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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
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
足立高徳 氏 (立命館大学)
A Note on Algorithmic Trading based on Some Personal Experience
足立高徳 氏 (立命館大学)
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.
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
小沢登高 氏 (京大数理研)
The Furstenberg boundary and $C^*$-simplicity
小沢登高 氏 (京大数理研)
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
岩田繁英 氏 (東京海洋大学大学院海洋科学技術研究科)
回遊を伴う漁業資源の個体群動態と管理戦略
岩田繁英 氏 (東京海洋大学大学院海洋科学技術研究科)
回遊を伴う漁業資源の個体群動態と管理戦略
[ 講演概要 ]
我が国では回遊を伴う水産資源を広く利用している．イワシ類、マグロ類、サン
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
源の年齢層は大きく変化する．特に我が国沿岸では同じ種を漁獲する場合であっ
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、
回遊による漁獲年齢の変化に注目した研究は少ない．本研究は、回遊と年齢構造
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
群動態に対する漁獲の影響を加えて管理戦略について考える．具体的には成魚と
未成魚の２齢、２生息地のモデルを仮定した個体群動態のもとで、回遊が漁獲に
与える影響や各年齢の漁獲がすべての生息地における総漁獲への影響を考える.
回遊は死滅回遊とそれ以外の回遊パターンを仮定して考える．最終的に重量、
単価を仮定しどのようなときにどんな管理戦略が適しているか紹介し議論を進める．
我が国では回遊を伴う水産資源を広く利用している．イワシ類、マグロ類、サン
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
源の年齢層は大きく変化する．特に我が国沿岸では同じ種を漁獲する場合であっ
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、
回遊による漁獲年齢の変化に注目した研究は少ない．本研究は、回遊と年齢構造
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
群動態に対する漁獲の影響を加えて管理戦略について考える．具体的には成魚と
未成魚の２齢、２生息地のモデルを仮定した個体群動態のもとで、回遊が漁獲に
与える影響や各年齢の漁獲がすべての生息地における総漁獲への影響を考える.
回遊は死滅回遊とそれ以外の回遊パターンを仮定して考える．最終的に重量、
単価を仮定しどのようなときにどんな管理戦略が適しているか紹介し議論を進める．
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
石川大蔵 氏 (早稲田)
Rank 2 weak Fano bundles on cubic 3-folds (日本語)
石川大蔵 氏 (早稲田)
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.
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
星野 壮登 氏 (東京大学大学院数理科学研究科)
正則性構造理論による特異な確率偏微分方程式の近似について
星野 壮登 氏 (東京大学大学院数理科学研究科)
正則性構造理論による特異な確率偏微分方程式の近似について
[ 講演概要 ]
確率偏微分方程式の解は一般に超関数として定義されるが、非線形項をもつときは不適切である場合がある。近年Hairerによって、そのような方程式に対する一般的な近似理論が導入された。本講演ではその一つとしてＫＰＺ方程式を取り扱い、Hairerによる結果とその拡張について説明する。
確率偏微分方程式の解は一般に超関数として定義されるが、非線形項をもつときは不適切である場合がある。近年Hairerによって、そのような方程式に対する一般的な近似理論が導入された。本講演ではその一つとしてＫＰＺ方程式を取り扱い、Hairerによる結果とその拡張について説明する。
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
荒野悠輝 氏 (東大数理)
Unitary spherical representations of Drinfeld doubles (JAPANESE)
荒野悠輝 氏 (東大数理)
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.
