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Seminar information archive
Seminar information archive ～07/11｜Today's seminar 07/12 | Future seminars 07/13～
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Kien Nguyen Huu (Normandie Université/KU Leuven)
ON THE POWER SERIES OF DENEF AND LOESER'S MOTIVIC VANISHING CYCLES OF JET POLYNOMIALS (English)
Kien Nguyen Huu (Normandie Université/KU Leuven)
ON THE POWER SERIES OF DENEF AND LOESER'S MOTIVIC VANISHING CYCLES OF JET POLYNOMIALS (English)
[ Abstract ]
Let f be a non-constant polynomial in n variables over a field k of characteristic
0. Denef and Loeser introduced the notion of motivic vanishing cycles of f as an element in
the localization Mμˆ of the Grothendieck ring Kμˆ(Var ) of k-varieties with a good action of k0k
μˆ := lim μm by inverting the affne line equipped with the trivial action of μˆ, where μm
is the group scheme over k of mth roots of unity. In particular, if k is the field of complex
numbers then Denef and Loeser showed that their motivic vanishing cycles and the complex
φf [n − 1] has the same Hodge characteristic, where φf is the complex of vanishing cycles
in the usual sense. Motivated by the Igusa conjecture for exponential sums and the strong
monodromy conjecture, we introduce the notion of Poincaré series of Denef-Loeser's van-
ishing cycles of jet polynomials of f, where jet polynomials of f are polynomials appearing
naturally when we compute the jet schemes of f. By using Davison-Meinhardt's conjecture
which was proved by Nicaise and Payne in 2019, we can show that our Poincaré series is a
rational function over a quotient ring of Mμˆ by very natural relations. In particular, we can k
recovery Denef and Loeser's motivic vanishing cycles from our Poincaré series. Moreover, we can show that our Poincaré series owns a universal property in the sense that if k is a number field then the Igusa local zeta functions, the motivic Igusa zeta functions, the Poincaré series of exponential sums modulo pm of f can be obtained from our Poincaré se- ries by suitable specialization maps preserving the rationality. If time permits, I will present some initial consequences that have arisen during the study of our Poincaré series.
Let f be a non-constant polynomial in n variables over a field k of characteristic
0. Denef and Loeser introduced the notion of motivic vanishing cycles of f as an element in
the localization Mμˆ of the Grothendieck ring Kμˆ(Var ) of k-varieties with a good action of k0k
μˆ := lim μm by inverting the affne line equipped with the trivial action of μˆ, where μm
is the group scheme over k of mth roots of unity. In particular, if k is the field of complex
numbers then Denef and Loeser showed that their motivic vanishing cycles and the complex
φf [n − 1] has the same Hodge characteristic, where φf is the complex of vanishing cycles
in the usual sense. Motivated by the Igusa conjecture for exponential sums and the strong
monodromy conjecture, we introduce the notion of Poincaré series of Denef-Loeser's van-
ishing cycles of jet polynomials of f, where jet polynomials of f are polynomials appearing
naturally when we compute the jet schemes of f. By using Davison-Meinhardt's conjecture
which was proved by Nicaise and Payne in 2019, we can show that our Poincaré series is a
rational function over a quotient ring of Mμˆ by very natural relations. In particular, we can k
recovery Denef and Loeser's motivic vanishing cycles from our Poincaré series. Moreover, we can show that our Poincaré series owns a universal property in the sense that if k is a number field then the Igusa local zeta functions, the motivic Igusa zeta functions, the Poincaré series of exponential sums modulo pm of f can be obtained from our Poincaré se- ries by suitable specialization maps preserving the rationality. If time permits, I will present some initial consequences that have arisen during the study of our Poincaré series.
2024/06/20
Tuesday Seminar on Topology
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
[ Abstract ]
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
[ Reference URL ]The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/19
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Abhinandan (University of Tokyo)
Prismatic $F$-crystals and Wach modules (English)
Abhinandan (University of Tokyo)
Prismatic $F$-crystals and Wach modules (English)
[ Abstract ]
For an absolutely unramified extension $K/\mathbb{Q}_p$ with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, the ring of integers of $K$. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic $F$-crystals over the absolute prismatic site of $O_K$. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
For an absolutely unramified extension $K/\mathbb{Q}_p$ with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, the ring of integers of $K$. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic $F$-crystals over the absolute prismatic site of $O_K$. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
2024/06/18
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroshi Ando (Chiba Univ.)
