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過去の記録
過去の記録 ～12/04｜本日 12/05 | 今後の予定 12/06～
2019年05月22日(水)
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
河上 龍郎 氏 (東大数理)
Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic
河上 龍郎 氏 (東大数理)
Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic
[ 講演概要 ]
In characteristic zero, cotangent bundle of n(>1)-dimensional smooth projective varieties does not contain a big line bundle. This is a part of Bogomolov vanishing and this vanishing plays an important role in the proof of Miyaoka-Yau inequality. In positive characteristic, it is known that Bogomolov vanishing does not hold. There exists a general type surface whose cotangent bundle contains an ample line bundle. So, it is natural to ask when Bogomolov type vanishing holds in positive characteristic. In this talk, I discuss Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic.
In characteristic zero, cotangent bundle of n(>1)-dimensional smooth projective varieties does not contain a big line bundle. This is a part of Bogomolov vanishing and this vanishing plays an important role in the proof of Miyaoka-Yau inequality. In positive characteristic, it is known that Bogomolov vanishing does not hold. There exists a general type surface whose cotangent bundle contains an ample line bundle. So, it is natural to ask when Bogomolov type vanishing holds in positive characteristic. In this talk, I discuss Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic.
2019年05月21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: Common Room 16:30-17:00
Maria de los Angeles Guevara 氏 (大阪市立大学)
On the dealternating number and the alternation number (ENGLISH)
Tea: Common Room 16:30-17:00
Maria de los Angeles Guevara 氏 (大阪市立大学)
On the dealternating number and the alternation number (ENGLISH)
[ 講演概要 ]
Links can be divided into alternating and non-alternating depending on if they possess an alternating diagram or not. After the proof of the Tait flype conjecture on alternating links, it became an important question to ask how a non-alternating link is “close to” alternating links. The dealternating and alternation numbers, which are invariants introduced by C. Adams et al. and A. Kawauchi, respectively, can deal with this question. By definitions, for any link, its alternation number is less than or equal to its dealternating number. It is known that in general the equality does not hold. However, in general, it is not easy to show a gap between these invariants. In this seminar, we will show some results regarding these invariants. In particular, for each pair of positive integers, we will construct infinitely many knots, which have dealternating and alternation numbers determined for these integers. Therefore, an arbitrary gap between the values of these invariants will be obtained.
Links can be divided into alternating and non-alternating depending on if they possess an alternating diagram or not. After the proof of the Tait flype conjecture on alternating links, it became an important question to ask how a non-alternating link is “close to” alternating links. The dealternating and alternation numbers, which are invariants introduced by C. Adams et al. and A. Kawauchi, respectively, can deal with this question. By definitions, for any link, its alternation number is less than or equal to its dealternating number. It is known that in general the equality does not hold. However, in general, it is not easy to show a gap between these invariants. In this seminar, we will show some results regarding these invariants. In particular, for each pair of positive integers, we will construct infinitely many knots, which have dealternating and alternation numbers determined for these integers. Therefore, an arbitrary gap between the values of these invariants will be obtained.
2019年05月20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) 128号室
奥間 智弘 氏 (山形大学)
Cohomology and normal reduction numbers of normal surface singularities (Japanese)
奥間 智弘 氏 (山形大学)
Cohomology and normal reduction numbers of normal surface singularities (Japanese)
[ 講演概要 ]
The normal reduction number of a normal surface singularity relates the maximal degree of the generators of associated graded algebra for certain line bundles on resolution spaces. We show fundamental properties of this invariant and formulas for some special cases. This talk is based on the joint work with Kei-ichi Watanabe and Ken-ichi Yoshida.
The normal reduction number of a normal surface singularity relates the maximal degree of the generators of associated graded algebra for certain line bundles on resolution spaces. We show fundamental properties of this invariant and formulas for some special cases. This talk is based on the joint work with Kei-ichi Watanabe and Ken-ichi Yoshida.
