本文印刷
全画面プリント
過去の記録
過去の記録 ～07/26｜本日 07/27 | 今後の予定 07/28～
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
福島登志夫 氏 (国立天文台)
Precise and fast computation of elliptic integrals and elliptic functions (日本語)
福島登志夫 氏 (国立天文台)
Precise and fast computation of elliptic integrals and elliptic functions (日本語)
[ 講演概要 ]
Summarized is the recent progress of the methods to compute (i) Legendre's normal form complete elliptic integrals of all three kinds, $K(m)$, $E(m)$, and $\Pi(n|m)$, (ii) Legendre's normal form incomplete elliptic integrals of all three kinds, $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$, (iii) Jacobian elliptic functions, $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $\mathrm{dn}(u|m)$, and $\mathrm{am}(u|m)$, (iv) the inverse functions of $K(m)$ and $E(m)$, $m_K(K)$ and $m_E(E)$, (v) the inverse of a general incomplete elliptic integral in Jacobi's form, $G(\mathrm{am}(u|m),n|m)$, with respect to $u$, and (vi) the partial derivatives of $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $dn(u|m)$, $E(\mathrm{am}(u|m)|m)$, and $\Pi(\mathrm{am}(u|m),n|m)$ with respect to $u$ and those of $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$ with respect to $\phi$. In order to avoid the information loss when $n\ll 1$ and/or $m \ll 1$, focused are the associate incomplete elliptc integrals defined as $B(\phi|m)=[E(\phi|m)-(1-m)F(\phi|m)]/m$, $D(\phi|m)=[F(\phi|m)-E(\phi|m)]/m$, and $J(\phi,n|m)=[\Pi(\phi,n|m)-F(\phi|m)]/n$, and their complete versions, $B(m)=[E(m)-(1-m)K(m)]/m$, $D(m)=[K(m)-E(m)]/m$, and $J(n|m)=[\Pi(n|m)-K(m)]/n$. The main techniques used are (i) the piecewise approximation for single variable functions as $K(m)$, and (ii) the combination of repeated usage of the half and double argument transformations and the truncated Maclaurin series expansions with respect to $u = F(\phi|m)$. The new methods are of the full double precision accuracy without any chance of cancellation against small input arguments. They run significantly faster than the existing methods: (i) 2.5 times faster than Cody's Chebyshev polynomial approximations for $K(m)$ and $E(m)$, (ii) 2.5 times faster than Bulirsch's cel for $\Pi(n|m)$, (iii) slightly faster than Bulirsch's el1 for $F(\phi|m)$, (iv) 3.5 times faster than Carlson's $R_D$ for $E(\phi|m)$, (v) 3.5 times faster than Carlson's $R_C$, $R_D$, $R_F$, and $R_J$ for $\Pi(\phi,n|m)$, and (vi) 1.5 times faster than Bulirsch's \texttt{sncndn} for $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, and $\mathrm{dn}(u|m)$.
Summarized is the recent progress of the methods to compute (i) Legendre's normal form complete elliptic integrals of all three kinds, $K(m)$, $E(m)$, and $\Pi(n|m)$, (ii) Legendre's normal form incomplete elliptic integrals of all three kinds, $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$, (iii) Jacobian elliptic functions, $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $\mathrm{dn}(u|m)$, and $\mathrm{am}(u|m)$, (iv) the inverse functions of $K(m)$ and $E(m)$, $m_K(K)$ and $m_E(E)$, (v) the inverse of a general incomplete elliptic integral in Jacobi's form, $G(\mathrm{am}(u|m),n|m)$, with respect to $u$, and (vi) the partial derivatives of $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, $dn(u|m)$, $E(\mathrm{am}(u|m)|m)$, and $\Pi(\mathrm{am}(u|m),n|m)$ with respect to $u$ and those of $F(\phi|m)$, $E(\phi|m)$, and $\Pi(\phi,n|m)$ with respect to $\phi$. In order to avoid the information loss when $n\ll 1$ and/or $m \ll 1$, focused are the associate incomplete elliptc integrals defined as $B(\phi|m)=[E(\phi|m)-(1-m)F(\phi|m)]/m$, $D(\phi|m)=[F(\phi|m)-E(\phi|m)]/m$, and $J(\phi,n|m)=[\Pi(\phi,n|m)-F(\phi|m)]/n$, and their complete versions, $B(m)=[E(m)-(1-m)K(m)]/m$, $D(m)=[K(m)-E(m)]/m$, and $J(n|m)=[\Pi(n|m)-K(m)]/n$. The main techniques used are (i) the piecewise approximation for single variable functions as $K(m)$, and (ii) the combination of repeated usage of the half and double argument transformations and the truncated Maclaurin series expansions with respect to $u = F(\phi|m)$. The new methods are of the full double precision accuracy without any chance of cancellation against small input arguments. They run significantly faster than the existing methods: (i) 2.5 times faster than Cody's Chebyshev polynomial approximations for $K(m)$ and $E(m)$, (ii) 2.5 times faster than Bulirsch's cel for $\Pi(n|m)$, (iii) slightly faster than Bulirsch's el1 for $F(\phi|m)$, (iv) 3.5 times faster than Carlson's $R_D$ for $E(\phi|m)$, (v) 3.5 times faster than Carlson's $R_C$, $R_D$, $R_F$, and $R_J$ for $\Pi(\phi,n|m)$, and (vi) 1.5 times faster than Bulirsch's \texttt{sncndn} for $\mathrm{sn}(u|m)$, $\mathrm{cn}(u|m)$, and $\mathrm{dn}(u|m)$.
