過去の記録

過去の記録 ~12/05本日 12/06 | 今後の予定 12/07~

トポロジー火曜セミナー

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
吉永 正彦 氏 (大阪大学)
Milnor fibers of hyperplane arrangements (JAPANESE)
[ 講演概要 ]
A (central) hyperplane arrangement is a union of finitely many hyperplanes in a linear space. There are many relationships between the intersection lattice of the arrangement and geometry of related spaces. In this talk, we focus on the Milnor fiber of a hyperplane arrangement. The first Betti number of the Milnor fiber is expected to be determined by the combinatorial structure of the intersection lattice, however, it is still open. We discuss two results on the problem. The first (discouraging) one is concerning the dimension of (-1)-eigenspace of the monodromy action on the first cohomology group. We show that it is related to 2-torsions in the first homology of double covering of the (projectivized) complement (j.w. Ishibashi and Sugawara). The second (encouraging) one is related to the Aomoto complex, which is defined in purely combinatorial way. We show that a q-analogue of Aomoto complex determines all nontrivial monodromy eigenspaces of the Milnor fiber.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2022年11月03日(木)

講演会

11:00-12:30   オンライン開催
Professor O. Emanouilov (Colorado State Univ.) による連続セミナー
Professor O. Emanouilov 氏 (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

2022年11月02日(水)

代数学コロキウム

17:00-18:00   ハイブリッド開催
Laurent Fargues 氏 (Mathematics Institute of Jussieu–Paris Rive Gauche・東京大学大学院数理科学研究科)
Some compact generators of D_{lis} (Bun_G,\Lambda) (English)
[ 講演概要 ]
I will speak about some aspect of my joint work with Scholze on the geomerization of the local Langlands correspondence. More precisely, I will explain how to construct explicitly some compact generators of the derived category of étale sheaves on Bun_G, the Artin v-stack of G-bundles on the curve. Those compact generators generalize the classical compactly induced representations in the classical local Langlands program. For this we construct some particular charts on Bun_G and this will be the occasion to review some geometric constructions in our joint work.

2022年11月01日(火)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室
石倉宙樹 氏 (東大数理)
Permutation stability of finitely generated free metabelian groups
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

トポロジー火曜セミナー

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
キム ミンギュ 氏 (東京大学大学院数理科学研究科)
An obstruction problem associated with finite path-integral (JAPANESE)
[ 講演概要 ]
Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) ハイブリッド開催/002号室
河上龍郎 氏 (京大数学教室)
Extendability of differential forms via Cartier operators (Japanese)
[ 講演概要 ]
For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.
In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.
For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.

2022年10月31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
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
井上 瑛二 氏 (理化学研究所)
The non-archimedean μ-entropy in toric case (Japanese)
[ 講演概要 ]
The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.
In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

2022年10月27日(木)

情報数学セミナー

16:50-18:20   数理科学研究科棟(駒場) 123号室
高島 克幸 氏 (早稲田大学)
耐量子計算機暗号の進展 (Japanese)
[ 講演概要 ]
米国標準技術研究所NIST により,次世代標準暗号方式として,鍵共有にはCRYSTALS-Kyber が選ばれ,デジタル署名には CRYSTALS-Dilithiumを筆頭に Falcon と SPHINCS+ という 2 方式も選定された.SPHINCS+ を除く 3 方式は全て格子暗号と呼ばれる暗号技術に属する.
本講演では,まず,格子上のフーリエ解析に基づくRegevの格子暗号構成フレームワークを概説し,それに基づく具体的な構成法を順に紹介する.そして,加群格子・イデアル格子といった特別な格子に基づく暗号構成の基礎付けを見た後に,Cramerらによる近似Ideal-SVP 問題に対する多項式時間量子アルゴリズムを概説する.そこでは,漸近的に準指数関数近似度を達成するために円分体の諸性質が巧みに使われているので,その整数論的な技法について主に紹介する.

講演会

11:00-12:30   オンライン開催
Professor O. Emanouilov (Colorado State Univ.) による連続セミナー
Professor O. Emanouilov 氏 (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

2022年10月25日(火)

代数幾何学セミナー

10:30-11:45   数理科学研究科棟(駒場) ハイブリッド開催/002号室
伊藤敦 氏 (岡山大学)
Projective normality of general polarized abelian varieties (Japanese)
[ 講演概要 ]
Projective normality is an important property of polarized varieties. Hwang and To prove that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $\chi(X,L) \geq (8g)^g/2g!$. In this talk, I will explain that their bound can be weaken as $\chi(X,L) > 2^{2g-1}$, which is sharp. A key tool in the proof is an invariant introduced by Jiang and Pareschi, which measures the basepoint freeness of $\mathbb{Q}$-divisors on abelian varieties.