2019年05月16日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
岡本 龍明 氏 (NTT)
ビットコイン：電子マネー革命 (Japanese)
岡本 龍明 氏 (NTT)
ビットコイン：電子マネー革命 (Japanese)
[ 講演概要 ]
1980年代から暗号分野では電子マネーの研究が行われてきたが，いずれも権威ある(電子マネー)発行機関の存在を前提としていた．ところが，2008年に誕生したビットコインは，特権的な機関は存在せず，非中央集権的な形でマネー（コイン）を発行する仕組みを作り上げた．今回は基本的な暗号機能を利用してどのように非中央集権的にコインを発行するのかなど，ビットコインの仕組みを説明する．
1980年代から暗号分野では電子マネーの研究が行われてきたが，いずれも権威ある(電子マネー)発行機関の存在を前提としていた．ところが，2008年に誕生したビットコインは，特権的な機関は存在せず，非中央集権的な形でマネー（コイン）を発行する仕組みを作り上げた．今回は基本的な暗号機能を利用してどのように非中央集権的にコインを発行するのかなど，ビットコインの仕組みを説明する．
2019年05月15日(水)
FMSPレクチャーズ
17:30-18:30 数理科学研究科棟(駒場) 122号室
*The date and room have changed.
Gábor Domokos 氏 (Hungarian Academy of Sciences/Budapest University of Technology and Economics)
'Oumuamua, the Gömböc and the Pebbles of Mars (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Domokos.pdf
*The date and room have changed.
Gábor Domokos 氏 (Hungarian Academy of Sciences/Budapest University of Technology and Economics)
'Oumuamua, the Gömböc and the Pebbles of Mars (ENGLISH)
[ 講演概要 ]
In this talk I will concentrate on two examples from planetary science, which made the headlines in recent years to highlight the power and significance of nonlinear geometric partial differential equations (PDEs) explaining puzzles presented by Nature. One key link between PDE theory of shape evolution and natural phenomena is the Gömböc, the first mono-monostatic object whose existence was first conjectured by V.I. Arnold in 1995. I will explain the connection and illustrate the process how mathematical models of Nature may be identified.
[ 参考URL ]In this talk I will concentrate on two examples from planetary science, which made the headlines in recent years to highlight the power and significance of nonlinear geometric partial differential equations (PDEs) explaining puzzles presented by Nature. One key link between PDE theory of shape evolution and natural phenomena is the Gömböc, the first mono-monostatic object whose existence was first conjectured by V.I. Arnold in 1995. I will explain the connection and illustrate the process how mathematical models of Nature may be identified.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Domokos.pdf
FMSPレクチャーズ
15:00-17:20 数理科学研究科棟(駒場) 122号室
J. Scott Carter 氏 (University of South Alabama / Osaka City University)
Part 1 : Categorical analogues of surface singularities
Part 2 : Prismatic Homology (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Carter.pdf
J. Scott Carter 氏 (University of South Alabama / Osaka City University)
Part 1 : Categorical analogues of surface singularities
Part 2 : Prismatic Homology (ENGLISH)
[ 講演概要 ]
Part 1 :
Isotopy classes of surfaces that are embedded in 3-space can be described as a free 4-category that has one object and one weakly invertible arrow. That description coincides with a fundamental higher homotopy group. The surface singularities that correspond to cusps and optimal points on folds can be used to develop categorical analogues of swallow-tails and horizontal cusps. In this talk, the 4-category will be constructed from the ground up, and the general structure will be described.
Part 2 :
A qualgebra is a set that has two binary operations whose relationships to each other are similar to the relations between group multiplication and conjugation. The axioms themselves are described in terms of isotopies of knotted trivalent graphs and the handle-body knots that are represented. The moves naturally live in prisms. By using a generalization of the tensor product of chain complexes, a homology theory is presented that encapsulates these axioms and the higher order relations between them. We show how to use this homology theory to give a solution a system of tensor equations related to the Yang-Baxter relation.
[ 参考URL ]Part 1 :
Isotopy classes of surfaces that are embedded in 3-space can be described as a free 4-category that has one object and one weakly invertible arrow. That description coincides with a fundamental higher homotopy group. The surface singularities that correspond to cusps and optimal points on folds can be used to develop categorical analogues of swallow-tails and horizontal cusps. In this talk, the 4-category will be constructed from the ground up, and the general structure will be described.
