過去の記録

2015年06月15日(月)

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
Christopher Hacon 氏 (University of Utah/RIMS)
Boundedness of the KSBA functor of
SLC models (English)
[ 講演概要 ]
Let $X$ be a canonically polarized smooth $n$-dimensional projective variety over $\mathbb C$ (so that $\omega _X$ is ample), then it is well-known that a fixed multiple of the canonical line bundle defines an embedding of $X$ in projective space. It then follows easily that if we fix certain invariants of $X$, then $X$ belongs to finitely many deformation types. Since canonical models are rarely smooth, it is important to generalize this result to canonically polarized $n$-dimensional projectivevarieties with canonical singularities. Moreover, since these varieties specialize to non-normal varieties it is also important to generalize this result to semi-log canonical pairs. In this talk we will explain a strong version of the above result that applies to semi-log canonical pairs.This is joint work with C. Xu and J. McKernan
[ 講演参考URL ]
http://www.math.utah.edu/~hacon/

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

The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)
[ 講演概要 ]
We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.

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

ランダム媒質中の多次元拡散家庭の再帰性・非再帰性について
(田村要造氏，楠岡誠一郎氏との共同研究)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

ハミルトン系に対する並列エネルギー保存解法 (日本語)
[ 講演概要 ]

2015年06月12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

The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)
[ 講演概要 ]
For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.

2015年06月11日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

$u_t = \Delta u^m - \nabla \cdot (u^{q-1} \nabla v)$,
$v_t = \Delta v - v + u$.
ここで, $m \ge 1$, $q \ge 2$ とする. この問題に対する時間大域的弱解の存在については, 最初にSugiyama-Kunii (2006)によって $q \le m$ という条件が提示され, その後Ishida-Yokota (2012)によって最大正則性原理を用いたアプローチにより$q < m +2/N$ (Nは空間次元)という条件下で示された. しかし, これらの研究において, 解の時間大域的な挙動の解明という観点から重要である「解の有界性」は未解決のまま残されている. なお, $q < m +2/N$ という条件は, $m=1$, $q=2$のときに対応する通常のKeller-Segel系に対する研究から, 初期値の大きさに制限なく時間大域的弱解の存在が言える条件としては最良であると考えられる. 有界領域上のNeumann問題に対しては, Tao-Winkler (2012), Ishida-Seki-Yokota (2014)によって同様の条件の下で時間大域解の存在だけでなく解の有界性まで示されているが, Gagliardo-Nirenbergの補間不等式を繰り返し用いるために計算が複雑であり, 証明の見通しが良いとは言い難い. 本講演では, 特別な場合に対するSenba-Suzuki (2006)の方法を参考に, Ishida-Yokota (2012)による最大正則性原理を用いるアプローチに小さな修正を施すことによって, 解の有界性が容易に導かれることを示す.

2015年06月10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
David Kerr 氏 (Texas A&M Univ.)
Dynamics, dimension, and $C^*$-algebras

2015年06月09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

[ 講演概要 ]
この講演では完全ラグランジュはめ込みのdisplacementエネルギーと擬正則円盤
のシンプレクティック面積に関するある不等式を与える. 証明はChekanovが有理
ラグランジュ部分多様体のdisplacementエネルギーに関する不等式を示す際に用
いた技法を, ラグランジュはめ込みのFloerホモロジーに拡張して行う. また時

2015年06月08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

Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)
[ 講演概要 ]
By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.

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

On a stochastic Rayleigh-Plesset equation and a certain stochastic Navier-Stokes equation

2015年06月05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

Veech groups of Veech surfaces and periodic points (日本語)
[ 講演概要 ]

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 056号室

A Note on Algorithmic Trading based on Some Personal Experience
[ 講演概要 ]
I overview a brief history of HFT based on my 14 years' personal experience of the algorithmic trading business at a wall-street company. Starting with descriptions about layers of the algo business, I mention a stochastic index arbitrage business that I employed in some detail. After reviewing some HFT specific issues such as super short-period alpha, I try to forecast what is going on with HFT in near future.