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
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
長町一平 氏 (東京大学数理科学研究科)
On a good reduction criterion for polycurves with sections (Japanese)
長町一平 氏 (東京大学数理科学研究科)
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
小木曽岳義 氏 (城西大学)
Clifford quartic forms の局所関数等式とhomaloidal EKP-polynomials
小木曽岳義 氏 (城西大学)
Clifford quartic forms の局所関数等式とhomaloidal EKP-polynomials
[ 講演概要 ]
局所関数等式が正則概均質ベクトル空間の基本相対不変式とその双対空間の多項式のペアから与えられることは知られている。我々は Clifford quartic form と呼ばれるある４次斉次多項式を構成し, それが概均質ベクトル空間の相対不変式ではないにも関わらず局所関数等式を満たすことを示した。局所関数等式を満たす多項式を特徴付ける問題は興味深い未解決問題であるが, この問題に関連し、 Etingof, Kazhdan, Polishchuk は（もっと一般的な設定で）ある予想を提示した。我々は、 Clifford quartic form を用いて, この予想に反例があることを示した。 (この講演は佐藤文広氏との共同研究に基づいている。）
局所関数等式が正則概均質ベクトル空間の基本相対不変式とその双対空間の多項式のペアから与えられることは知られている。我々は Clifford quartic form と呼ばれるある４次斉次多項式を構成し, それが概均質ベクトル空間の相対不変式ではないにも関わらず局所関数等式を満たすことを示した。局所関数等式を満たす多項式を特徴付ける問題は興味深い未解決問題であるが, この問題に関連し、 Etingof, Kazhdan, Polishchuk は（もっと一般的な設定で）ある予想を提示した。我々は、 Clifford quartic form を用いて, この予想に反例があることを示した。 (この講演は佐藤文広氏との共同研究に基づいている。）
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
久我 健一 氏 (千葉大学)
Introduction to formalization of topology using a proof assistant. (JAPANESE)
Tea : 16:30-17:00 Common Room
久我 健一 氏 (千葉大学)
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.
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
久本 智之 氏 (名古屋大学)
On uniform K-stability (Japanese)
久本 智之 氏 (名古屋大学)
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.
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
松本雄也 氏 (東大数理)
Good reduction of K3 surfaces (日本語 or English)
https://www.ms.u-tokyo.ac.jp/~ymatsu/index_j.html
松本雄也 氏 (東大数理)
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.
[ 参考URL ]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.
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
北別府 悠 氏 (京都大学大学院理学研究科)
A finite diameter theorem on RCD spaces
北別府 悠 氏 (京都大学大学院理学研究科)
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)
http://faculty.ms.u-tokyo.ac.jp/Carlsson.html
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.
[ 参考URL ]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.
http://faculty.ms.u-tokyo.ac.jp/Carlsson.html
2015年05月20日(水)
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
Shou-Wu Zhang 氏 (Princeton University)
Colmez' conjecture in average (English)
Shou-Wu Zhang 氏 (Princeton University)
Colmez' conjecture in average (English)
[ 講演概要 ]
This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.
Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
(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.)
This is a report on a joint work with Xinyi Yuan on a conjectured formula of Colmez about the Faltings heights of CM abelian varieties. I will sketch a deduction of this formula in average of CM types from our early work on Gross-Zagier formula. When combined with a recent work of Tsimerman, this result implies the Andre-Oort conjecture for the moduli of abelian varieties.
Our method is different than a recently announced proof of a weaker form of the average formula by Andreatta, Howard, Goren, and Madapusi Pera: we use neither high dimensional Shimura varieties nor Borcherds' liftings.
(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.)
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
磯野優介 氏 (京大数理研)
Unique prime factorization and bicentralizer problem for a class of type III factors
磯野優介 氏 (京大数理研)
Unique prime factorization and bicentralizer problem for a class of type III factors
2015年05月19日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
山田澄生 氏 (学習院大学)
Convex bodies and geometry of some associated Minkowski functionals (日本語)
山田澄生 氏 (学習院大学)
Convex bodies and geometry of some associated Minkowski functionals (日本語)
[ 講演概要 ]
In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).
In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).
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
Anton Evseev 氏 (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
Anton Evseev 氏 (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ 講演概要 ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.
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
加藤 晃史 氏 (東京大学大学院数理科学研究科)
Quiver mutation loops and partition q-series (JAPANESE)
Tea : 16:30-17:00 Common Room
加藤 晃史 氏 (東京大学大学院数理科学研究科)
Quiver mutation loops and partition q-series (JAPANESE)
[ 講演概要 ]
Quivers and their mutations are ubiquitous in mathematics and
mathematical physics; they play a key role in cluster algebras,
wall-crossing phenomena, gluing of ideal tetrahedra, etc.
Recently, we introduced a partition q-series for a quiver mutation loop
(a loop in a quiver exchange graph) using the idea of state sum of statistical
mechanics. The partition q-series enjoy some nice properties such
as pentagon move invariance. We also discuss their relation with combinatorial
Donaldson-Thomas invariants, as well as fermionic character formulas of
certain conformal field theories.
This is a joint work with Yuji Terashima.