Part 2 :
A qualgebra is a set that has two binary operations whose relationships to each other are similar to the relations between group multiplication and conjugation. The axioms themselves are described in terms of isotopies of knotted trivalent graphs and the handle-body knots that are represented. The moves naturally live in prisms. By using a generalization of the tensor product of chain complexes, a homology theory is presented that encapsulates these axioms and the higher order relations between them. We show how to use this homology theory to give a solution a system of tensor equations related to the Yang-Baxter relation.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Carter.pdf
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 118号室
今学期は基本水曜日とします。部屋も去年度と異なります。
藤野修 氏 (大阪大学)
On quasi-log canonical pairs
(Japanese)
今学期は基本水曜日とします。部屋も去年度と異なります。
藤野修 氏 (大阪大学)
On quasi-log canonical pairs
(Japanese)
[ 講演概要 ]
The notion of quasi-log canonical pairs was introduced by Florin Ambro. It is a kind of generalizations of that of log canonical pairs. Now we know that quasi-log canonical pairs are ubiquitous in the theory of minimal models. In this talk, I will explain some basic properties and examples of quasi-log canonical pairs. I will also discuss some new developments around quasi-log canonical pairs. Some parts are joint works with Haidong Liu.
The notion of quasi-log canonical pairs was introduced by Florin Ambro. It is a kind of generalizations of that of log canonical pairs. Now we know that quasi-log canonical pairs are ubiquitous in the theory of minimal models. In this talk, I will explain some basic properties and examples of quasi-log canonical pairs. I will also discuss some new developments around quasi-log canonical pairs. Some parts are joint works with Haidong Liu.
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
木原貴行 氏 (名古屋大)
Combinatorial aspects of Borel functions
木原貴行 氏 (名古屋大)
Combinatorial aspects of Borel functions
2019年05月14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: Common Room 16:30-17:00
J. Scott Carter 氏 (University of South Alabama, 大阪市立大学)
Diagrammatic Algebra (ENGLISH)
Tea: Common Room 16:30-17:00
J. Scott Carter 氏 (University of South Alabama, 大阪市立大学)
Diagrammatic Algebra (ENGLISH)
[ 講演概要 ]
Three main ideas will be explored. First, a higher dimensional category (a category that has arrows, double arrows, triple arrows, and quadruple arrows) that is based upon the axioms of a Frobenius algebra will be outlined. Then these structures will be promoted into one higher dimension so that braiding can be introduced. Second, relationships between braiding and multiplication will be studied from a homological perspective. Third, the next order relations will be used to formulate a system of abstract tensor equations that are analogous to the Yang-Baxter relation. In this way, a broad outline of the notion of diagrammatic algebra will be presented.
Three main ideas will be explored. First, a higher dimensional category (a category that has arrows, double arrows, triple arrows, and quadruple arrows) that is based upon the axioms of a Frobenius algebra will be outlined. Then these structures will be promoted into one higher dimension so that braiding can be introduced. Second, relationships between braiding and multiplication will be studied from a homological perspective. Third, the next order relations will be used to formulate a system of abstract tensor equations that are analogous to the Yang-Baxter relation. In this way, a broad outline of the notion of diagrammatic algebra will be presented.
2019年05月13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) 128号室
只野 誉 氏 (東京理科大学)
Some Bonnet--Myers Type Theorems for Transverse Ricci Solitons on Complete Sasaki Manifolds (Japanese)
只野 誉 氏 (東京理科大学)
Some Bonnet--Myers Type Theorems for Transverse Ricci Solitons on Complete Sasaki Manifolds (Japanese)
[ 講演概要 ]
The aim of this talk is to discuss the compactness of complete Ricci solitons and its generalizations. Ricci solitons were introduced by R. Hamilton in 1982 and are natural generalizations of Einstein manifolds. They correspond to self-similar solutions to the Ricci flow and often arise as singularity models of the flow. The importance of Ricci solitons was demonstrated by G. Perelman, where they played crucial roles in his affirmative resolution of the Poincare conjecture.
In this talk, after we review basic facts on Ricci solitons, I would like to introduce some Bonnet--Myers type theorems for complete Ricci solitons. Our results generalize the previous Bonnet--Myers type theorems due to W. Ambrose (1957), J. Cheeger, M. Gromov, and M. Taylor (1982), M. Fernandez-Lopez and E. Garcia-Rio (2008), M. Limoncu (2010, 2012), Z. Qian (1997), Y. Soylu (2017), and G. Wei and W. Wylie (2009). Moreover, I would also like to extend such Bonnet--Myers type theorems to the case of transverse Ricci solitons on complete Sasaki manifolds. Our results generalize the previous Bonnet--Myers type theorems for complete Sasaki manifolds due to I. Hasegawa and M. Seino (1981) and Y. Nitta (2009).
The aim of this talk is to discuss the compactness of complete Ricci solitons and its generalizations. Ricci solitons were introduced by R. Hamilton in 1982 and are natural generalizations of Einstein manifolds. They correspond to self-similar solutions to the Ricci flow and often arise as singularity models of the flow. The importance of Ricci solitons was demonstrated by G. Perelman, where they played crucial roles in his affirmative resolution of the Poincare conjecture.