Lie theoretic approach to the unitary groups of $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Hiroshi Ando (Chiba Univ.)
Lie theoretic approach to the unitary groups of $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
MORI Ryunosuke (Meiji University)
Blocking and propagation in two-dimensional cylinders with spatially undulating boundary (Japanese)
https://forms.gle/TrFmSZQ1ZeqvSjfP7
MORI Ryunosuke (Meiji University)
Blocking and propagation in two-dimensional cylinders with spatially undulating boundary (Japanese)
[ Abstract ]
We consider blocking and propagation phenomena of mean curvature flow with a driving force in two-dimensional cylinders with spatially undulating boundary. In this problem, Matano, Nakamura and Lou in 2006, 2013 characterize the effect of the shape of the boundary to blocking and propagation of the solutions under some slop condition about the boundary that implies time global existence of the classical solutions. In this talk, we consider the effect of the shape of the boundary to blocking and propagation of this problem under more general situation that the solutions may develop singularities near the boundary.
[ Reference URL ]We consider blocking and propagation phenomena of mean curvature flow with a driving force in two-dimensional cylinders with spatially undulating boundary. In this problem, Matano, Nakamura and Lou in 2006, 2013 characterize the effect of the shape of the boundary to blocking and propagation of the solutions under some slop condition about the boundary that implies time global existence of the classical solutions. In this talk, we consider the effect of the shape of the boundary to blocking and propagation of this problem under more general situation that the solutions may develop singularities near the boundary.
https://forms.gle/TrFmSZQ1ZeqvSjfP7
Seminar on Probability and Statistics
13:00-14:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Lorenzo Mercuri (University of Milan)
A compound CARMA(p,q)-Hawkes process for pricing financial derivatives (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZ0rcOmvpjwuGNHx8ht0rMs1rD3HcEajoJv6
Lorenzo Mercuri (University of Milan)
A compound CARMA(p,q)-Hawkes process for pricing financial derivatives (English)
[ Abstract ]
Recently, a new self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has been introduced. The model generalizes the well-known Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p,q) model where the associated state process is driven by the counting process itself. The new model maintains the same level of tractability of the Hawkes (e.g., Infinitesimal generator, backward and forward Kolmogorov equation, joint characteristic function and so on). However, it is able to reproduce more complex time-dependency structure observed in several market data.
Starting from this model, we introduce a Compound CARMA(p,q)-Hawkes with a random jump size independent of the counting and the intensity processes. This can be used as the main block for a new option pricing model, due to log-affine structure of the characteristic function of the underlying log-price driven by a pure jump compound CARMA(p,q)-Hawkes.
Further, we extend this model by scaling it with a measurable function of the time and the left-limit of the price itself. Exploiting the Markov structure of the new model, we derive the forward Kolmogorov equation that leads us to a Dupire-like formula. Some numerical results will also be presented.
[ Reference URL ]Recently, a new self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has been introduced. The model generalizes the well-known Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p,q) model where the associated state process is driven by the counting process itself. The new model maintains the same level of tractability of the Hawkes (e.g., Infinitesimal generator, backward and forward Kolmogorov equation, joint characteristic function and so on). However, it is able to reproduce more complex time-dependency structure observed in several market data.
Starting from this model, we introduce a Compound CARMA(p,q)-Hawkes with a random jump size independent of the counting and the intensity processes. This can be used as the main block for a new option pricing model, due to log-affine structure of the characteristic function of the underlying log-price driven by a pure jump compound CARMA(p,q)-Hawkes.
Further, we extend this model by scaling it with a measurable function of the time and the left-limit of the price itself. Exploiting the Markov structure of the new model, we derive the forward Kolmogorov equation that leads us to a Dupire-like formula. Some numerical results will also be presented.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZ0rcOmvpjwuGNHx8ht0rMs1rD3HcEajoJv6
2024/06/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
15:40-17:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Lectures and TeaTime start earlier. We are having teatime from 15:00 in the common room on the second floor. Please join us.
