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過去の記録
過去の記録 ～04/25｜本日 04/26 | 今後の予定 04/27～
2022年11月24日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 370号室
対面・オンラインハイブリッド開催
板倉 恭平 氏 (東京大学 大学院数理科学研究科)
シュタルク・シュレディンガー作用素に対する放射条件評価と定常散乱理論 (Japanese)
https://forms.gle/admRaVnmPjFyp5op9
対面・オンラインハイブリッド開催
板倉 恭平 氏 (東京大学 大学院数理科学研究科)
シュタルク・シュレディンガー作用素に対する放射条件評価と定常散乱理論 (Japanese)
[ 講演概要 ]
本講演では1体粒子系のシュタルク・シュレディンガー作用素に対し，古典力学から類推される最良な重み付き放射条件評価の導出を行い，これを土台として定常波動作用素の存在性と完全性を調べる．さらに関連する話題として，定常散乱行列のユニタリ性，一般化フーリエ変換の構成，および最小増大度をもつ一般化固有関数に対する定常散乱行列と近似外向・内向波を用いた空間遠方での漸近挙動の特徴づけについても考察する．本研究では，対応する古典力学を適切に反映させたエスケープ関数と，それに付随するアグモン-ヘルマンダー空間の使用が肝要となる．本講演の内容は足立匡義氏(京都大学)，伊藤健一氏(東京大学)，Skibsted Erik氏(オーフス大学)との共同研究に基づく．
[ 参考URL ]本講演では1体粒子系のシュタルク・シュレディンガー作用素に対し，古典力学から類推される最良な重み付き放射条件評価の導出を行い，これを土台として定常波動作用素の存在性と完全性を調べる．さらに関連する話題として，定常散乱行列のユニタリ性，一般化フーリエ変換の構成，および最小増大度をもつ一般化固有関数に対する定常散乱行列と近似外向・内向波を用いた空間遠方での漸近挙動の特徴づけについても考察する．本研究では，対応する古典力学を適切に反映させたエスケープ関数と，それに付随するアグモン-ヘルマンダー空間の使用が肝要となる．本講演の内容は足立匡義氏(京都大学)，伊藤健一氏(東京大学)，Skibsted Erik氏(オーフス大学)との共同研究に基づく．
https://forms.gle/admRaVnmPjFyp5op9
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
安田 雅哉 氏 (立教大学)
格子暗号の安全性を支える格子問題の解読法 (Japanese)
安田 雅哉 氏 (立教大学)
格子暗号の安全性を支える格子問題の解読法 (Japanese)
[ 講演概要 ]
格子暗号は耐量子計算機暗号の一つであり、完全準同型暗号などの高機能暗号の構成にも有用である。本講演では、格子暗号の安全性を支える数学問題である格子問題を解読する方法を紹介する。具体的には、格子問題を解くための必須の技術であるLLLやBKZなどの格子基底簡約アルゴリズムを紹介すると共に、LWEやNTRUの格子問題への適用方法を説明する。
格子暗号は耐量子計算機暗号の一つであり、完全準同型暗号などの高機能暗号の構成にも有用である。本講演では、格子暗号の安全性を支える数学問題である格子問題を解読する方法を紹介する。具体的には、格子問題を解くための必須の技術であるLLLやBKZなどの格子基底簡約アルゴリズムを紹介すると共に、LWEやNTRUの格子問題への適用方法を説明する。
2022年11月22日(火)
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 002号室
90分ハイブリッド開催です。
谷本祥 氏 (名古屋多元)
Non-free sections of Fano fibrations (日本語)
90分ハイブリッド開催です。
谷本祥 氏 (名古屋多元)
Non-free sections of Fano fibrations (日本語)
[ 講演概要 ]
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.
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
佐藤僚亮 氏 (中央大物理)
Multiplicative characters and Gaussian fluctuation limits
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
佐藤僚亮 氏 (中央大物理)
Multiplicative characters and Gaussian fluctuation limits
[ 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。
北野 晃朗 氏 (創価大学)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
北野 晃朗 氏 (創価大学)
Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
[ 講演概要 ]
A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
[ 参考URL ]A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2022年11月21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。
神本 丈 氏 (九州大学)
Resolution of singularities for $C^{\infty}$ functions and meromorphy of local zeta functions (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
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。
神本 丈 氏 (九州大学)
Resolution of singularities for $C^{\infty}$ functions and meromorphy of local zeta functions (Japanese)
[ 講演概要 ]
In this talk, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but may include flat functions. As an application, we investigate analytic continuation of local zeta functions associated with $C^{\infty}$ functions of two variables.