トポロジー火曜セミナー

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
小川 竜 氏 (東海大学)
Stabilized convex symplectic manifolds are Weinstein (JAPANESE)
[ 講演概要 ]
There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2022年10月24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
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
藤澤 太郎 氏 (東京電機大学)
A new approach to the nilpotent orbit theorem via the $L^2$ extension theorem of Ohsawa-Takegoshi type (Japanese)
[ 講演概要 ]
I will talk about a new proof of (a part of) the nilpotent orbit theorem for unipotent variations of Hodge structure. This approach is largely inspired by the recent works of Deng and of Sabbah-Schnell. In my proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays essential roles.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

2022年10月21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) オンライン 号室
参加を希望される方は、談話会・数理科学講演会ウェブページ [参考URL] から参加登録をお願い申し上げます。
Neal Bez 氏 (埼玉大学 理工学研究科)
The Fourier restriction conjecture (English)
[ 講演概要 ]
The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2

統計数学セミナー

①14:30-15:40- ②16:20-17:30   数理科学研究科棟(駒場) 126号室
ハイブリッド開催
Estate Khmaladze 氏 (Victoria University of Wellington)
On the theory of distribution free testing of statistical hypothesis
  ①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.
  ②Further testing problems: parametric regression and Markov chains. (ENGLISH)
[ 講演概要 ]
The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.

Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.

In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.

Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.
[ 参考URL ]
https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link

2022年10月20日(木)

東京名古屋代数セミナー

16:40-18:10   オンライン開催
オンライン開催の詳細は講演参考URLをご覧ください。
Martin Kalck 氏 (Freiburg University)
A surface and a threefold with equivalent singularity categories (English)
[ 講演概要 ]
We discuss a triangle equivalence between singularity categories of an
affine surface and an affine threefold.
Both are isolated cyclic quotient singularities.
This seems to be the first (non-trivial) example of a singular
equivalence involving varieties of even and odd Krull dimension.

The same approach recovers a result of Dong Yang showing a singular
equivalence between certain cyclic quotient singularities in dimension
2 and certain finite dimensional commutative algebras.

This talk is based on https://arxiv.org/pdf/2103.06584.pdf
[ 参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2022年10月19日(水)

統計数学セミナー

10:30-11:40   数理科学研究科棟(駒場) 号室
完全オンライン形式で開催
山岸 颯 氏 (東京大学大学院数理科学研究科)
fractional Brownian motion(fBm)に関係する汎関数のオーダー評価とfBmで駆動される確率微分方程式の二次変分の漸近展開について

[ 講演概要 ]
混合正規分布に収束するSkorohod積分の漸近展開の理論に基づき,fBmで駆動される確率微分方程式の二次変分で表される汎関数の漸近展開公式を得た.
汎関数の確率展開や漸近展開公式に現れるランダムな表象を求めることが一般論の適用において必要となるが,その際,ランダムなウェイトを持つfBmの反復積分の積の和で表される汎関数が複数現れ,これらのオーダーを繰り返し評価することが求められる. 今回講演者はこのオーダー評価を機械的に行うために和の構造を捉えた重み付きグラフを用いた指数を導入した.この講演はarXiv:2206.00323に基づく.
[ 参考URL ]
https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link

講演会

16:45-18:15   数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催 オンライン参加希望の場合は、参考URLより18日の17時までに登録をお願いします。
Mykhaylo Shkolnikov 氏 (プリンストン大学)
Probabilistic solutions of singular free boundary problems (English)
[ 講演概要 ]
The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will discuss this new concept in the context of Stefan problems from mathematical physics that describe melting/solidification of a solid/liquid (e.g., ice/water) in the presence of supercooling. In particular, I will present new global existence, regularity and uniqueness results for the two geometrically simplest settings: flat and radial. Based on joint works with Sergey Nadtochiy, Francois Delarue and Yucheng Guo.
[ 参考URL ]
https://forms.gle/XXH2cAb18pQhC6w96

代数学コロキウム

17:00-18:00   ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加をお願いいたします。
Shane Kelly 氏 (東京大学大学院数理科学研究科)
A nilpotent variant cdh-topology (English)
[ 講演概要 ]
I will speak about a version of the cdh-topology which can see nilpotents, and applications to algebraic K-theory. This is joint work in progress with Shuji Saito.