Kento Ueda (The University of Tokyo) 15:40-16:40
非整数ブラウン運動で駆動される確率微分方程式の数値解の漸近展開 (日本語)
Homogenization results for reflecting diffusions in a continuum percolation cluster (日本語)
Lectures and TeaTime start earlier. We are having teatime from 15:00 in the common room on the second floor. Please join us.
Kento Ueda (The University of Tokyo) 15:40-16:40
非整数ブラウン運動で駆動される確率微分方程式の数値解の漸近展開 (日本語)
[ Abstract ]
本研究は非整数ブラウン運動(fBm)で駆動される確率微分方程式の数値解に対する極限定理(漸近誤差)に関する研究である。このfBmおよびそれによって駆動される方程式は非マルコフな時系列モデルとして用いられ、その数値解に対する極限定理は数学的興味のほか、数値シミュレーションの誤差の推定への応用が期待される。数値解の極限定理は駆動するfBmが1次元か否か、また1次元ならドリフト項が存在するか否か、さらにfBmのハースト指数、そして対象とする数値解法によって定理の主張も適用できる証明法も異なり、そのために条件ごとに様々な先行研究が存在する。このうち、本研究は1次元かつドリフト項が存在する場合に誤差分布の導出と正当化を行ったものであり、一般の数値解法に適用できる。同範囲の先行研究では高次ミルシュタイン法、クランク-ニコルソン法に対してハースト指数が1/3より大きい場合に関して漸近誤差を特定できるが、本研究では高次ミルシュタイン法の漸近誤差を任意のハースト指数に対して完全に決定するとともに、クランク-ニコルソン法に対してもハースト指数が1/4以上の場合に漸近誤差を特定している。なお、本講演では導出した誤差分布を視覚的に観察し、漸近誤差への直観的な理解を深められるよう、漸近誤差に対する数値実験の結果を詳しく説明する。
Yutaka Takeuchi ( Keio University) 16:45-17:45本研究は非整数ブラウン運動(fBm)で駆動される確率微分方程式の数値解に対する極限定理(漸近誤差)に関する研究である。このfBmおよびそれによって駆動される方程式は非マルコフな時系列モデルとして用いられ、その数値解に対する極限定理は数学的興味のほか、数値シミュレーションの誤差の推定への応用が期待される。数値解の極限定理は駆動するfBmが1次元か否か、また1次元ならドリフト項が存在するか否か、さらにfBmのハースト指数、そして対象とする数値解法によって定理の主張も適用できる証明法も異なり、そのために条件ごとに様々な先行研究が存在する。このうち、本研究は1次元かつドリフト項が存在する場合に誤差分布の導出と正当化を行ったものであり、一般の数値解法に適用できる。同範囲の先行研究では高次ミルシュタイン法、クランク-ニコルソン法に対してハースト指数が1/3より大きい場合に関して漸近誤差を特定できるが、本研究では高次ミルシュタイン法の漸近誤差を任意のハースト指数に対して完全に決定するとともに、クランク-ニコルソン法に対してもハースト指数が1/4以上の場合に漸近誤差を特定している。なお、本講演では導出した誤差分布を視覚的に観察し、漸近誤差への直観的な理解を深められるよう、漸近誤差に対する数値実験の結果を詳しく説明する。
Homogenization results for reflecting diffusions in a continuum percolation cluster (日本語)
[ Abstract ]
アブストラクト: ランダム媒質の研究において均一化は重要な問題の一つである. 均一化はいくつかの定式化が知られている, 本講演ではランダム媒質上の確率過程に関する極限定理であるquenched invariance principleと, その精密化である局所中心極限定理を考える. この様な定式化について, 離散的なモデルの場合には多くの結果が知られている. 連続的なモデルに関しても, random environment 上の拡散過程に関する結果は多く知られている. 一方拡散過程が反射壁を持つ場合に関しては, 境界の影響等により問題が複雑化するためquenchedな結果は知られていなかった. 本講演では連続パーコレーションが幾何的な条件を満たす場合, その上の反射壁を持つ拡散過程に関してquenched invariance principleと局所中心極限定理が成り立つという結果を紹介する.
