## 過去の記録

### 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.
[ 講演参考URL ]
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.
[ 講演参考URL ]

### 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.
[ 講演参考URL ]
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.
[ 講演参考URL ]

### 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

シフト作用素とトーリックミラー対称性 (ENGLISH)
[ 講演概要 ]

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．
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Iritani.pdf

#### 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.
[ 講演参考URL ]
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.
[ 講演参考URL ]

### 2015年03月16日(月)

#### 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

シフト作用素とトーリックミラー対称性 (ENGLISH)
[ 講演概要 ]

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．
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Iritani.pdf

### 2015年03月13日(金)

#### 談話会・数理科学講演会

14:00-15:00   数理科学研究科棟(駒場) 大講義室号室

モジュラー多様体のコホモロジー、保型形式のL-関数、Lie群の球関数
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~takayuki/index-j.html

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 大講義室号室

(JAPANESE)
[ 講演概要 ]
これまで40年近く行ってきた研究を振り返ってみると、確率論及びその周辺の色々な話題について研究してきた。その研究のきっかけは何であったかを思い返してみると、大学時代からの人との出会いに大きく影響されてきたように思う。「私の確率論研究の履歴書」ともいうべき形で、どのような研究をしてきたかをおおざっぱに述べると共に、そしてそのきっかけとなった人との出会いについて述べていきたい。具体的な数式が出てくるのは数学の話は最後の10分間にのみに出てくるようにする予定。
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/teacher/kusuoka.html

#### 談話会・数理科学講演会

15:10-16:10   数理科学研究科棟(駒場) 大講義室号室

Bogomolov 不等式と Miyaoka-Yau 不等式 (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/teacher/miyaoka.html

### 2015年03月10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 Common Room ; This seminar will be held as FMSP Lectures.
Andrei Pajitnov 氏 (Univ. de Nantes)
Arnold conjecture, Floer homology,
and augmentation ideals of finite groups.
(ENGLISH)
[ 講演概要 ]
Let H be a generic time-dependent 1-periodic
Hamiltonian on a closed weakly monotone
symplectic manifold M. We construct a refined version
of the Floer chain complex associated to (M,H),
and use it to obtain new lower bounds for the number P(H)
of the 1-periodic orbits of the corresponding hamiltonian
vector field. We prove in particular that
if the fundamental group of M is finite
and solvable or simple, then P(H)
is not less than the minimal number
of generators of the fundamental group.

This is joint work with Kaoru Ono.

### 2015年02月24日(火)

#### 博士論文発表会

15:00-16:15   数理科学研究科棟(駒場) 128号室

Covariance Estimation from Ultra-High-Frequency Date（超高頻度データに対する共分散推定） (JAPANESE)

### 2015年02月23日(月)

#### 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
Zhenghan Wang 氏 (Microsoft Research Station Q)
Classification of (2+1)-TQFTs and its applications to physics and quantum computation (English)

### 2015年02月19日(木)

#### 東京無限可積分系セミナー

13:30-17:00   数理科学研究科棟(駒場) 002号室

スケイン代数と写像類群 (JAPANESE)
[ 講演概要 ]

ＬＭＯ関手の拡張 (JAPANESE)
[ 講演概要 ]
Cheptea-葉廣-Massuyeau は，閉 3 次元多様体の LMO 不変量の拡張として LMO 関手を導入した．LMO 関手は「高々 1 個の境界成分を持つ曲面の間の Lagrangian コボルディズムを射とするモノイダル圏」から「top-substantial Jacobi 図の形式的級数を射とするモノイダル圏」へのテンソル積を保つ関手である．本講演では，曲面が任意個数の境界成分を持つ場合に対する LMO 関手の拡張を紹介する．さらにその d 次の項が d 次の有限型不変量であることを説明する．

#### 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
Dobrislav Dobrev 氏 (Board of Governors of the Federal Reserve System, Division of International Finance)
TBA
[ 講演概要 ]
TBA

### 2015年02月18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
Piotr Achinger 氏 (University of California, Berkeley)
Wild ramification and $K(\pi, 1)$ spaces (English)
[ 講演概要 ]
A smooth variety in characteristic zero is Zariski-locally a $K(\pi,1)$ space, i.e., has trivial higher homotopy groups. This fact is of crucial importance in Artin's proof that $\ell$-adic cohomology agrees with singular cohomology over $\mathbb{C}$. The characteristic $p$ variant of this is not known --- we do not even know whether the affine plane is a $K(\pi, 1)$ in positive characteristic! I will show how to reduce this question to a Bertini-type’' statement regarding wild ramification of $\ell$-adic local systems on affine spaces, which might be of independent interest. I will verify this statement in the special case of local systems of rank $1$ and speculate on how one might treat the general case.

#### 数値解析セミナー

14:30-16:00   数理科学研究科棟(駒場) 002号室

Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations (日本語)
[ 講演概要 ]

#### 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

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 $\mathrm{dn}(u|m)$.

### 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

On a new geometric construction of a family of Galois representations associated to modular forms
（保型形式に付随するガ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

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

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

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

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

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

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
[ 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.