2015年02月10日(火)
博士論文発表会
9:30-10:45 数理科学研究科棟(駒場) 118号室
三原 朋樹 氏 (東京大学大学院数理科学研究科)
On a new geometric construction of a family of Galois representations associated to modular forms
（保型形式に付随するガロア表現の族の新たな幾何的構成について） (JAPANESE)
三原 朋樹 氏 (東京大学大学院数理科学研究科)
On a new geometric construction of a family of Galois representations associated to modular forms
（保型形式に付随するガロア表現の族の新たな幾何的構成について） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
VISIBLE ACTIONS OF REDUCTIVE ALGEBRAIC GROUPS ON COMPLEX ALGEBRAIC VARIETIES（簡約代数群の複素代数多様体への可視的作用について） (JAPANESE)
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
VISIBLE ACTIONS OF REDUCTIVE ALGEBRAIC GROUPS ON COMPLEX ALGEBRAIC VARIETIES（簡約代数群の複素代数多様体への可視的作用について） (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 118号室
中村 あかね 氏 (東京大学大学院数理科学研究科)
Autonomous limit of 4-dimensional Painlev´e-type equations and singular fibers of spectral curve fibrations（4次元Painlev´e 型方程式の自励極限とスペクトラル曲線ファイブレーションの特異ファイバー） (JAPANESE)
中村 あかね 氏 (東京大学大学院数理科学研究科)
Autonomous limit of 4-dimensional Painlev´e-type equations and singular fibers of spectral curve fibrations（4次元Painlev´e 型方程式の自励極限とスペクトラル曲線ファイブレーションの特異ファイバー） (JAPANESE)
博士論文発表会
14:30-15:45 数理科学研究科棟(駒場) 118号室
三田 史彦 氏 (東京大学大学院数理科学研究科)
Fukaya categories and blow-ups（深谷圏とブローアップ） (JAPANESE)
三田 史彦 氏 (東京大学大学院数理科学研究科)
Fukaya categories and blow-ups（深谷圏とブローアップ） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 122号室
中村 勇哉 氏 (東京大学大学院数理科学研究科)
Studies on the minimal log discrepancies（極小ログ食い違い係数の研究） (JAPANESE)
中村 勇哉 氏 (東京大学大学院数理科学研究科)
Studies on the minimal log discrepancies（極小ログ食い違い係数の研究） (JAPANESE)
博士論文発表会
14:30-15:45 数理科学研究科棟(駒場) 122号室
周 冠宇 氏 (東京大学大学院数理科学研究科)
Numerical analysis of various domain-penalty and boundary-penalty methods（様々な領域処罰法および境界処罰法の数値解析） (JAPANESE)
周 冠宇 氏 (東京大学大学院数理科学研究科)
Numerical analysis of various domain-penalty and boundary-penalty methods（様々な領域処罰法および境界処罰法の数値解析） (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 122号室
劉 逸侃 氏 (東京大学大学院数理科学研究科)
Mathematical analysis and numerical methods for phase transformation and anomalous diffusion（相転移と特異拡散に対する数学解析と数値解法について） (ENGLISH)
劉 逸侃 氏 (東京大学大学院数理科学研究科)
Mathematical analysis and numerical methods for phase transformation and anomalous diffusion（相転移と特異拡散に対する数学解析と数値解法について） (ENGLISH)
統計数学セミナー
16:30-17:40 数理科学研究科棟(駒場) 052号室
Ioane Muni Toke 氏 (Ecole Centrale Paris and University of New Caledonia)
Zero-intelligence modelling of limit order books
Ioane Muni Toke 氏 (Ecole Centrale Paris and University of New Caledonia)
Zero-intelligence modelling of limit order books
[ 講演概要 ]
Limit order books (LOB) are at the core of electronic financial markets.