2022年10月18日(火)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室
Valerio Proietti 氏 (東大数理)
A geometric Elliott invariant and noncommutative rigidity of mapping tori (English)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2022年10月13日(木)

情報数学セミナー

16:50-18:20   数理科学研究科棟(駒場) 123号室
駒野 雄一 氏 (株式会社東芝)
暗号実装への攻撃と対策の数理 (Japanese)
[ 講演概要 ]
暗号方式の安全性が数学的に保証されていても、暗号方式を実装した暗号製品に対して、暗号演算中に観測される情報(サイドチャネル情報)を解析することにより、暗号製品内部で処理される秘密情報を推定(攻撃)することができる。このような攻撃はサイドチャネル攻撃と呼ばれ、暗号製品から観測される処理時間や消費電力などを用いる攻撃やそれへの対策手法が数多く提案されている。本講演では、サイドチャネル攻撃とその対策の原理を数学的な視点から紹介する。

2022年10月12日(水)

代数学コロキウム

17:00-18:00   ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加をお願いいたします。
Abhinandan 氏 (東京大学大学院数理科学研究科)
Syntomic complex with coefficients (English)
[ 講演概要 ]
In the proof of $p$-adic crystalline comparison theorem, one of the most important steps in the approach of Fontaine and Messing is to establish a comparison between syntomic cohomology and p-adic étale cohomology via (Fontaine-Messing) period map. This approach was successfully generalized to the semistable case by Kato and a complete proof of crystalline and semistable comparison theorems for schemes was given by Tsuji. Few years ago, Colmez and Nizioł gave a new interpretation of the (local) Fontaine-Messing period map in terms of complexes of $(\varphi,\Gamma)$-modules and used it to prove semistable comparison theorem for $p$-adic formal schemes. We will present a generalisation (of crystalline version of this interpretation by Colmez and Nizioł) to coefficients arising from relative Fontaine-Laffaille modules of Faltings (on syntomic side) and relative Wach modules introduced by the speaker (on $(\varphi,\Gamma)$-module side).

2022年10月11日(火)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室
武石拓也 氏 (京都工芸繊維大)
Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

トポロジー火曜セミナー

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
浅尾 泰彦 氏 (福岡大学)
Magnitude homology of graphs (JAPANESE)
[ 講演概要 ]
Magnitude is introduced by Leinster in 00’s as an ``Euler characteristic of metric spaces”. It is defined for the metric structure itself rather than the topology induced from the metric. Magnitude homology is a categorification of magnitude in a sense that ordinary homology categorifies the Euler characteristic. The speaker’s interest is in geometric meaning of this theory. In this talk, after an introduction to basic ideas, I will explain that magnitude truly extends the Euler characteristic. From this perspective, magnitude homology can be seen as one of the categorification of the Euler characteristic, and the path homology (Grigor’yan—Muranov—Lin—S-T. Yau et.al) appears as a part of another one. These structures are aggregated in a spectral sequence obtained from the classifying space of "filtered set enriched categories" which includes ordinary small categories and metric spaces.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2022年10月06日(木)

情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室
岡本 龍明 氏 (NTT)
組織化された複雑性の新しい定量的定義について (Japanese)
[ 講演概要 ]
科学が扱う問題は、複雑性の観点で大きく3つに大別される。一つは、「単純な」問題で、これは数個の物体の力学的運動を扱うような問題である。もう一つは、「組織化されていない複雑な」問題で、ランダムに運動する非常に多数の分子の集団を扱うような問題である。最後が、「組織化された複雑な」問題で、生物や人間社会のように複雑に組織化された構成要素の集団を扱うような問題である。そのような問題の複雑さの度合いを「定量的に定義」することは大変重要な課題である。「組織化されていない複雑な」問題では、「エントロピー」がその複雑性の定量的な定義としてすでに確立している。一方、「組織化された複雑な」問題に対しては、いまだに広く受け入れられている定量的定義は確立されていない。本講演では、まず「組織化された複雑な問題」について従来提案された様々な定量的定義の問題点について述べる。次に、最近発表された新しい定量的な定義を紹介し、それが従来の定義の問題点をすべて解決していることを述べる。さらにその定義をどのように応用するかについて紹介する。なお、この講演は以下の論文に基づく。
Tatsuaki Okamoto, ‘‘A New Quantitative Definition of the Complexity of Organized Matters,’’ Complexity, Volume 2022, Article ID 1889348 (2022)
https://www.hindawi.com/journals/complexity/2022/1889348/

2022年10月05日(水)

代数幾何学セミナー

13:00-14:00   数理科学研究科棟(駒場) 056号室
今学期より対面ハイブリッドでセミナーを再開します。本セミナーは京大と共催です。オンライン情報はメーリングリストで公開しています。
Yuri Tschinkel 氏 (Mathematics and Physical Sciences Division, Simons Foundation/ Courant Institute, New York University)
Equivariant birational geometry (joint with A. Kresch) (English)
[ 講演概要 ]
Ideas from motivic integration led to the introduction of new invariants in equivariant birational geometry, the study of actions of finite groups on algebraic varieties, up to equivariant birational transformations.
These invariants allow us to distinguish actions in many new cases, shedding light on the structure of the Cremona group. The structure of the invariants themselves is also interesting: there are unexpected connections to modular curves and cohomology of arithmetic groups.

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