アブストラクト: ランダム媒質の研究において均一化は重要な問題の一つである. 均一化はいくつかの定式化が知られている, 本講演ではランダム媒質上の確率過程に関する極限定理であるquenched invariance principleと, その精密化である局所中心極限定理を考える. この様な定式化について, 離散的なモデルの場合には多くの結果が知られている. 連続的なモデルに関しても, random environment 上の拡散過程に関する結果は多く知られている. 一方拡散過程が反射壁を持つ場合に関しては, 境界の影響等により問題が複雑化するためquenchedな結果は知られていなかった. 本講演では連続パーコレーションが幾何的な条件を満たす場合, その上の反射壁を持つ拡散過程に関してquenched invariance principleと局所中心極限定理が成り立つという結果を紹介する.
2024/06/11
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Taro Sogabe (Kyoto Univ.)
The ext groups and homotopy groups of the automorphism groups of Cuntz-Krieger algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Taro Sogabe (Kyoto Univ.)
The ext groups and homotopy groups of the automorphism groups of Cuntz-Krieger algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
[ Abstract ]
Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
[ Reference URL ]Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
[ Abstract ]
Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
[ Reference URL ]Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yukimi Goto (Gakushuin University)
Phase Transition in a Lattice Nambu–Jona-Lasinio Model (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yukimi Goto (Gakushuin University)
Phase Transition in a Lattice Nambu–Jona-Lasinio Model (日本語)
[ Abstract ]
量子色力学で重要な概念としてカイラル対称性の破れとそれに伴うフェルミオンの質量生成があるが、その証明は困難が多い。その理解に格子上の量子色力学は成功していると見られているものの、数学的結果はいまだ限られている。
この講演では格子上のフェルミオンの定式化のひとつであるスタッガード・フェルミオンをもちいて、それらが4つのフェルミオンと相互作用する模型（lattice Nambu–Jona-Lasinio model）を考える。この模型は離散的なカイラル対称性しかもたないものの、質量が自発的に生成することと、それに伴う対称性の破れを証明できる。また、連続的なフレーバー対称性をもつ場合は南部・ゴールドストーン・モードと呼ばれるスペクトルにギャップのない無限系の基底状態が出現することを説明する。
本講演は高麗徹氏との共同研究にもとづく。
量子色力学で重要な概念としてカイラル対称性の破れとそれに伴うフェルミオンの質量生成があるが、その証明は困難が多い。その理解に格子上の量子色力学は成功していると見られているものの、数学的結果はいまだ限られている。
この講演では格子上のフェルミオンの定式化のひとつであるスタッガード・フェルミオンをもちいて、それらが4つのフェルミオンと相互作用する模型（lattice Nambu–Jona-Lasinio model）を考える。この模型は離散的なカイラル対称性しかもたないものの、質量が自発的に生成することと、それに伴う対称性の破れを証明できる。また、連続的なフレーバー対称性をもつ場合は南部・ゴールドストーン・モードと呼ばれるスペクトルにギャップのない無限系の基底状態が出現することを説明する。
本講演は高麗徹氏との共同研究にもとづく。
FJ-LMI Seminar
13:30-14:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
https://fj-lmi.cnrs.fr/seminars/
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
[ Abstract ]
In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.
[ Reference URL ]In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.
https://fj-lmi.cnrs.fr/seminars/
2024/06/07
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Ivan Cheltsov (University of Edinburgh)
K-stability of pointless Fano 3-folds (English)
Ivan Cheltsov (University of Edinburgh)
K-stability of pointless Fano 3-folds (English)
[ Abstract ]
In this talk we will show how to prove that all pointless smooth Fano 3-folds defined over a subfield of the field of complex numbers are Kahler-Einstein unless they belong to 8 exceptional deformation families. This is a joint work in progress with Hamid Abban (Nottingham) and Frederic Mangolte (Marseille).
In this talk we will show how to prove that all pointless smooth Fano 3-folds defined over a subfield of the field of complex numbers are Kahler-Einstein unless they belong to 8 exceptional deformation families. This is a joint work in progress with Hamid Abban (Nottingham) and Frederic Mangolte (Marseille).