A LOB centralizes all orders of all market participants on a given
exchange, matching buy and sell orders of all types.
In a first part, we observe that a LOB is a queueing system and that
this analogy is fruitful to derive stationary properties of these
structures. Using a basic Poisson model, we compute analytical formulas
for the average shape of the LOB. Our model allows for non-unit size of
limit orders, leading to new predictions on the granularity of financial
markets that turn out to be empirically valid.
In a second part, we study the LOB during the call auction, a market
design often used during the opening and closing phases of the trading
day. We show that in a basic Poisson model of the call auction, the
distributions for the traded volume and the range of clearing prices are
analytically computable. In the case of a liquid market, we derive weak
limits of these distributions and test them empirically.
Limit order books (LOB) are at the core of electronic financial markets.
A LOB centralizes all orders of all market participants on a given
exchange, matching buy and sell orders of all types.
In a first part, we observe that a LOB is a queueing system and that
this analogy is fruitful to derive stationary properties of these
structures. Using a basic Poisson model, we compute analytical formulas
for the average shape of the LOB. Our model allows for non-unit size of
limit orders, leading to new predictions on the granularity of financial
markets that turn out to be empirically valid.
In a second part, we study the LOB during the call auction, a market
design often used during the opening and closing phases of the trading
day. We show that in a basic Poisson model of the call auction, the
distributions for the traded volume and the range of clearing prices are
analytically computable. In the case of a liquid market, we derive weak
limits of these distributions and test them empirically.
2015年02月09日(月)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
吉田 建一 氏 (東京大学大学院数理科学研究科)
Stable presentation length of 3-manifold groups（三次元多様体の基本群の安定表示長） (JAPANESE)
吉田 建一 氏 (東京大学大学院数理科学研究科)
Stable presentation length of 3-manifold groups（三次元多様体の基本群の安定表示長） (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 118号室
勝島 義史 氏 (東京大学大学院数理科学研究科)
The Stokes phenomena of additive linear difference equations（加法的線形差分方程式のストークス現象）
(JAPANESE)
勝島 義史 氏 (東京大学大学院数理科学研究科)
The Stokes phenomena of additive linear difference equations（加法的線形差分方程式のストークス現象）
(JAPANESE)
博士論文発表会
14:30-15:45 数理科学研究科棟(駒場) 118号室
小池 貴之 氏 (東京大学大学院数理科学研究科)
Studies on singular Hermitian metrics with minimal singularities on numerically effective line bundles（数値的半正な正則直線束の極小特異エルミート計量に関する研究） (JAPANESE)
小池 貴之 氏 (東京大学大学院数理科学研究科)
Studies on singular Hermitian metrics with minimal singularities on numerically effective line bundles（数値的半正な正則直線束の極小特異エルミート計量に関する研究） (JAPANESE)
博士論文発表会
16:00-17:15 数理科学研究科棟(駒場) 118号室
江 辰 氏 (東京大学大学院数理科学研究科)
On boundedness of volumes and birationality in birational geometry（双有理幾何学における体積と双有理性の有界性について） (ENGLISH)
江 辰 氏 (東京大学大学院数理科学研究科)
On boundedness of volumes and birationality in birational geometry（双有理幾何学における体積と双有理性の有界性について） (ENGLISH)
博士論文発表会
9:30-10:45 数理科学研究科棟(駒場) 118号室
吉安 徹 氏 (東京大学大学院数理科学研究科)
On Lagrangian caps and their applications（ラグランジュキャップとその応用について）
吉安 徹 氏 (東京大学大学院数理科学研究科)
On Lagrangian caps and their applications（ラグランジュキャップとその応用について）
博士論文発表会
9:30-10:45 数理科学研究科棟(駒場) 122号室
中島 武信 氏 (東京大学大学院数理科学研究科)
A remark on default risks in financial models: a filtering model and a remark on copula（デフォルトリスクに対するファイナンスモデルに関する考察：フィルタリングモデルとコピュラモデルについて） (JAPANESE)
中島 武信 氏 (東京大学大学院数理科学研究科)
A remark on default risks in financial models: a filtering model and a remark on copula（デフォルトリスクに対するファイナンスモデルに関する考察：フィルタリングモデルとコピュラモデルについて） (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 122号室
森本 裕介 氏 (東京大学大学院数理科学研究科)
Monte Carlo Methods for Non linear Problems in Mathematical Finance（数理ファイナンスにおける非線形問題のモンテカルロ法による数値計算） (JAPANESE)
森本 裕介 氏 (東京大学大学院数理科学研究科)
Monte Carlo Methods for Non linear Problems in Mathematical Finance（数理ファイナンスにおける非線形問題のモンテカルロ法による数値計算） (JAPANESE)
博士論文発表会
14:30-15:45 数理科学研究科棟(駒場) 122号室
岡村 和樹 氏 (東京大学大学院数理科学研究科)