In this talk, after we review basic facts on Ricci solitons, I would like to introduce some Bonnet--Myers type theorems for complete Ricci solitons. Our results generalize the previous Bonnet--Myers type theorems due to W. Ambrose (1957), J. Cheeger, M. Gromov, and M. Taylor (1982), M. Fernandez-Lopez and E. Garcia-Rio (2008), M. Limoncu (2010, 2012), Z. Qian (1997), Y. Soylu (2017), and G. Wei and W. Wylie (2009). Moreover, I would also like to extend such Bonnet--Myers type theorems to the case of transverse Ricci solitons on complete Sasaki manifolds. Our results generalize the previous Bonnet--Myers type theorems for complete Sasaki manifolds due to I. Hasegawa and M. Seino (1981) and Y. Nitta (2009).
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 056号室
相島健助 氏 (法政大学情報科学部)
対称固有値問題に対する反復改良法 (Japanese)
相島健助 氏 (法政大学情報科学部)
対称固有値問題に対する反復改良法 (Japanese)
[ 講演概要 ]
本講演では，対称行列の固有値問題の数値解法について議論する．具体的には，対称固有値問題のすべての固有値と固有ベクトルの近似値が得られている場合に，さらに精度を上げるための反復改良法を提案しその収束理論を与える．
対称固有値問題のすべての固有値と固有ベクトルを計算する場合，後退誤差解析の意味で数値的に安定な手法が既に確立されており，数値線形代数の標準ライブラリLAPACK或いはMATLABのような汎用ソフトにも実装され広く利用されている．ただし，悪条件問題において固有ベクトルの数値計算は原理的に困難であることには注意を要する．この困難に対し，本研究で提案する適合的に計算精度を変更しながら行う反復改良法は一つの有力な技術になりうる．また主要計算部分が行列積で表現でき，この性質は実装面での長所となる．本講演では，提案手法の着想や導出過程そして数値的な性能と二次収束性の証明について述べる．本研究は荻田武史氏（東京女子大学）との共同研究である．
本講演では，対称行列の固有値問題の数値解法について議論する．具体的には，対称固有値問題のすべての固有値と固有ベクトルの近似値が得られている場合に，さらに精度を上げるための反復改良法を提案しその収束理論を与える．
対称固有値問題のすべての固有値と固有ベクトルを計算する場合，後退誤差解析の意味で数値的に安定な手法が既に確立されており，数値線形代数の標準ライブラリLAPACK或いはMATLABのような汎用ソフトにも実装され広く利用されている．ただし，悪条件問題において固有ベクトルの数値計算は原理的に困難であることには注意を要する．この困難に対し，本研究で提案する適合的に計算精度を変更しながら行う反復改良法は一つの有力な技術になりうる．また主要計算部分が行列積で表現でき，この性質は実装面での長所となる．本講演では，提案手法の着想や導出過程そして数値的な性能と二次収束性の証明について述べる．本研究は荻田武史氏（東京女子大学）との共同研究である．
2019年05月09日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
岡本 龍明 氏 (NTT)
暗号理論の発展 (Japanese)
岡本 龍明 氏 (NTT)
暗号理論の発展 (Japanese)
[ 講演概要 ]
前回紹介したゼロ知識証明の発展として、最近（2013年以降に）提案された実用性の高い非対話ゼロ知識証明(ZK-SNARK)は、すでに仮想通貨で用いられており、今後さらにさまざまな分野に応用が広がると思われる。また、1980年代に確立された暗号安全性理論は1990年代を通じて発展を続け2001年にはそれまでのいずれよりも強い安全性概念として汎用的結合可能性（UC）の形で集大成された．今回は、ZK-SNARKおよびUCの紹介を行う。（参考図書：岡本龍明著「現代暗号の誕生と発展」（近代科学社））
前回紹介したゼロ知識証明の発展として、最近（2013年以降に）提案された実用性の高い非対話ゼロ知識証明(ZK-SNARK)は、すでに仮想通貨で用いられており、今後さらにさまざまな分野に応用が広がると思われる。また、1980年代に確立された暗号安全性理論は1990年代を通じて発展を続け2001年にはそれまでのいずれよりも強い安全性概念として汎用的結合可能性（UC）の形で集大成された．今回は、ZK-SNARKおよびUCの紹介を行う。（参考図書：岡本龍明著「現代暗号の誕生と発展」（近代科学社））
2019年05月08日(水)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 118号室
橋詰 健太 氏 (東大数理)
On Minimal model theory for log canonical pairs with big boundary divisors
橋詰 健太 氏 (東大数理)
On Minimal model theory for log canonical pairs with big boundary divisors
[ 講演概要 ]
In 2010, Birkar--Cascini--Hacon--McKernan established the minimal model theory for Kawamata log terminal pairs with big boundary divisors, and a lot of theorems in the birational geometry are
proved by applying this result. It is expected that this result can be generalized to log canonical pairs. Currently, it is known that the minimal model theory for log canonical pairs can be reduced to the case of big boundary divisors. In this talk, we introduce a partial generalization of the result by Birkar--Cascini--Hacon--McKernan. Roughly speaking, we generalized their result to lc pairs with big boundary divisors having only small lc centers. We also explain another generalization, which is originally announced by Hu, and we discuss termination of log minimal model program in a spacial case. This is a joint work with Zhengyu Hu, and the work is in progress.
