:30-15:00, 15:30-17:30 3/17 13:30-15:00, 15:30-17:30 の4講義 Kavli IPMU(柏キャンパス)での開催
入谷 寛 氏 (京都大学理学研究科)
シフト作用素とトーリックミラー対称性 (ENGLISH)
[ 講演概要 ]
近年,同変量子コホモロジーに対するシフト作用素が
Braverman, Maulik, Okounkov, Pandharipande らにより導入された.
これはSeidel表現の同変持ち上げであり,異なる同変変数の値
に対する量子接続の間のintertwinerを与える.本連続講演では,
このシフト作用素がトーリック多様体のミラーを本質的に復元する
ことを説明したい.具体的には

1. Giventalのミラー定理
2. Landau-Ginzburgポテンシャルと原始形式
3. 拡張されたI関数

がシフト作用素の基本的な性質から得られることを示す.
またガンマ整構造がシフト作用素の決める差分方程式
の解を与えていることにも触れたい.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Iritani.pdf

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