## 過去の記録

#### 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

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

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

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

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

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 ]
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 ]

### 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 ]
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 ]

### 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．
[ 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.
[ 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.
[ 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．
[ 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 ]

[ 参考URL ]
https://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。
[ 参考URL ]
https://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 ]

[ 参考URL ]
https://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.