In 2010, Birkar--Cascini--Hacon--McKernan established the minimal model theory for Kawamata log terminal pairs with big boundary divisors, and a lot of theorems in the birational geometry are
proved by applying this result. It is expected that this result can be generalized to log canonical pairs. Currently, it is known that the minimal model theory for log canonical pairs can be reduced to the case of big boundary divisors. In this talk, we introduce a partial generalization of the result by Birkar--Cascini--Hacon--McKernan. Roughly speaking, we generalized their result to lc pairs with big boundary divisors having only small lc centers. We also explain another generalization, which is originally announced by Hu, and we discuss termination of log minimal model program in a spacial case. This is a joint work with Zhengyu Hu, and the work is in progress.
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
山本祐輝 氏 (東京大学数理科学研究科)
On the types for supercuspidal representations of inner forms of GL_n (Japanese)
山本祐輝 氏 (東京大学数理科学研究科)
On the types for supercuspidal representations of inner forms of GL_n (Japanese)
[ 講演概要 ]
Aを非アルキメデス的局所体F上の中心的単純環とし，Gをその乗法群とする．
Gのsmooth表現を考察する際に有用な理論の一つとしてtypeの理論が存在する．
type (J, ¥lambda) とはGのコンパクト部分群Jと J の既約部分表現 ¥lambda の組であって，Gの既約表現をある意味で分類することのできるものである．
S¥'echerre-Stevenにより，Gのtypeの族としてsimple typeという概念が構成されている．
本講演ではGのtypeについて説明した後，JをGの極大コンパクト部分群Kとして固定した場合にtypeがどれだけ存在するかについて議論する．
特に，Gのsupercuspidal表現 ¥pi に対し，¥pi がsimple typeとしてある種の不分岐的な条件を満たすようなものを含むときに，Kの表現で ¥pi に対応するtypeがGでの共役を除き一意であることを示す．
Aを非アルキメデス的局所体F上の中心的単純環とし，Gをその乗法群とする．
Gのsmooth表現を考察する際に有用な理論の一つとしてtypeの理論が存在する．
type (J, ¥lambda) とはGのコンパクト部分群Jと J の既約部分表現 ¥lambda の組であって，Gの既約表現をある意味で分類することのできるものである．
S¥'echerre-Stevenにより，Gのtypeの族としてsimple typeという概念が構成されている．
本講演ではGのtypeについて説明した後，JをGの極大コンパクト部分群Kとして固定した場合にtypeがどれだけ存在するかについて議論する．
特に，Gのsupercuspidal表現 ¥pi に対し，¥pi がsimple typeとしてある種の不分岐的な条件を満たすようなものを含むときに，Kの表現で ¥pi に対応するtypeがGでの共役を除き一意であることを示す．
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
磯野優介 氏 (京大数理研)
Unitary conjugacy for type III subfactors and W*-superrigidity
磯野優介 氏 (京大数理研)
Unitary conjugacy for type III subfactors and W*-superrigidity
2019年05月02日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
岡本龍明 氏 (NTT)
現代暗号の理論 (Japanese)
岡本龍明 氏 (NTT)
現代暗号の理論 (Japanese)
[ 講演概要 ]
1970年代に誕生した現代暗号は、1980年代にその理論的な基礎づけが確立された．今回は、その中核となる概念として，安全性証明のための標準モデル，証明手法としてのシミュレーションパラダイムおよび識別不可能性などを紹介するとともに，それらの概念に基づく代表的暗号機能として，ゼロ知識証明を紹介する．
1970年代に誕生した現代暗号は、1980年代にその理論的な基礎づけが確立された．今回は、その中核となる概念として，安全性証明のための標準モデル，証明手法としてのシミュレーションパラダイムおよび識別不可能性などを紹介するとともに，それらの概念に基づく代表的暗号機能として，ゼロ知識証明を紹介する．
2019年04月30日(火)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 122号室
Jean-Francois Dat 氏 (Sorbonne University)
Moduli space of l-adic Langlands parameters and the stable Bernstein center (English)
Jean-Francois Dat 氏 (Sorbonne University)
Moduli space of l-adic Langlands parameters and the stable Bernstein center (English)
[ 講演概要 ]
