## Seminar information archive

Seminar information archive ～09/18｜Today's seminar 09/19 | Future seminars 09/20～

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.

Liouville symmetry groups and pseudo-isotopies (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.

**Emmy Murphy**(University of Toronto)Liouville symmetry groups and pseudo-isotopies (ENGLISH)

[ Abstract ]

Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.

[ Reference URL ]Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2024/06/24

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

. (Japanese)

[ Reference URL ]

https://forms.gle/gTP8qNZwPyQyxjTj8

**Kazumasa Narita**(Nagoya Univ.). (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.

Temperley - Lieb 演算子の持ち上げとRazumov - Stroganov 予想について (日本語)

We are having teatime from 15:15 in the common room on the second floor. Please join us.

**Fumihiko Nakano**(Tohoku University)Temperley - Lieb 演算子の持ち上げとRazumov - Stroganov 予想について (日本語)

[ Abstract ]

Razumov - Stroganov 予想とはリンクパターン上の生成する線型空間上のあるハミルトニアンの基底状態に対応するFPLの個数が現れるという予想で、２０１０年に解決されたが、O(1)-loop model, 交代符号行列を介して２次元統計力学の模型や組み合わせ論との様々なつながりがあり、今も注目されている。Temperley - Lieb 演算子の持ち上げを用いたRS予想のより平易な証明について議論する。

Razumov - Stroganov 予想とはリンクパターン上の生成する線型空間上のあるハミルトニアンの基底状態に対応するFPLの個数が現れるという予想で、２０１０年に解決されたが、O(1)-loop model, 交代符号行列を介して２次元統計力学の模型や組み合わせ論との様々なつながりがあり、今も注目されている。Temperley - Lieb 演算子の持ち上げを用いたRS予想のより平易な証明について議論する。

### 2024/06/21

#### Tokyo-Nagoya Algebra Seminar

16:30-18:00 Online

松井スペクトラムを用いた復元定理の再解釈 (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Daigo Ito**(UC Berkeley)松井スペクトラムを用いた復元定理の再解釈 (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

#### Colloquium

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

The minimal exponent of hypersurface singularities (English)

https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

**Mircea Mustaţă**(The University of Michigan)The minimal exponent of hypersurface singularities (English)

[ Abstract ]

The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.

[ Reference URL ]The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.

https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing

#### Algebraic Geometry Seminar

13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

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.

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.)

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.)

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.)

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.)

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.)

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.

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。

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) 16:45-17:45Homogenization 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.)

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.

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.)

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.

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.)

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.)

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

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.)

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.

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].

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.)

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.)

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/

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