Quivers and their mutations are ubiquitous in mathematics and
mathematical physics; they play a key role in cluster algebras,
wall-crossing phenomena, gluing of ideal tetrahedra, etc.
Recently, we introduced a partition q-series for a quiver mutation loop
(a loop in a quiver exchange graph) using the idea of state sum of statistical
mechanics. The partition q-series enjoy some nice properties such
as pentagon move invariance. We also discuss their relation with combinatorial
Donaldson-Thomas invariants, as well as fermionic character formulas of
certain conformal field theories.
This is a joint work with Yuji Terashima.
2015年05月18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
足立 真訓 氏 (東京理科大学)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
足立 真訓 氏 (東京理科大学)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
[ 講演概要 ]
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR 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
Will Donovan 氏 (IPMU)
Twists and braids for general 3-fold flops (English)
http://db.ipmu.jp/member/personal/4007en.html
Will Donovan 氏 (IPMU)
Twists and braids for general 3-fold flops (English)
[ 講演概要 ]
When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
[ 参考URL ]When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
http://db.ipmu.jp/member/personal/4007en.html
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
尾崎克久 氏 (芝浦工業大学システム理工学部)
エラーフリー変換を用いた行列積の高精度計算
(日本語)
尾崎克久 氏 (芝浦工業大学システム理工学部)
エラーフリー変換を用いた行列積の高精度計算
(日本語)
[ 講演概要 ]
すべての成分が浮動小数点数である行列の積に関して，数値計算を用いて高信頼な結果を得る手法について研究を行っている．本講演では，HPCの技術者がチューニングをした高速なライブラリを直に使用する高精度行列積アルゴリズムについて紹介したい．アルゴリズムの概要，長所と短所，エラーフリーであることの証明から解説し，区間演算への応用や最近開発できた事後保証型のアルゴリズムについても紹介したい．
すべての成分が浮動小数点数である行列の積に関して，数値計算を用いて高信頼な結果を得る手法について研究を行っている．本講演では，HPCの技術者がチューニングをした高速なライブラリを直に使用する高精度行列積アルゴリズムについて紹介したい．アルゴリズムの概要，長所と短所，エラーフリーであることの証明から解説し，区間演算への応用や最近開発できた事後保証型のアルゴリズムについても紹介したい．
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
徐 路 氏 (東京大学大学院数理科学研究科)
Central limit theorem for stochastic heat equations in random environments
徐 路 氏 (東京大学大学院数理科学研究科)
Central limit theorem for stochastic heat equations in random environments
2015年05月14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
太田雅人 氏 (東京理科大学理学部数学科)
Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)
太田雅人 氏 (東京理科大学理学部数学科)
Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)
[ 講演概要 ]
デルタ関数をポテンシャルとして含む空間1次元の非線形シュレディンガー方程式を考える．この方程式の定在波解は双曲線関数を用いて具体的に書き表すことができる．そのため，方程式がスケール不変でないにも関わらず，角振動数をパラメータとする定在波解の族のエネルギーや電荷のパラメータ依存性を具体的に計算することができ，定在波解の軌道安定性と不安定性を完全に分類することができる．この講演では，軌道不安定な定在波解の近傍から出発した解が有限時間で爆発するための条件について考察する．このとき，定在波解は強不安定であるというが，今回得られた強不安定性の十分条件と軌道不安定性に関する従来の条件との関係を数値的に調べ，関連する問題を紹介する．
デルタ関数をポテンシャルとして含む空間1次元の非線形シュレディンガー方程式を考える．この方程式の定在波解は双曲線関数を用いて具体的に書き表すことができる．そのため，方程式がスケール不変でないにも関わらず，角振動数をパラメータとする定在波解の族のエネルギーや電荷のパラメータ依存性を具体的に計算することができ，定在波解の軌道安定性と不安定性を完全に分類することができる．この講演では，軌道不安定な定在波解の近傍から出発した解が有限時間で爆発するための条件について考察する．このとき，定在波解は強不安定であるというが，今回得られた強不安定性の十分条件と軌道不安定性に関する従来の条件との関係を数値的に調べ，関連する問題を紹介する．
2015年05月13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
窪田陽介 氏 (東大数理)
Controlled topological phases and the bulk-edge correspondence for
topological insulators (English)
窪田陽介 氏 (東大数理)
Controlled topological phases and the bulk-edge correspondence for
topological insulators (English)
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