Motivated by the description of the integral l-adic cohomology of certain Shimura varieties in middle degree, Emerton and Helm have conjectured the existence of a certain local Langlands correspondence for l-adic families of n-dimensional Galois representations. The proof of this conjecture by Helm and Moss relies on a beautiful isomorphism between the ring of functions of the moduli space of l-adic representations and the integral Bernstein center of GL_n(F). We will present a work in progress with Helm, Korinczuk and Moss towards a generalization of this result for arbitrary (tamely ramified) reductive groups.
Motivated by the description of the integral l-adic cohomology of certain Shimura varieties in middle degree, Emerton and Helm have conjectured the existence of a certain local Langlands correspondence for l-adic families of n-dimensional Galois representations. The proof of this conjecture by Helm and Moss relies on a beautiful isomorphism between the ring of functions of the moduli space of l-adic representations and the integral Bernstein center of GL_n(F). We will present a work in progress with Helm, Korinczuk and Moss towards a generalization of this result for arbitrary (tamely ramified) reductive groups.
2019年04月26日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 056号室
吉田善章 氏 (東京大学新領域創成科学研究科)
Lie-Poisson代数の「変形」とカイラルな場の理論 (日本語)
吉田善章 氏 (東京大学新領域創成科学研究科)
Lie-Poisson代数の「変形」とカイラルな場の理論 (日本語)
[ 講演概要 ]
物理の理論は「物」と「時空」の二つを使って記述される．物の特性は「エネルギー」の数学的表現（ハミルトニアン）に還元される．他方，時空の特性はその「幾何学」を特徴づける群の構造として定式化される．物の奇妙な運動（例えば回転方向に好き嫌い＝カイラリティーをもつラトルバックというコマ）は，エネルギーが変な形をしているか，あるいは時空が変な法則をもっているかのいずれかに起因すると考えるのだが，ここでは後者の可能性を追求する．カイラリティー（Krein対称性の破れ）をもつPoisson多様体（Hamilton力学系）の構造を，その基底にあるLie代数の変形に帰着して考える理論を紹介する．
物理の理論は「物」と「時空」の二つを使って記述される．物の特性は「エネルギー」の数学的表現（ハミルトニアン）に還元される．他方，時空の特性はその「幾何学」を特徴づける群の構造として定式化される．物の奇妙な運動（例えば回転方向に好き嫌い＝カイラリティーをもつラトルバックというコマ）は，エネルギーが変な形をしているか，あるいは時空が変な法則をもっているかのいずれかに起因すると考えるのだが，ここでは後者の可能性を追求する．カイラリティー（Krein対称性の破れ）をもつPoisson多様体（Hamilton力学系）の構造を，その基底にあるLie代数の変形に帰着して考える理論を紹介する．
2019年04月25日(木)
応用解析セミナー
16:00-18:00 数理科学研究科棟(駒場) 118号室
この日は２つ講演があります．教室と時間にご注意下さい．
Matteo Muratori 氏 (Polytechnic University of Milan) 16:00-17:00
The porous medium equation on noncompact Riemannian manifolds with initial datum a measure
(English)
On sharp large deviations for the bridge of a general diffusion
(English)
この日は２つ講演があります．教室と時間にご注意下さい．
Matteo Muratori 氏 (Polytechnic University of Milan) 16:00-17:00
The porous medium equation on noncompact Riemannian manifolds with initial datum a measure
(English)
[ 講演概要 ]
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds. We show existence of solutions that take a finite Radon measure as initial datum, possibly sign-changing. We then prove uniqueness in the class of nonnegative solutions, upon assuming a quadratic lower bound on the Ricci curvature. Our result is "optimal" in the sense that any weak solution necessarily solves a Cauchy problem with initial datum a finite Radon measure. Moreover, as byproducts of the techniques we employ, we obtain some new results in potential analysis on manifolds, concerning the validity of a modified version of the mean-value inequality for superharmonic functions and related properties of potentials of positive Radon measures. Finally, we briefly discuss some work in progress regarding stability of the porous medium equation with respect to the Wasserstein distance, on Riemannian manifolds with Ricci curvature bounded below.