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Taiki Shibata (Okayama University of Science)
スーパー代数群の表現と奇鏡映について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Taiki Shibata (Okayama University of Science)
スーパー代数群の表現と奇鏡映について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2024/06/04
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Ryoya Arimoto (RIMS, Kyoto Univ.)
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryoya Arimoto (RIMS, Kyoto Univ.)
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
[ Abstract ]
The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
[ Reference URL ]The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/31
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
https://forms.gle/ZmHhZW6bxUyKewro8
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
[ Abstract ]
Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
[ Reference URL ]Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
https://forms.gle/ZmHhZW6bxUyKewro8
2024/05/30
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Tim Laux (University of Regensburg, Germany)
Energy convergence of the Allen-Cahn equation for mean convex mean curvature flow (English)
https://forms.gle/8KnFWfHFbkn9fAqaA
Tim Laux (University of Regensburg, Germany)
Energy convergence of the Allen-Cahn equation for mean convex mean curvature flow (English)
[ Abstract ]
In this talk, I'll present a work in progress in which I positively answer a question of Ilmanen (JDG 1993) on the strong convergence of the Allen-Cahn equation to mean curvature flow when starting from well-prepared initial data around a mean convex surface. As a corollary, the conditional convergence result with Simon (CPAM 2018) becomes unconditional in the mean convex case.
[ Reference URL ]In this talk, I'll present a work in progress in which I positively answer a question of Ilmanen (JDG 1993) on the strong convergence of the Allen-Cahn equation to mean curvature flow when starting from well-prepared initial data around a mean convex surface. As a corollary, the conditional convergence result with Simon (CPAM 2018) becomes unconditional in the mean convex case.
https://forms.gle/8KnFWfHFbkn9fAqaA
2024/05/29
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2024/05/28
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
[ Abstract ]
The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
[ Reference URL ]The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/27
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Ryoichiro Noda (Kyoto University)
測度付き抵抗距離空間上の確率過程の局所時間のスケール極限について (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Ryoichiro Noda (Kyoto University)
測度付き抵抗距離空間上の確率過程の局所時間のスケール極限について (日本語)
[ Abstract ]
抵抗距離空間は電気回路の一般化であり，ディリクレ形式の理論により測度付き抵抗距離空間には確率過程が定まる．Croydon-Hambly-Kumagai (2017)は収束する抵抗距離空間が一様体積倍化条件を満たすならば対応する確率過程とその局所時間が収束することを示した．その後Croydon (2018)はより弱い条件である非爆発条件の下で確率過程の収束を示したが，局所時間の収束については未解決のままであった．本講演では非爆発条件及び距離エントロピーに関する適当な条件の下で確率過程とその局所時間の収束が従うこと，そしてこの結果の応用例について解説する．また同様の結果は離散時間マルコフ連鎖とその局所時間に対しても成立し，時間が許せばこの結果についても紹介する．
抵抗距離空間は電気回路の一般化であり，ディリクレ形式の理論により測度付き抵抗距離空間には確率過程が定まる．Croydon-Hambly-Kumagai (2017)は収束する抵抗距離空間が一様体積倍化条件を満たすならば対応する確率過程とその局所時間が収束することを示した．その後Croydon (2018)はより弱い条件である非爆発条件の下で確率過程の収束を示したが，局所時間の収束については未解決のままであった．本講演では非爆発条件及び距離エントロピーに関する適当な条件の下で確率過程とその局所時間の収束が従うこと，そしてこの結果の応用例について解説する．また同様の結果は離散時間マルコフ連鎖とその局所時間に対しても成立し，時間が許せばこの結果についても紹介する．
2024/05/24
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Kenta Sato (Kyusyu University)
Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic
Kenta Sato (Kyusyu University)
Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic
[ Abstract ]
In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.
In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.
2024/05/23
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Adina Ciomaga (University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)
Homogenization of nonlocal Hamilton Jacobi equations (English)
Adina Ciomaga (University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)
Homogenization of nonlocal Hamilton Jacobi equations (English)
[ Abstract ]
I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.
I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.
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