Some results concerning the range of random walk of several types（複数の種類のランダムウォークの訪問点に関連する結果） (JAPANESE)
岡村 和樹 氏 (東京大学大学院数理科学研究科)
Some results concerning the range of random walk of several types（複数の種類のランダムウォークの訪問点に関連する結果） (JAPANESE)
博士論文発表会
16:00-17:15 数理科学研究科棟(駒場) 122号室
胡 国荣 氏 (東京大学大学院数理科学研究科)
Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators（非負自己共役作用素に関するBesov及びTriebel-Lizorkin空間） (JAPANESE)
胡 国荣 氏 (東京大学大学院数理科学研究科)
Besov and Triebel-Lizorkin spaces associated to non-negative self-adjoint operators（非負自己共役作用素に関するBesov及びTriebel-Lizorkin空間） (JAPANESE)
2015年02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
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
[ 講演概要 ]
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
2015年01月28日(水)
FMSPレクチャーズ
12:00-16:00 数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books III
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books III
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 参考URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015年01月27日(火)
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
大田 佳宏 氏 (東京大学 数理科学連携基盤センター)
遺伝子の転写機構解明のための数理モデル (Japanese)
大田 佳宏 氏 (東京大学 数理科学連携基盤センター)
遺伝子の転写機構解明のための数理モデル (Japanese)
[ 講演概要 ]
遺伝子の転写とは、DNA 配列を鋳型に RNA polymerase II (RNAP II) という酵素によって遺伝子が読まれ RNA が合成される現象を指し「生命の基本原理」とも考えられている。一方で、転写の生成物である RNA は時間変異性が高く微小不均一性を持つため、細胞を用いた実験において高時間分解能の現象観察を行うことは難しいのが現状である。そこで、観察不可能な領域における高分解能の検証を可能とし、構築したモデルの再現性を保証するため、超離散系や代数的トポロジーなどの数理科学的手法が必須となる。ここでは、セルオートマトンを用いた遺伝子転写機構の数理モデルの研究と、さらに「数学による新規創薬」を目標とした、タンパク質立体構造解析における数理モデルについて紹介したい。
遺伝子の転写とは、DNA 配列を鋳型に RNA polymerase II (RNAP II) という酵素によって遺伝子が読まれ RNA が合成される現象を指し「生命の基本原理」とも考えられている。一方で、転写の生成物である RNA は時間変異性が高く微小不均一性を持つため、細胞を用いた実験において高時間分解能の現象観察を行うことは難しいのが現状である。そこで、観察不可能な領域における高分解能の検証を可能とし、構築したモデルの再現性を保証するため、超離散系や代数的トポロジーなどの数理科学的手法が必須となる。ここでは、セルオートマトンを用いた遺伝子転写機構の数理モデルの研究と、さらに「数学による新規創薬」を目標とした、タンパク質立体構造解析における数理モデルについて紹介したい。
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
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
[ 講演概要 ]
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
FMSPレクチャーズ
13:00-16:20 数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books II
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books II
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 参考URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015年01月26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
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
[ 講演概要 ]
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
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
Jungkai Chen 氏 (National Taiwan University)
Positivity in varieties of maximal Albanese dimension (ENGLISH)
Jungkai Chen 氏 (National Taiwan University)
Positivity in varieties of maximal Albanese dimension (ENGLISH)
[ 講演概要 ]
Given a variety of maximal Albanese dimension, it is known that the holomorphic Euler characteristic is non-negative. It is an interesting question to characterize varieties with vanishing Euler characteristic.
In our previous work (jointly with Debarre and Jiang), we prove that Ein-Lazarsgfeld's example is essentially the only variety of maximal Albanese and Kodaira dimension with vanishing Euler characteristic in dimension three. In the recent joint work with Jiang, we prove a decomposition theorem for the push-forward of canonical sheaf. As a consequence, we are able to generalized our previous characterization. The purpose of this talk is give a survey of these two works.
Given a variety of maximal Albanese dimension, it is known that the holomorphic Euler characteristic is non-negative. It is an interesting question to characterize varieties with vanishing Euler characteristic.
In our previous work (jointly with Debarre and Jiang), we prove that Ein-Lazarsgfeld's example is essentially the only variety of maximal Albanese and Kodaira dimension with vanishing Euler characteristic in dimension three. In the recent joint work with Jiang, we prove a decomposition theorem for the push-forward of canonical sheaf. As a consequence, we are able to generalized our previous characterization. The purpose of this talk is give a survey of these two works.
< 前へ 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188 次へ >