Maurizia Rossi 氏 (University of Pisa) 17:00-18:00We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds. We show existence of solutions that take a finite Radon measure as initial datum, possibly sign-changing. We then prove uniqueness in the class of nonnegative solutions, upon assuming a quadratic lower bound on the Ricci curvature. Our result is "optimal" in the sense that any weak solution necessarily solves a Cauchy problem with initial datum a finite Radon measure. Moreover, as byproducts of the techniques we employ, we obtain some new results in potential analysis on manifolds, concerning the validity of a modified version of the mean-value inequality for superharmonic functions and related properties of potentials of positive Radon measures. Finally, we briefly discuss some work in progress regarding stability of the porous medium equation with respect to the Wasserstein distance, on Riemannian manifolds with Ricci curvature bounded below.
On sharp large deviations for the bridge of a general diffusion
(English)
[ 講演概要 ]
In this talk we provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided b enjoyes a simple condition that is always satisfied in dimension 1. On the other hand, we show that the drift can be influential if this assumption is not satisfied. This talk is based on a joint work with P. Baldi and L. Caramellino.
In this talk we provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided b enjoyes a simple condition that is always satisfied in dimension 1. On the other hand, we show that the drift can be influential if this assumption is not satisfied. This talk is based on a joint work with P. Baldi and L. Caramellino.
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 128号室
夏学期は暗号理論の講演
岡本 龍明 氏 (NTT)
現代暗号の誕生と発展 (JAPANESE)
夏学期は暗号理論の講演
岡本 龍明 氏 (NTT)
現代暗号の誕生と発展 (JAPANESE)
[ 講演概要 ]
現代暗号は40年ほど前に誕生したが、現在ではインターネットなどの安全性を保証する基盤技術として広く利用され、さらに応用面においても理論面でもこの10年余りの発展は著しい。
本セミナー（前期）では、このような現代暗号をその誕生から最近の発展まで、基本的暗号理論、ビットコインとブロックチェーン、ポスト量子暗号と格子暗号、完全準同型暗号、関数型暗号などを中心に、前提知識を必要としないで分かりやすく解説することをめざす（7, 8コマ程度）。
以上の講義の後に、高島克幸氏より楕円曲線に基づく暗号理論、とくに最近話題の同種写像暗号などを中心に解説して頂く（数コマ程度）。
まず、第１回(4月25日）では、現代暗号が誕生した経緯とそれらが現在どのような形で利用されているかについて紹介する。
現代暗号は40年ほど前に誕生したが、現在ではインターネットなどの安全性を保証する基盤技術として広く利用され、さらに応用面においても理論面でもこの10年余りの発展は著しい。
本セミナー（前期）では、このような現代暗号をその誕生から最近の発展まで、基本的暗号理論、ビットコインとブロックチェーン、ポスト量子暗号と格子暗号、完全準同型暗号、関数型暗号などを中心に、前提知識を必要としないで分かりやすく解説することをめざす（7, 8コマ程度）。
以上の講義の後に、高島克幸氏より楕円曲線に基づく暗号理論、とくに最近話題の同種写像暗号などを中心に解説して頂く（数コマ程度）。
まず、第１回(4月25日）では、現代暗号が誕生した経緯とそれらが現在どのような形で利用されているかについて紹介する。
2019年04月24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
Joseph Ayoub 氏 (University of Zurich)
P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes (English)
Joseph Ayoub 氏 (University of Zurich)
P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes (English)
[ 講演概要 ]
A^1-localisation is a universal construction which produces "cohomology theories" for which the affine line A^1 is contractible. It plays a central role in the theory of motives à la Morel-Voevodsky. In this talk, I'll discuss the analogous construction where the affine line is replaced by the projective line P^1. This is the P^1-localisation which is arguably an unnatural construction since it produces "cohomology theories" for which the projective line P^1 is contractible. Nevertheless, I'll explain a few positive results and some computations around this construction which naturally lead to a definition of Kodaira-Spencer classes of arithmetic nature. (Unfortunately, it is yet unclear if these classes are really interesting and nontrivial.)