[ 参考URL ]In this talk, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but may include flat functions. As an application, we investigate analytic continuation of local zeta functions associated with $C^{\infty}$ functions of two variables.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022年11月17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
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
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
池松 泰彦 氏 (九州大学)
多変数多項式暗号の世界 (Japanese)
池松 泰彦 氏 (九州大学)
多変数多項式暗号の世界 (Japanese)
[ 講演概要 ]
多変数多項式暗号(MPKC)は多変数多項式求解問題を安全性の根拠とし、耐量子計算機暗号(PQC)の一つとしてこれまで様々な研究が行われている。特に署名方式であるRainbowは米国標準技術研究所(NIST)が行なっているPQC標準化計画の最終選考まで進み、活発に研究がなされてきた。残念ながらRainbowには有効な攻撃方法が発見され標準化には選ばれなかったが、選考過程でMPKCの安全性に関する研究は大きく進展した。この講演では、Rainbowに関するそれら一連の進展を解説する。さらに、RainbowのベースとなっているUOV署名方式についても最近の進展を解説したい。
多変数多項式暗号(MPKC)は多変数多項式求解問題を安全性の根拠とし、耐量子計算機暗号(PQC)の一つとしてこれまで様々な研究が行われている。特に署名方式であるRainbowは米国標準技術研究所(NIST)が行なっているPQC標準化計画の最終選考まで進み、活発に研究がなされてきた。残念ながらRainbowには有効な攻撃方法が発見され標準化には選ばれなかったが、選考過程でMPKCの安全性に関する研究は大きく進展した。この講演では、Rainbowに関するそれら一連の進展を解説する。さらに、RainbowのベースとなっているUOV署名方式についても最近の進展を解説したい。
2022年11月16日(水)
代数学コロキウム
17:00-18:00 ハイブリッド開催
Zijian Yao 氏 (University of Chicago)
The eigencurve over the boundary of the weight space (English)
Zijian Yao 氏 (University of Chicago)
The eigencurve over the boundary of the weight space (English)
[ 講演概要 ]
The eigencurve is a geometric object that p-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious, except that over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of GL2. If time permits, we will discuss some generalizations towards groups beyond GL2. This is partially joint with H. Diao.
The eigencurve is a geometric object that p-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious, except that over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of GL2. If time permits, we will discuss some generalizations towards groups beyond GL2. This is partially joint with H. Diao.
2022年11月15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
森迪也 氏 (東大数理)
Ring isomorphisms of locally measurable operator algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
森迪也 氏 (東大数理)
Ring isomorphisms of locally measurable operator 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。
Arthur Soulié 氏 (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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。
Arthur Soulié 氏 (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
[ 講演概要 ]
The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
[ 参考URL ]The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
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
張 繼剛 氏 (NTU/東大数理)
Positivity of anticanonical divisors in algebraic fibre spaces (日本語)
張 繼剛 氏 (NTU/東大数理)
Positivity of anticanonical divisors in algebraic fibre spaces (日本語)
[ 講演概要 ]
It is known that the positivity of the anti-canonical divisor is an important property that is closely related to the geometric structure of a variety. Given an algebraic fibre space f : X → Y between normal projective varieties with mild singularities, and let F be a general fibre of f. In this talk, we will introduce results relating the positivity of −KX and −KY under some conditions on the asymptotic base loci of −KX. In particular, we will obtain an inequality between the anti-canonical Iitaka dimensions κ(X, −KX) ≤ κ(F, −KF ) + κ(Y, −KY ) under the assumption that the stable base locus B(−KX) does not dominant over Y .
It is known that the positivity of the anti-canonical divisor is an important property that is closely related to the geometric structure of a variety. Given an algebraic fibre space f : X → Y between normal projective varieties with mild singularities, and let F be a general fibre of f. In this talk, we will introduce results relating the positivity of −KX and −KY under some conditions on the asymptotic base loci of −KX. In particular, we will obtain an inequality between the anti-canonical Iitaka dimensions κ(X, −KX) ≤ κ(F, −KF ) + κ(Y, −KY ) under the assumption that the stable base locus B(−KX) does not dominant over Y .
2022年11月14日(月)
複素解析幾何セミナー
15:00-16:30 オンライン開催
オンラインのみで、開始時間が15:00からとなっておりますのでご注意ください。参加の際は参考URLからご登録ください。
宮地 秀樹 氏 (金沢大学)
The double holomorphic tangent space of the Teichmueller spaces (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
オンラインのみで、開始時間が15:00からとなっておりますのでご注意ください。参加の際は参考URLからご登録ください。
宮地 秀樹 氏 (金沢大学)
The double holomorphic tangent space of the Teichmueller spaces (Japanese)
[ 講演概要 ]
The double holomorphic tangent space of a complex manifold is the holomorphic tangent space of the holomorphic tangent bundle of the complex manifold. In this talk, we will give an intrinsic description of the double tangent spaces of the Teichmueller spaces of closed Riemann surfaces of genus at least 2.
[ 参考URL ]The double holomorphic tangent space of a complex manifold is the holomorphic tangent space of the holomorphic tangent bundle of the complex manifold. In this talk, we will give an intrinsic description of the double tangent spaces of the Teichmueller spaces of closed Riemann surfaces of genus at least 2.
https://forms.gle/hYT2hVhDE3q1wDSh6
2022年11月10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
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08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
有本諒也 氏 (京大数理研)
On the type of the von Neumann algebra of an open subgroup of the Neretin group
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
有本諒也 氏 (京大数理研)
On the type of the von Neumann algebra of an open subgroup of the Neretin group
[ 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。
吉永 正彦 氏 (大阪大学)
Milnor fibers of hyperplane arrangements (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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 ]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.
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
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)
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.
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
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)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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 ]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.
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)
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.
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)
https://forms.gle/hYT2hVhDE3q1wDSh6
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 ]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.
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)
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．
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
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)
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.
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.
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