2015年06月03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

The Furstenberg boundary and $C^*$-simplicity

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

[ 講演概要 ]

マ類、外洋性サメ類などが挙げられる．回遊により地域ごとに漁獲される水産資

ても未成魚を漁獲する地域と成魚を漁獲する地域が異なる場合が多い．しかし、

を考慮した個体群動態モデルを基本モデルとする．次にモデルから得られる個体

2015年06月01日(月)

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

Rank 2 weak Fano bundles on cubic 3-folds (日本語)
[ 講演概要 ]
A vector bundle on a projective variety is called weak Fano if its
projectivization is a weak Fano manifold. This is a　generalization of
Fano bundles.
In this talk, we will obtain a classification of rank 2 weak Fano
bundles on a nonsingular　cubic hypersurface in a projective 4-space.
Specifically, we will show that there exist rank 2 indecomposable weak
Fano bundles on it.

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

[ 講演概要 ]

2015年05月28日(木)

東京無限可積分系セミナー

17:00-18:30   数理科学研究科棟(駒場) 002号室

Unitary spherical representations of Drinfeld doubles (JAPANESE)
[ 講演概要 ]
It is known that the Drinfeld double of the quantized
enveloping algebra of a semisimple Lie algebra looks similar to the
quantized enveloping algebra of the complexification of the Lie algebra.
In this talk, we investigate the unitary representation theory of such
Drinfeld double via its analogy to that of the complex Lie group.
We also talk on an application to operator algebras.

2015年05月27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
John F. R. Duncan 氏 (Case Western Reserve Univ.)
Vertex operator algebras in umbral Moonshine

代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

On a good reduction criterion for polycurves with sections (Japanese)

2015年05月26日(火)

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

Clifford quartic forms の局所関数等式とhomaloidal EKP-polynomials
[ 講演概要 ]

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

Introduction to formalization of topology using a proof assistant. (JAPANESE)
[ 講演概要 ]
Although the program of formalization goes back to David
Hilbert, it is only recently that we can actually formalize
substantial theorems in modern mathematics. It is made possible by the
development of certain type theory and a computer software called a
proof assistant. We begin this talk by showing our formalization of
some basic geometric topology using a proof assistant COQ. Then we
introduce homotopy type theory (HoTT) of Voevodsky et al., which
interprets type theory from abstract homotopy theoretic perspective.
HoTT proposes "univalent" foundation of mathematics which is
particularly suited for computer formalization.

2015年05月25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

On uniform K-stability (Japanese)
[ 講演概要 ]
It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.

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

Good reduction of K3 surfaces (日本語 or English)
[ 講演概要 ]
We consider degeneration of K3 surfaces over a 1-dimensional base scheme
of mixed characteristic (e.g. Spec of the p-adic integers).
Under the assumption of potential semistable reduction, we first prove
that a trivial monodromy action on the l-adic etale cohomology group
implies potential good reduction, where potential means that we allow a
finite base extension.
Moreover we show that a finite etale base change suffices.
The proof for the first part involves a mixed characteristic
3-dimensional MMP (Kawamata) and the classification of semistable
degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima).
For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~ymatsu/index_j.html

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

A finite diameter theorem on RCD spaces

2015年05月21日(木)

講演会

16:00-17:00   数理科学研究科棟(駒場) 056号室
Tea:15:30～16:00　コモンルーム
Gunnar Carlsson　 氏 (Stanford University, Ayasdi INC)
The Shape of Data
(ENGLISH)
[ 講演概要 ]
There is a tremendous amount of attention being paid to the notion of
"Big Data". In many situations, however, the problem is not so much the
size of the data but rather its complexity. This observation shows that
it is now important to find methods for representing complex data in a
compressed and understandable fashion. Representing data by shapes
turns out to be useful in many situations, and therefore topology, the
mathematical sub discipline which studies shape, becomes quite
relevant. There is now a collection of methods based on topology for
analyzing complex data, and in this talk we will discuss these methods,
with numerous examples.
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/Carlsson.html