A^1-localisation is a universal construction which produces "cohomology theories" for which the affine line A^1 is contractible. It plays a central role in the theory of motives à la Morel-Voevodsky. In this talk, I'll discuss the analogous construction where the affine line is replaced by the projective line P^1. This is the P^1-localisation which is arguably an unnatural construction since it produces "cohomology theories" for which the projective line P^1 is contractible. Nevertheless, I'll explain a few positive results and some computations around this construction which naturally lead to a definition of Kodaira-Spencer classes of arithmetic nature. (Unfortunately, it is yet unclear if these classes are really interesting and nontrivial.)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 118号室
今学期は基本水曜日とします。部屋も去年度と異なります。
吉川翔 氏 (東大数理)
Varieties of dense globally F-split type with a non-invertible polarized
endomorphism
今学期は基本水曜日とします。部屋も去年度と異なります。
吉川翔 氏 (東大数理)
Varieties of dense globally F-split type with a non-invertible polarized
endomorphism
[ 講演概要 ]
Broustet and Gongyo conjectured that if a normal projective variety X has a non-invertible polaried endomorphism, then X is of Calabi-Yau type. Furthermore, Schwede and Smith conjectured that a projective variety is of Calabi-Yau type if and only if of dense globally F-split type. Therefore it is a natural question to ask if a normal projective variety X has a non-invertible polaried endomorphism, then X is of dense globally F-split type. In this talk, I will introduce simple points and difficult points of the question. Furthermore I will give the affirmative answer of my question for 2-dimensional case.
Broustet and Gongyo conjectured that if a normal projective variety X has a non-invertible polaried endomorphism, then X is of Calabi-Yau type. Furthermore, Schwede and Smith conjectured that a projective variety is of Calabi-Yau type if and only if of dense globally F-split type. Therefore it is a natural question to ask if a normal projective variety X has a non-invertible polaried endomorphism, then X is of dense globally F-split type. In this talk, I will introduce simple points and difficult points of the question. Furthermore I will give the affirmative answer of my question for 2-dimensional case.
2019年04月23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: Common Room 16:30-17:00
Christine Vespa 氏 (Université de Strasbourg)
Higher Hochschild homology as a functor (ENGLISH)
Tea: Common Room 16:30-17:00
Christine Vespa 氏 (Université de Strasbourg)
Higher Hochschild homology as a functor (ENGLISH)
[ 講演概要 ]
Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).
In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).
(This is joint work with Geoffrey Powell.)
Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).
In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).
(This is joint work with Geoffrey Powell.)
2019年04月22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) 128号室
久本 智之 氏 (名古屋大学)
Optimal destabilizer for a Fano manifold (Japanese)
久本 智之 氏 (名古屋大学)
Optimal destabilizer for a Fano manifold (Japanese)
[ 講演概要 ]
Around 2005, S. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence of the normalized Donaldson-Futaki invariants.
For a Fano manifold we construct a sequence of multiplier ideal sheaves from a new geometric flow and answer to Donaldson's question.
Around 2005, S. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence of the normalized Donaldson-Futaki invariants.
For a Fano manifold we construct a sequence of multiplier ideal sheaves from a new geometric flow and answer to Donaldson's question.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 056号室
及川一誠 氏 (一橋大学大学院経営管理研究科)
HDG法の超収束について (Japanese)
及川一誠 氏 (一橋大学大学院経営管理研究科)
HDG法の超収束について (Japanese)
[ 講演概要 ]
近年，hybridizable discontinuous Galerkin (HDG) 法の超収束性に関して研究が進展し，様々な結果が得られている．それらは大きく分けて，数値流束の安定化項に$L^2$射影を施すLehrenfeld-Sch{\" o}berl安定化と，HDG射影を用いるM-decomposition理論との２つに分類される．本講演では両者に関する概要を，講演者の研究結果を交えながら述べる．
近年，hybridizable discontinuous Galerkin (HDG) 法の超収束性に関して研究が進展し，様々な結果が得られている．それらは大きく分けて，数値流束の安定化項に$L^2$射影を施すLehrenfeld-Sch{\" o}berl安定化と，HDG射影を用いるM-decomposition理論との２つに分類される．本講演では両者に関する概要を，講演者の研究結果を交えながら述べる．
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